<p> ;</p>
<ol>
<li>State the law of conservation of energy. (1mk)</li>
</ol>
<p> ;</p>
<ol start="2">
<li>Define the terms and state the <strong>I</strong> units of each.</li>
</ol>
<p><strong> (i) </strong>Work (2mk)</p>
<p><strong> (ii) </strong>Energy (2mk)</p>
<p><strong> (iii) </strong>Power (2mk)</p>
<p><strong> (iv) </strong>Machine (2mk)</p>
<p> ;</p>
<ol start="3">
<li>Name a device that is used to convert;</li>
</ol>
<ul>
<li>Sound to electrical energy</li>
<li>Electrical energy to kinetic energy.</li>
<li>Electrical energy to sound energy</li>
<li>Electrical energy to light energy</li>
<li>Solar energy to electricity energy</li>
</ul>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong><u>KINETIC AND POTENTIAL ENERGY </u></strong></p>
<p> ;</p>
<ol>
<li>Differentiate kinetic energy from potential energy.(1mk)</li>
</ol>
<p> ;</p>
<ol start="2">
<li>A hammer is used to hit a round piece of lead into a flat shape. It is observed that the temperature of the piece of lead rises through several degrees. State the energy transformation. (2mk)</li>
</ol>
<p> ;</p>
<ol start="3">
<li>A ball rolls on a table in a straight line. A part from the transitional kinetic energy, state the other form of kinetic energy possessed by the ball.</li>
</ol>
<p> ;</p>
<ol start="4">
<li>State the energy transformations that occur when a ball is kicked vertically (1mk)</li>
<li>A bullet of mass <strong>20g</strong> traveling at <strong>400ms<sup>-1</sup></strong> is stopped by a concrete wall. Calculate the amount of energy transferred to the wall. (2mks)</li>
</ol>
<p> ;</p>
<ol start="6">
<li>A stone of mass <strong>24kg</strong> is dropped down from a building <strong>50m</strong> Calculate the<strong> KE</strong> gained as it hits the ground.</li>
</ol>
<p> ;</p>
<ol start="7">
<li>A ball is dropped vertically from the top of a cliff. If it attains a velocity of <strong>20m/s</strong> as it hits the ground, find the height of the cliff.</li>
</ol>
<p> ;</p>
<ol start="8">
<li>A <strong>50</strong> tonne rocket takes off vertically and attains a velocity of <strong>800m/s</strong> at an altitude of <strong>20km</strong>. calculate at this point;</li>
</ol>
<ul>
<li>Its <strong>KE</strong></li>
<li>Its <strong>PE</strong></li>
</ul>
<p> ;</p>
<p> ;</p>
<ol start="9">
<li>A metal ball suspended vertically with a wire is displaced through an angle as shown in the diagram below. The body is released from<strong> A </strong>and swings back to <strong>‘B</strong>’. Given that the maximum velocity at the lowest point<strong> B</strong> is <strong>5 m/s. </strong>Find the height <strong>h</strong> from which the ball is released.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>B</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong><em>h</em></strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="10">
<li>The figure below shows a swinging pendulum.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>C</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>B</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>State the energy conservation taking place as the pendulum moves from<strong> A </strong>to<strong> B </strong>and <strong>B</strong> to <strong>C</strong> (2mk)</p>
<p> ;</p>
<ol start="11">
<li>The figure shows a simple pendulum of length 80cm. The pendulum bob whose mass is <strong>50g</strong> oscillates between points <strong>A</strong> and<strong> B</strong>, through its rest position <strong> A</strong> and <strong>C</strong> are both <strong>80cm</strong> higher than <strong>B</strong>.</li>
</ol>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>C</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>B</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> </strong><strong> h=80cm</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li>a) i) indicate with an arrow, on the path <strong>ACB</strong>, the direction of the greatest velocity of the bob as it moves from <strong>A</strong> to <strong>B</strong>. 1mk</li>
<li>ii) State the form of energy possessed by the pendulum bob at point <strong>A</strong>. 1mk</li>
</ol>
<p> ;</p>
<ol>
<li>b) Determine:</li>
<li>i) The velocity of the bob at point <strong>C</strong>, 3mk</li>
<li>ii) The tension in the string as the bob passes point <strong>C</strong>. 3mk</li>
</ol>
<p>Take acceleration due to gravity <strong>g=10m/s<sup>2</sup></strong>)</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="12">
<li>The figure below shows a 200g mass placed on a frictionless surface and attached to spring.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Spring </strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>200g</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>The spring is compressed and released. Given that the elastic potential energy of the compressed spring is 2.7 x 10<sup>-2 </sup>J, determine the maximum speed with which the block moves after it is released. (4mk)</p>
<p> ;</p>
<ol start="13">
<li>A body is released from a height <strong>h</strong>. sketch a graph of potential energy against kinetic energy as the body falls to the ground. (2mk)</li>
</ol>
<p> ;</p>
<ol start="14">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>P.E (J)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>12</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>2</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>6</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>8</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>2</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>6</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>8</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Height (m)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The figure below shows how the Potential Energy <strong>(P.E</strong>) of a ball thrown vertically upwards. On the same axes, plot a graph of kinetic energy of the ball.</li>
</ul>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p> ;</p>
<ol start="15">
<li>A load of 1<strong>00N</strong> is raised <strong>20m</strong> in<strong> 50s</strong>. Calculate;</li>
</ol>
<ul>
<li>The gain in potential energy</li>
<li>The power developed</li>
</ul>
<p> ;</p>
<ol start="16">
<li>A body of mass<strong> m</strong> initially at rest is acted on by a force<strong> F </strong>for a time <strong>t</strong>, as a result its velocity changes to a final value <strong>v</strong>.</li>
<li>a) Use this information to show that the gain is kinetic energy <strong>E= ½ mv<sup>2</sup></strong></li>
<li>b) Calculate the kinetic energy of a car of mass <strong>1000 kg </strong>traveling at <strong>36</strong>km/h</li>
</ol>
<p> ;</p>
<ol start="17">
<li>A man uses a bow to fire an arrow of mass <strong>2kg </strong>vertically upwards into the air. He stretches the bow by <strong>0.15m </strong>with a maximum force of <strong>100N</strong></li>
</ol>
<p>(i) Calculate the energy transferred to the arrow (3mks)</p>
<p>(ii) Calculate the speed with which the arrow leaves the bow assuming all energy is transferred to the arrow (2mks)</p>
<p>(iii) Determine the greatest height reached by the arrow before it begins to fall (3mks)</p>
<p>(iv) Calculate the time the arrow will remain in the air (3mks)</p>
<p> ;</p>
<ol start="18">
<li>A body has <strong>16 Joules</strong> of kinetic energy. What would be its kinetic energy if its velocity was double?</li>
</ol>
<p> ;</p>
<ol start="19">
<li>The initial velocity of a body of mass <strong>50kg</strong> is <strong>10ms<sup>&#8211;</sup></strong><sup>1</sup>. A constant resultant force of <strong>15N</strong> is then applied. How long will it take before the kinetic energy doubles (4mks)</li>
</ol>
<p> ;</p>
<ol start="20">
<li>A boy lifts <strong>80</strong> sand bags from the floor of a room onto a shelf <strong>6m</strong> high in <strong>100s</strong>.</li>
</ol>
<p>(i) Find the useful work done in lifting the sand bags. 2mks</p>
<p>(ii) State the total potential energy developed when all the sand bags are</p>
<p>on the shelf 1mk</p>
<p>(iii) Determine the boy’s useful power output. 2mks</p>
<p>(iv) One sand bag fell from the shelf. Explain what happens to its kinetic</p>
<p>energy when it hits the ground.</p>
<p> ;</p>
<ol start="21">
<li>A pump draws water from a tank and issues it from the end of a hosepipe which is 2.5m vertically above the level from which the water is drawn. The cross –sectional area of the hosepipe is 1.0 x 10<sup>-3</sup>m<sup>2</sup> and the water leaves the end of the hosepipe at a speed of 5m/s. <strong>Calculate</strong> the power of the pump. (density of water = 1000Kg) (<strong><em>125Watts</em></strong>)</li>
</ol>
<p> ;</p>
<ol start="22">
<li>A load of<strong> 60kg</strong> moves from rest position to a point E along a frictionless path <strong>ABCDE</strong></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>2</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>6</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>8</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Height (m)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>D</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>B</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>C</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>F</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>12</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(a) Calculate the</p>
<p>(i) Maximum Kinetic energy of the load. (3mks)</p>
<p>(ii) Maximum velocity (3mks)</p>
<p>(iii) Velocity at <strong>C</strong> (3mks)</p>
<p> ;</p>
<ol start="23">
<li>The graph below was obtained in an experiment to investigate the stretching of materials.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>8</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>2</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>12</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>6</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>160</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>240</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1200</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>40</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>200</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Extension (cm) (volts) </strong></td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td width="45"></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(i) </strong>Determine the constant of the spring used. (2mk)</p>
<p><strong>(ii)</strong> Determine the elastic limit of the material. (1mk)</p>
<p><strong>(iii)</strong>Determine the work done on the spring by a force of <strong>120N</strong>.(3 mk)</p>
<p> ;</p>
<p><strong><u>WORK</u></strong></p>
<ol>
<li>A girl carries <strong>20</strong> litres of water in a jerry can on her head and walk fro <strong>200m</strong> on a horizontal level ground. Explain why the girl does no work (assume air resistance is negligible).</li>
</ol>
<p> ;</p>
<ol start="2">
<li>A certain machine uses an effort of <strong>400N</strong> to raise a load of <strong>600N</strong>. If the efficiency of the machine is <strong>75%</strong> determine its velocity ratio. (3mk)</li>
</ol>
<p> ;</p>
<ol start="3">
<li>A force of <strong>120N</strong> stretches a spring by <strong>15cm</strong>. How much work is done in stretching this spring by <strong>20cm</strong>?</li>
<li>A crane lifts a load of <strong>2000kg </strong>through a vertical distance of <strong>0m</strong> in <strong>6</strong> seconds. Determine the;</li>
<li>Work done <strong>(2mk)</strong></li>
<li>Power developed by the crane <strong> (2mk)</strong></li>
</ol>
<p><strong> iii) </strong>Efficiency of the crane given that it is operated by an electric</p>
<p>motor rated <strong>12.5 kW</strong></p>
<p> ;</p>
<ol start="5">
<li>A crane lifts a load of <strong>500 kg</strong> through a vertical distance of <strong>2m</strong> in <strong>8 s</strong> determine</li>
<li>Work done by the crane (2mk)</li>
<li>Power developed by the crane (2mk)</li>
</ol>
<ul>
<li>Efficiency of the crane given that its operated by all electric motor rated <strong>2kW</strong> (2mk)</li>
</ul>
<ol>
<li>State two effects which contribute to the efficiency being less than <strong>100% </strong> (2mk)</li>
</ol>
<p> ;</p>
<ol start="6">
<li>A lady of mass <strong>80kg </strong>walks up a flight of <strong>10 </strong>stairs each <strong>20 cm </strong>high in <strong>5 s</strong>. Determine the power she develops. (3mk)</li>
</ol>
<p> ;</p>
<ol start="7">
<li><strong>210</strong> litres of water is pumped through a height of <strong>20m</strong> in <strong>2</strong> minutes. Determine the power rating of the of the pump if it is <strong>75%</strong> efficient (3mks)</li>
<li>The energy wasted in using a machine is <strong>600J</strong>. If the machine is <strong>70%</strong> Calculate the volume of water pumped by the machine through a height of <strong>15m</strong>. (3mks)</li>
</ol>
<p> ;</p>
<ol start="9">
<li>A force of <strong>6N</strong> extends a spring by <strong>2m</strong>. Calculate the work done in extending the spring (3mk)</li>
</ol>
<p> ;</p>
<ol start="10">
<li>A bullet of mass <strong>8 g</strong> traveling at <strong>400 m/s</strong> is stopped by a concrete wall. Calculate the amount of heat energy transferred to the wall. (2mk)</li>
</ol>
<p> ;</p>
<ol start="11">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>2000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>6000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-2000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-4000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-6000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Force (N)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>40</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>60</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>70</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Distance (m)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>B</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>C</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>D</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>F</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>G</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>H</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>I</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The fig. below shows a <strong>force</strong><strong> &#8211;</strong><strong> distance</strong> graph for a car being on a horizontal ground</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li><strong> a)</strong> Calculate the total work done</li>
<li><strong>b)</strong> If the velocity just before reaching point <strong>D</strong> is <strong>6m/s</strong>, calculate the power developed by the agent providing the force at this point.</li>
</ol>
<p> ;</p>
<ol start="12">
<li>The figure below shows a body being acted upon by a varying force over a</li>
</ol>
<p>distance of <strong>5m</strong>.</p>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>Force (N</strong><strong>)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Distance (m</strong><strong>)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>2</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>4</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>3</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>5</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-30</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="13">
<li>The figure below shows a<strong> forc</strong><strong>e –</strong><strong> distance</strong> graph for a motorbike moving</li>
</ol>
<p>with a varying force for<strong> 20</strong>seconds over a distance of <strong>50m.</strong></p>
<table width="100%">
<tbody>
<tr>
<td><strong>100</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>200</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>300</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-100</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-200</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-300</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>40</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Distance (m)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50</strong></td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td width="83"></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Calculate</p>
<ol>
<li>The average velocity</li>
<li>The total work done</li>
<li>The power developed by the motor bike</li>
</ol>
<p> ;</p>
<ol start="14">
<li>Figure below shows a force distance graph for a car being moved on a</li>
</ol>
<p>horizontal ground</p>
<table width="100%">
<tbody>
<tr>
<td><strong>Distance (m)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>F </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1500</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 40</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-500</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-1000</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>500</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1000</strong></td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td width="37"></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong> </strong></p>
<p>(i) Calculate total work done when the car moved from A to F.</p>
<p>(ii) Determine the power of the car if it takes <strong>0.6</strong> seconds to move it from <strong>A</strong> to <strong>F</strong>.</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="15">
<li>Figure below shows a force distance graph for a car being moved on a horizontal ground</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>60</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Distance (m)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>K </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> F </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1200</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 40</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-400</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>-800</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>400</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>800</strong></td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td width="81"></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p>(i) Calculate total work done when the car moved from <strong>K</strong> to <strong>L</strong>. (4mk</p>
<p>(ii) Determine the power of the car if it takes <strong>8s</strong> to move it from <strong>K</strong> to <strong>L</strong>.</p>
<p>(2mk</p>
<p><strong> </strong></p>
<ol>
<li>Define the following terms as used in machines</li>
</ol>
<ul>
<li>Mechanical advantage (1mk)</li>
<li>Efficiency (1mk)</li>
<li>Velocity ratio (1mk)</li>
</ul>
<p> ;</p>
<ol start="2">
<li>State the factor that affects / determines each of the following in a machine.</li>
</ol>
<p><strong> (i)</strong> Mechanical advantage<strong> (M.A</strong>) (1mk)</p>
<p><strong> (ii)</strong> Velocity Ratio (<strong>V.R</strong>) (1mk)</p>
<p> ;</p>
<ol start="3">
<li>State two reasons why the efficiency of a machine is always less than 100% (2mk)</li>
<li>In a wheel and axle system, state the advantage of having a large wheel diameter compared to the diameter for a frictionless system. (1mk)</li>
</ol>
<p> ;</p>
<p> ;</p>
<p><strong><u>LEVERS</u></strong></p>
<ol>
<li>Figure shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point <strong>P</strong>. A force of 200N is applied at <strong>R</strong>.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>P</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>100 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Liquid</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Area= 180cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A Bale</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>200 N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A =50 cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>R</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) Calculate the force <strong>F</strong> exerted by small piston on the liquid. (2mks)</p>
<p>(ii) Find the weight of the Bale supported by the large piston (2mks)</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="2">
<li>Figure below shows a simple bottle opener being used to remove the top from a bottle which is the position of the load, fulcrum and effort? (1mk)</li>
</ol>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>B</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>C</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="3">
<li>Figure shows a lever</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>5m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 60N</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Determine</p>
<ul>
<li>The effort applied</li>
<li>The <strong>VR</strong>.</li>
<li>The MA.</li>
<li>The efficiency.</li>
<li>Suggest two ways in which the mechanical advantage could be increas</li>
</ul>
<p> ;</p>
<ol start="4">
<li>The figure below shows a wheel of mass <strong>10kg</strong> and radius <strong>1 m </strong>being pulled by a boy against a step <strong>4 m </strong>high. What force is just sufficient to turn the wheel so that it will rise over the step</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong> 0.4m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Boy</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="5">
<li>Figure shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point <strong>P</strong>. A force of <strong>100N</strong> is applied at <strong>R</strong>.</li>
</ol>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>Liquid</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>5 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>100 N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> </strong><strong>P </strong><strong>Fixed</strong></p>
<p><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>R</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Calculate</p>
<ul>
<li><strong>(i) </strong>The force <strong>F</strong> exerted by small piston on the liquid.</li>
<li><strong>(ii) </strong>The VR of the lever.</li>
<li><strong>(iii) </strong>The MA of the lever.</li>
<li><strong>(iv) </strong>The efficiency of the lever.</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="6">
<li>The figure shows a device for closing a steam outlet. The area of the piston is</li>
</ol>
<p><strong>4.0 x 10<sup>-4</sup>m<sup>2</sup></strong> and the pressure of the steam in the boiler is <strong>2.0 x 10<sup>5</sup>Nmâ<sup>2</sup></strong>.</p>
<table width="100%">
<tbody>
<tr>
<td><strong>Cork </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>15m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Pivot</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>45cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Steam pressure from boiler</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> W</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Determine</p>
<ul>
<li><strong>(i) </strong>The weight W the weight <strong>W</strong> that will just hold the bar in the horizontal position shown.</li>
<li><strong>(ii) </strong></li>
</ul>
<table width="100%">
<tbody>
<tr>
<td><strong>Slave piston</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The <strong>VR</strong> of the lever.</li>
<li><strong>(iii) </strong>The <strong>MA</strong> of the lever.</li>
<li><strong>(iv) </strong>The efficiency of the lever.</li>
</ul>
<p> ;</p>
<ol start="7">
<li>State <strong>one</strong> advantage of hydraulic brakes over mechanical brakes. (1mk)</li>
</ol>
<p><strong><em> </em></strong></p>
<p> ;</p>
<p> ;</p>
<p><strong><u>WHEEL AND AXLE</u></strong></p>
<ol>
<li>The machine wheel and axle has a lot of application in real life. <strong>Name any two</strong> practical examples of such machine. (2mks)</li>
</ol>
<p> ;</p>
<ol start="2">
<li>A machine consists of a wheel of radius <strong>40cm </strong>and axle of radius <strong>10cm</strong>. Determine its efficiency when used to lift a load of <strong>300N</strong> using an effort of <strong>100N</strong> (3mk)</li>
</ol>
<p> ;</p>
<ol start="3">
<li>A machine with a wheel of diameter 1.2m and an axle of diameter 0.4m lifts a lot of mass 9kg with an effort of 100N. Given that the acceleration due to gravity is 10m/s<sup>2</sup></li>
</ol>
<p>(i) The velocity ratios of the machine (1mk)</p>
<p>(ii) The mechanical advantage of the machine (1mk)</p>
<p> ;</p>
<ol start="4">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>R</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>r</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>W</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>F</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> Wheel</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> Axle</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The figure below shows a wheel and axle being used to raise a load W by applying an effort F. The radius of the large wheel is <strong>R </strong>and of the small wheel <strong>r </strong>as shown</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) Show that the velocity ratio (VR) of this machine is given by <strong>R/r</strong>. (2mks)</p>
<p>(ii) Given that <strong>r =7cm</strong>, <strong>R = 10.5cm</strong>, determine the effort required to raise a</p>
<p>load of <strong>40N</strong> if the efficiency of the machine is <strong>75% </strong> (3mks)</p>
<p> ;</p>
<ol start="5">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Load 200N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> Effort=40N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Wheel </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Axle </strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The figure below shows the cross – section of a wheel and axle of radius <strong>3 cm </strong>and <strong>1cm</strong> respectively used to lift a load. Use it to answer the questions that follow.</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p>Calculate:`</p>
<p><strong>(i)</strong> The mechanical advantage <strong>(M.A)</strong> of the system. (2mks)</p>
<p><strong>(ii)</strong> The velocity ratio <strong>(V.R</strong>) of the system. (2mks)</p>
<p><strong>(iii)</strong> The efficiency of the machine. (2mks)</p>
<p> ;</p>
<ol start="6">
<li>A machine consisting of a wheel of radius<strong> 50cm</strong> and an axle of radius <strong>10cm</strong> is used to lift a load of if the efficiency of the system is <strong>75%</strong>. Calculate the effort needed <strong>(3mk)</strong></li>
</ol>
<p> ;</p>
<ol start="7">
<li>the figure below shows a windless. An effort is applied on the handle which is turned on a radius of <strong>60 cm</strong>. As the handle turns, a rope is wound around the drum of diameter <strong>24 cm</strong>, thus raising a bucket of water out of the well</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Handle </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 24cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 60cm</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li>a) If an effort of<strong> 20N</strong> is needed to lift a bucket full of water of mass <strong>8kg</strong>, Calculate:</li>
</ol>
<p>(i) the energy gained by the mass when the drum turns through one</p>
<p>revolution (3mks)</p>
<p>(ii) The work done by the effort during this revolution (3mks)</p>
<ol>
<li>b) Suggest a reason why the two quantities in a(i) and (ii) are not equal (1mk)</li>
<li>c) Calculate:</li>
</ol>
<p>(i) the velocity ratio of the machine (1mk)</p>
<p>(ii) the efficiency of the windlass (2mks)</p>
<ol>
<li>d) Describe with a reason how the effort required to lift the bucket of water varies from the point where it is under water to where the whole bucket leaves the water surface (2mks)</li>
</ol>
<p> ;</p>
<p><strong> <u>INCLINED PLANES</u></strong></p>
<ol>
<li>Figure below shows an inclined plane.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>h</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Ï´</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Length L</strong></td>
</tr>
</tbody>
</table>
<p><strong> </strong></p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Show that the velocity ratio (3mks)</p>
<p> ;</p>
<ol start="2">
<li>A person pulls a box of weight <strong>750N</strong> up an inclined plane<strong> 6m</strong> long using a force of <strong>500N</strong> as shown in figure below.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>h</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>500N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30<sup>0</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>750N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 6m</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ul>
<li><strong>(i) </strong>The<strong> VR</strong></li>
<li><strong>(ii) </strong>The height <strong>h</strong></li>
<li><strong>(iii) </strong>The work done by effort.</li>
<li><strong>(iv) </strong>The useful work done.</li>
<li><strong>(v) </strong>The efficiency of the plane.</li>
</ul>
<p> ;</p>
<ol start="3">
<li>A block of mass <strong>50kg</strong> is pulled up an inclined plane by a force of <strong>200N</strong> until it gets to the top as shown below</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong> 30Kg</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>2m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30<sup>0</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>200N</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<table width="100%">
<tbody>
<tr>
<td><strong>200N</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong> </strong></p>
<p><strong>(i)</strong> Find the work done by the force in moving the block up the incline. (3mk)</p>
<p><strong>(ii)</strong> Find the work done on the block against gravity. (2mk)</p>
<p> ;</p>
<ol start="4">
<li>A man uses an inclined plane to lift a <strong>50kg</strong> mass thru a vertical height of <strong>4m</strong>.if the plane is <strong>5%</strong> efficient and makes an angle of <strong>30<sup>0</sup></strong> with the horizontal, calculate;</li>
</ol>
<ul>
<li>The<strong> VR</strong></li>
<li>The effort needed</li>
<li>The work output</li>
<li>The work input.</li>
<li>The work done against friction.</li>
</ul>
<p> ;</p>
<ol start="5">
<li>An inclined plane of length <strong>12m</strong> and vertical height <strong>3m</strong> is used to lift a load <strong>L</strong> using an effort of If the plane has an efficiency of <strong>80%. </strong>Find the load<strong> L.</strong></li>
</ol>
<p> ;</p>
<ol start="6">
<li>A person pulls a box of mass <strong>30kg</strong> up an inclined plane<strong> 5m</strong> long at a constant speed as shown in figure below.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>F</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30<sup>0</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30kg</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>5m</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>If the friction force between the plane and the block is <strong>100N</strong>, Find:</p>
<ul>
<li>The effort that must be exerted on the box for it to move up the incline at a constant speed</li>
<li>The gain in potential energy of the box while at the top of the incline</li>
<li>The work done by the person in pulling the box</li>
</ul>
<ol start="7">
<li>The figure below shows a trolley of weight <strong>20N</strong> pulled by a force of<strong> 4N</strong> from the bottom to the top of an inclined plane at a uniform speed.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Weight </strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>h </strong><strong>=5 m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> D = 40 m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort E</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li>(i) State the value of the force acting downwards along the inclined plan (1mk)</li>
<li>ii) Explain how the value in part (a) (i) is obtained (2mk)</li>
<li>b) For the system, determine the:</li>
<li>i) Mechanical advantage: (2mk)</li>
<li>ii) Velocity ratio; (2mk)</li>
</ol>
<p>iii) Efficiency. (2mk)</p>
<p> ;</p>
<ol start="8">
<li>The following diagram shows a load of<strong> 50N</strong> being raised by pulling it along an Inclined plane of length <strong>0m.</strong></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>h </strong><strong>=0.5</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 2m</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>22N</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Determine</p>
<ol>
<li><strong>i)</strong> The work done by the<strong> 22 N</strong> force</li>
<li><strong>ii)</strong> The work done against the load</li>
</ol>
<p><strong>iii)</strong> The efficiency of the system</p>
<ol>
<li><strong>iv)</strong> Why is the efficiency less than <strong>100%</strong></li>
</ol>
<p> ;</p>
<ol start="9">
<li>The figure below shows an inclined plane placed at<strong> 30<sup>0</sup></strong> to the horizontal so that it can be used to raise a load through a height <strong>‘h’</strong>. The efficiency is <strong>96%.</strong></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>h</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30<sup>0</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load </strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) Determine Velocity Ratio of the machine (2mks)</p>
<p>(ii) the efforts needed to move a load of 800N along the plane at a constant</p>
<p>velocity. (2mks)</p>
<p>(b) (i) <strong>Draw</strong> a block and tackle pulley system of velocity ratio 4. In your</p>
<p>diagram, <strong>Show</strong> the effort and load position. (2mks)</p>
<p>(ii) If the pulley system raises a load of <strong>100N</strong> at steady rate. <strong>Calculate</strong></p>
<p>the efforts required to raise the load if it is <strong>80%</strong> efficient. (2mk)</p>
<ol start="10">
<li>A girl of mass <strong>50 kg</strong> climbs up a ramp <strong>200m</strong> long inclined at an angle <strong>10<sup>0</sup></strong> to the horizontal. Calculate the minimum work done by the girl. (3mk)</li>
</ol>
<p> ;</p>
<ol start="11">
<li>A man used a wooden plank to lift a log of wood from the ground to a stationary lorry on a flat ground as shown in figure below. The wooden plank was inclined at an angle of<strong> 30<sup>0</sup></strong> to the ground.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>30</strong><strong><sup>0</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Log</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Wooden plank</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) Indicate with an arrow on the diagram, the direction of the effort and the</p>
<p>load. (2mks)</p>
<p>(ii) Calculate the velocity ratio of the set up. (2mks)</p>
<p>(iii) Calculate the mechanical advantage of the set up if its efficiency is<strong> 65%</strong>. (2mks)</p>
<p><strong><u> </u></strong></p>
<p><strong><u>THE SCREW</u></strong></p>
<ol>
<li>A screw advances <strong>1mm</strong> when the screw is turned through <strong>two</strong> What is the pitch of the screw?</li>
</ol>
<p> ;</p>
<ol start="2">
<li>The figure below shows a cross-section of a handle of a screw jack <strong>70</strong> <strong>cm</strong> long and pitch of the screw is <strong>8 cm</strong>.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>0.8cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>70 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Handle</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Base</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Given that the efficiency is <strong>60%,</strong> calculate:</p>
<ol>
<li> i) The velocity ratio of the system. (2mk)</li>
<li>ii) If an effort of <strong>50N</strong> is applied calculate the load that can be lifted. (3mk)</li>
</ol>
<p> ;</p>
<ol start="3">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>0.5cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>25cm</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The handle of screw jack shown below is <strong>25cm</strong> long and the pitch of the screw is <strong>5cm</strong>.</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) What is the velocity ratio of the system. (3mk)</p>
<p>(ii) What force must be applied at the end of the handle when lifting a load of <strong>3300N</strong> if the efficiency of the jack is <strong>70%.</strong> (3mk)</p>
<ol start="4">
<li>An effort of <strong>40N</strong> is applied to the car jack whose hand moves through a circle of radius <strong>5cm</strong>. The pitch of the screw is <strong>2.5mm</strong>. Determine the efficiency of the jack if the mass of the car is <strong>252kg</strong></li>
</ol>
<p> ;</p>
<p><strong><u>THE GEARS </u></strong></p>
<ol>
<li>The fore gear of bicycle has <strong>48</strong> teeth while the rear one has <strong>24 </strong>teeth. Find its VR.</li>
<li>Calculate the VR of the gears below</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>32 teeth</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>16 teeth</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>EFFORT </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>LOAD</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="3">
<li>Calculate the combined VR of the gears below.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>LOAD</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>EFFORT</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="4">
<li>Figure shows part of a bicycle</li>
</ol>
<p> ;</p>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>32</strong><strong> teeth </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>16</strong><strong> teeth </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Chain </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50cm</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Determine;</p>
<ol>
<li><strong>i)</strong> The velocity ratio (4mk)</li>
<li><strong>ii)</strong> Efficiency of the bicycle if its mechanical advantage is <strong>15</strong> (3mk)</li>
</ol>
<p> ;</p>
<p><strong><u>THE BELT AND THE GEARS </u></strong></p>
<ol>
<li>Calculate the VR of the pulley belt below</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort</strong></p>
<p><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>R=50cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>r=20cm</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="2">
<li>In the figure below, the effort wheel has<strong> 32</strong> teeth and a radius of <strong>36cm</strong> while the load wheel has<strong> 16 </strong>teeth and <strong>9cm.</strong> calculate the <strong>V R</strong> of the machine.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort</strong></p>
<p><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="3">
<li>A bicycle has a driving cogwheel of radius <strong>10cm</strong> and <strong>24 </strong>teeth. The driver rear cog wheel has a radius of <strong>4cm</strong> and with <strong>8</strong> teeth.</li>
</ol>
<p>For the cog-wheel system determine</p>
<p>(i) Velocity ratio. (2mks)</p>
<p>(ii) The efficiency. (3mks)</p>
<p> ;</p>
<ol start="4">
<li>A bicycle has a driving cogwheel of radius 10cm and 24 teeth. The driver rear cog wheel has a radius of 4cm and with 8 teeth.</li>
</ol>
<p>For the cog-wheel system determine</p>
<p>(i) Velocity ratio. (2mk)</p>
<p>(ii) The efficiency. (3mk)</p>
<p> ;</p>
<p><strong><u>PULLEYS</u></strong></p>
<ol>
<li><strong>Draw</strong> a block and tackle pulley system of velocity ratio 4. In your diagram, <strong>Show</strong> the effort and load position. If the pulley system raises a load of 100N at steady rate. <strong>Calculate</strong> the efforts required to raise the load if it is <strong>80%</strong> (4mks)</li>
</ol>
<p> ;</p>
<ol start="2">
<li>A mechanic uses a pulley system with a velocity ratio of <strong>6 </strong>to raise an engine, of weight <strong>2800N</strong> through a vertical distance of <strong>5m</strong>. The mechanic pulls with an effort of <strong>500N</strong>. Calculate</li>
<li>The effort distance. (2mk)</li>
<li>The work done by the effort (mechanic) (2mk)</li>
</ol>
<ul>
<li>The useful work done by the pulley machine. (2mk)</li>
</ul>
<ol>
<li>The mechanical advantage of the machine. (2mk)</li>
<li>The efficiency of the machine. (2mk)</li>
<li>State two reasons why the efficiency of a machine is always less than <strong>100%</strong> (2mk)</li>
<li>Draw a pulley system of velocity ratio<strong> 5</strong> and having a total of<strong> 4</strong> pulleys and explain why its efficiency reduces as the size of the load reduces.(3mk)</li>
</ol>
<p> ;</p>
<ol start="4">
<li>The diagram fig below shows a system of four pulleys. Show on the diagram how the string can be fixed so that the pulley has a <strong>VR</strong> of <strong>3</strong></li>
</ol>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="5">
<li>The figure below shows a single fixed pulley being used to lift a load.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>State;</p>
<ul>
<li>The mechanical advantage of the pulley (1mk</li>
<li>The velocity ratio of the pulley (1mk)</li>
</ul>
<p> ;</p>
<ol start="6">
<li>A man used the pulley system shown below to raise a <strong>3kg</strong> load through a height of <strong>5m</strong> using an effort of <strong>25N</strong></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>3kg</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(a)</strong> Through what distance does the end <strong>E</strong> of the rope move (2mk)</p>
<p><strong>(b)</strong> Given that the pulley system is frictionless and that the efficiency is <strong>75 %, </strong>find</p>
<p><strong>(i)</strong> The mechanical advantage of the system (3mk)</p>
<p><strong> (ii)</strong> The mass of the lower pulley (2mk)</p>
<p> ;</p>
<ol start="7">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Pulley 2</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Pulley 1</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort =</strong><strong>500 N</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The figure below shows a pulley system used to raise a load by applying an effort of 500N</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>State the:</p>
<ul>
<li>Velocity ratio of the system. (1mk)</li>
<li>Purpose of pulley 2. (1mk)</li>
<li>Given that the machine has an efficiency of 80%, determine the maximum load that can be raised. (3mk)</li>
</ul>
<p> ;</p>
<p> ;</p>
<ol start="8">
<li>A pulley system has two pulleys on the lower block and one pulley on the upper block. In order to raise the load of <strong>6N</strong>, an effort of <strong>2N</strong> is applied.
<ul>
<li>Draw a sketch to show the pulley system. (3mk)</li>
<li>Calculate the efficiency of the pulley system (3mk)</li>
<li>If the lower block weighs <strong>4N</strong> what friction force opposes the motion? (3mk)</li>
</ul>
</li>
</ol>
<p> ;</p>
<ol start="9">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> EFFFICIENCY </strong></p>
<p><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>LOAD (N)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>100 </strong><strong>%</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>Figure shows the relationship between the efficiency and the load for a pulley system</li>
</ul>
<p><strong> </strong></p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Explain the shape of the curve (1mk</p>
<p> ;</p>
<ol start="10">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>10kg </strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80N</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>Using the pulley system shown, a mass of 10kg is raised 2m by an effort of 80N</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) How much potential energy does the load gain? (1mk)</p>
<p>(ii) How far does the effort end move in order to raise the load by 2m (1mk)</p>
<p>(iii) How much work is done by the effort. (1mk)</p>
<p>(iv) What is the efficiency of these pulleys? (2mks)</p>
<p>(v) If all the wasted energy is used to lift the bottom pulley, how much does</p>
<p>the pulley weigh? (3mks)</p>
<p> ;</p>
<ol start="11">
<li>Figure shows a pulley system</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>40kg</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>150N</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(i)</strong> What is the velocity ratio of the system (1mk)</p>
<p><strong>(ii)</strong> Calculate the efficiency of the system (3mks)</p>
<p><strong>(iii)</strong> Give two reasons why efficiency is not <strong>100%</strong> (2mks)</p>
<ol start="16">
<li>A block and tackle is made up of the two pulley wheels on top and one pulley wheel at the bottom as shown below.</li>
</ol>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong> </strong></p>
<ul>
<li>Draw the string which passes over the wheels and indicate where the</li>
</ul>
<p>effort and load is applied. (2mk)</p>
<ul>
<li>What is the velocity ratio of the machine? (1mk)</li>
<li>A load of <strong>600N</strong> is lifted by an effort of <strong>250N</strong>. Determine</li>
<li>The mechanical advantage of the system. (1mk)</li>
<li>The efficiency of the system. (2mk)</li>
<li>State two reasons why the efficiency of a machine is always less than <strong>100%</strong> (2mk)</li>
</ul>
<p> ;</p>
<ol start="17">
<li>Figure shows a block and tackle pulley system lifting a load of <strong>900N</strong></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>900N</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ul>
<li>Determine the velocity ratio of the machine. (1mk)</li>
<li>If an effort of <strong>225N</strong> is required to lift the load using the machines,</li>
</ul>
<p>determine the efficiency of the pulley system. (3mk)</p>
<ul>
<li>In the space provided below, sketch a graph of efficiency against load for</li>
</ul>
<p>the system (2mks)</p>
<p> ;</p>
<ol start="12">
<li>The Figure below shows a machine being used to raise a load.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Effort</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li><strong>a)</strong> Determine the velocity ratio <strong>(V.R) </strong>of the machine. (1mk)</li>
</ol>
<p>(b) If a load of <strong>800N</strong> is raised by applying an effort of <strong>272N</strong>, determine the efficiency of the machine. (2mk)</p>
<ol start="13">
<li>A block and tackle is made up of three pulley wheels on top and two pulley wheels at the bottom as shown below.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Load</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(a)</strong> Complete the diagram by drawing the chain which passes over the wheels</p>
<p>and indicate where the effort is applied (2mk)</p>
<p><strong>(b)</strong> What is the velocity ratio of the machine (1mk)</p>
<p><strong>(c)</strong> A load of <strong>1120N</strong> is lifted by an effort of <strong>250N</strong></p>
<p>Determine</p>
<p><strong> (i)</strong> The mechanical advantage (M.A) of the system (1mk)</p>
<p><strong>(ii)</strong> The efficiency, <strong>E</strong>, of the system (2mk)</p>
<p><strong>(d)</strong> How much percentage energy is wasted in the above system (1mk)</p>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> EFFFICIENCY </strong></p>
<p><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>LOAD (N)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>100 </strong><strong>%</strong></td>
</tr>
</tbody>
</table>
<p><strong>(e)</strong> Using the axes given below, sketch a graph of efficiency, <strong>E,</strong> against load (2mk</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Draw a block and tackle system with a velocity ratio of <strong>5</strong>. (2mk)</p>
<p> ;</p>
<ol start="14">
<li>The pulley system in the diagram has two wheels in each block.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li>a) Complete the diagram to show the string as the pulley is being used to lift the load <strong>L</strong>. (1 mk)</li>
<li>b) The block and tackle pulley system is used to investigate relationship between mechanical advantage and efficiency.</li>
</ol>
<p>(i) State the measurements to be taken in this investigation. (2mk)</p>
<p> ;</p>
<ol start="15">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>50N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E=50N</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The figure below shows a pulley used to raise a load of <strong>50N</strong>.</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li>a) What is the velocity ratio of the system? (1mk</li>
<li>b) Determine the mechanical advantage. (1mk)</li>
</ol>
<p> ;</p>
<ol start="16">
<li>A load was raised using the system shown below as in figure (a). The system was then modified as shown in figure (b) and used to raise the same load.</li>
</ol>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>(b)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>(a)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) The block and tackle system in <strong>(b)</strong> above was used to lift a load of <strong>80kg</strong>. Given that its efficiency is <strong>80%.</strong> Calculate the effort applied to lift the load. 4mk)</p>
<p>(ii) Explain the change in efficiency.</p>
<p> ;</p>
<ol start="17">
<li>Figure shows a pulley system being used to raise a load.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Load </strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>This pulley system has an efficiency of <strong>75%.</strong></p>
<p><strong> (i)</strong> Determine the velocity ratio of the system. (1mk)</p>
<p><strong> (ii)</strong> Calculate the mechanical advantage of the pulley system. (2mks)</p>
<p><strong> (iii)</strong> What effort is required to raise a load of<strong> 240kg</strong>? (2mks)</p>
<p><strong> (iv)</strong> Calculate the work done by a person using this machine in raising a</p>
<p>load of <strong>120kg</strong> through a vertical distance of <strong>2.5m</strong> (3mk)</p>
<p><strong> (v)</strong> Give two reasons to explain why the efficiency of a machine cannot</p>
<p>be <strong>100%.</strong> (2mk)</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="18">
<li>In the arrangement shown, the mass of<strong> 30 k</strong><strong>g</strong> hanging on the pulley helps to raise the unknown load. The person pulling up the other string finds that he had to do<strong> 800 Joule</strong><strong>s</strong> of work in order to raise the load<strong> 4m</strong><strong>.</strong></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Pull up</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30kg</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Unknown mass</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li><strong> a)</strong> Calculate the value of the unknown mass.</li>
<li><strong> b)</strong> State the assumptions you make in calculating the value<strong> (a)</strong> above</li>
<li>Using a pulley system, a girl lifts a load of <strong>1800N</strong> using an effort of <strong>400N</strong>. If the system is <strong>65%</strong> efficient, determine the velocity ratio of the system.</li>
</ol>
<p> ;</p>
<ol start="20">
<li>Sketch a labeled diagram to show how an arrangement of a single pulley may be used to provide a mechanical advantage of <strong>2</strong>.</li>
</ol>
<p> ;</p>
<p><strong><u>HYDRAULIC MACHINES</u></strong></p>
<p> ;</p>
<ol>
<li>A hydraulic brake system of a car has a master piston of radius of <strong>7cm</strong> while that of the slave piston is <strong>21 cm.</strong></li>
</ol>
<p><strong> (i) </strong>Find the velocity ratio of the system. (1mk)</p>
<p><strong>(ii) </strong><strong> </strong>If a force of <strong>1800 N</strong> is experienced at the slave piston find;</p>
<ul>
<li>The force exerted at the master piston</li>
<li>The efficiency of the system</li>
</ul>
<p> ;</p>
<ol start="2">
<li>The diagram below shows the principle of the hydraulic car jack that has a master piston of radius <strong>7cm</strong> and slave piston of radius <strong>21 cm</strong>.</li>
</ol>
<p> ;</p>
<table width="100%">
<tbody>
<tr>
<td><strong>Oil </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Slave piston</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>300N</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1800N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Master piston</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(i)</strong> Determine the velocity ratio of the hydraulic jack</p>
<p><strong>(ii) </strong>If the small piston moves down a distance of<strong> 7.2cm</strong>, determine how far upwards the larger piston moves.</p>
<p><strong>(iii)</strong> Determine;</p>
<ul>
<li>The effort exerted at the master piston</li>
<li>The efficiency of the system</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol start="3">
<li>The figure below shows a hydraulic lift used to lift a load <strong>L</strong>. The effort applied is <strong>150N</strong> at the end of a lever <strong>36cm</strong> long and pivoted at the other end and, plunger is <strong>6cm</strong> from the pivot. The area of the plunger piston <strong>C</strong> is <strong>4cm<sup>2</sup></strong> and that of the load piston<strong> D</strong> is <strong>400cm<sup>2</sup></strong>.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>30 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Plunger</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>C = 4cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Liquid</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>6 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>150 N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> </strong><strong>P </strong><strong>Fixed</strong></p>
<p><strong> </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>R</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>D = 400cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Calculate</p>
<ul>
<li>(i) The<strong>R </strong>of the lift</li>
<li>(ii) The effort exerted at the effort piston</li>
<li>(iii) The <strong>A</strong> of the system</li>
<li>(iv) The efficiency of the system</li>
</ul>
<p> ;</p>
<ol start="4">
<li>The figure below shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point <strong>P</strong>. A force of <strong>400N</strong> is applied at <strong>R</strong>.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>P</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>100 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Liquid</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Area= 360cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A Bale</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>400 N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A =30cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>R</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Calculate</p>
<p><strong> (i)</strong> The effort exerted at the smaller piston<strong>.</strong></p>
<p><strong> (ii) </strong>The<strong> V.R </strong>of the lift</p>
<p><strong> (iii)</strong> The <strong>M.A</strong> of the system</p>
<p><strong> (iii) </strong>The efficiency of the system</p>
<p><strong> (iv) </strong>What is the pressure exerted at the larger piston? (3mk)</p>
<p> ;</p>
<ol start="5">
<li>The diagram below represents a motor car hydraulic braking system</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Brake pedal</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Master piston</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Slave piston</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>15cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>5 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>16cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(i)</strong> State the property of the liquid used as brake fluid</p>
<p><strong> (ii) </strong>Find the <strong>velocity ratio</strong> of the system.</p>
<p><strong>(iii)</strong> An effort of <strong>120N</strong> is applied on the brake pedal, calculate</p>
<p><strong>(a)</strong> The force applied to the master piston</p>
<p><strong>(b)</strong> The force experienced at the slave piston</p>
<p><strong>(c)</strong> The efficiency of the system</p>
<ol start="18">
<li></li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>R</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A =40 cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>P</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Liquid</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Area= 320cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>A Bale</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>200N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20 cm</strong></td>
</tr>
</tbody>
</table>
<ul>
<li>The figure below shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point <strong>P</strong>. A force of <strong>200N</strong> is applied at <strong>R</strong>.</li>
</ul>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(i)</strong> State the property of the liquid used as brake fluid (2mk)</p>
<p><strong> (ii) </strong>Find the <strong>velocity ratio</strong> of the whole system. (2mk)</p>
<p><strong>(iii)</strong> Calculate the</p>
<ul>
<li>Force exerted on the smaller piston. (2mk)</li>
<li>If the smaller piston moves down by <strong>12m</strong>, by what height does the</li>
</ul>
<p>larger piston raise the load. (3mk)</p>
<p> ;</p>
<ol start="21">
<li>The diagram below represents a motor car hydraulic braking system</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>Pivot</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Brake pedal</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Master piston</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Slave piston</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80 cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>12cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>2 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>60 cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong>(i)</strong> State the property of the liquid used as brake fluid (1mk)</p>
<p><strong> (ii) </strong>Find the velocity ratio of the system. (1mk)</p>
<p><strong>(iii)</strong> An effort of <strong>300N</strong> is applied on the brake pedal, calculate</p>
<p><strong>(a)</strong> The force applied to the master piston (2mk)</p>
<p><strong>(b)</strong> The force experienced at the slave piston (2mk)</p>
<p><strong>(c)</strong> The efficiency of the system (2mk)</p>
<p> ;</p>
<ol start="22">
<li>The figure below shows a hydraulic lift used to lift a load.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>200N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> 2 cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>P</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80cm<sup>2</sup></strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Hinge </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50 cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>LOAD</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Q</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10cm</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Calculate</p>
<ol>
<li>The effort exerted at the smaller piston <strong>Q</strong> (2mk)</li>
<li>Calculate the load that can be supported by the above machine at <strong>P</strong> (2mk)</li>
<li>The<strong>R </strong>of the system (3mk)</li>
<li>The <strong>A</strong> of the system (3mk)</li>
<li>The efficiency of the system (2mk)</li>
</ol>
<p> ;</p>
<ol start="23">
<li>The figure below shows an effort of 100N being on a single moving pulley to exert a pressure on a gas in a cylinder.</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>F</strong><strong> = 100N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>1m</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>T</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>3m</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Piston </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>String </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>Gas </strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>The area of the piston is <strong>10cm<sup>2</sup></strong> and the volume of the gas is <strong>20cm<sup>3</sup></strong>.The</p>
<p>weight of the pulley, beam and frictional forces at the moveable part are taken</p>
<p>zero. If the beam is equilibrium:</p>
<ol>
<li>i) Calculate the force acting on the piston. (2mk) (<strong><em>300N)</em></strong></li>
<li>ii) Calculate the pressure exerted on the gas by the piston. (2mk)</li>
</ol>
<p>(iii) If the effort applied on the pulley is <strong>200N</strong>, by what distance has the pivot</p>
<p>been moved if the pressure remains constant. (2mk)</p>
<p><strong><em>( 300x (1+</em></strong><strong><em>x</em></strong><strong><em>) = 200 x (3-</em></strong><strong><em>x</em></strong><strong><em>))= 0.6m</em></strong></p>
<ol>
<li>iv) Now the pivot is moved towards the pulley and the piston of different cross section area is used. If the pressure exerted on the gas becomes <strong>5&#215;10<sup>7 </sup>Pa</strong> and the cross section area of the new piston is <strong>5cm<sup>2</sup></strong>. What is the amount of force acting on the piston? (2mk)<strong> (= 7.5 x 10<sup>3</sup>N)</strong></li>
</ol>
<p> ;</p>
<ol start="24">
<li>The figure below shows a hydraulic lift system. The radius of the small piston is 3 cm while that of the larger piston is 9cm. a force of 90Nis applied to the</li>
</ol>
<p>smaller piston.</p>
<table width="100%">
<tbody>
<tr>
<td><strong>90N</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>LOAD </strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>r</strong><strong> = 9cm</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong> r</strong><strong> = 3cm</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>Determine the:</p>
<p>(i) Maximum load that can be lifted. (3mk)</p>
<p>(ii) Efficiency of the system. (3mk)</p>
<p><strong> </strong></p>
<p><strong><u>THE PUMP</u></strong></p>
<ol>
<li>An electric pump can raise water from a lower-level reservoir to the high level reservoir at the rate of <strong>0 x 10<sup>5</sup></strong> <strong>kg per hour</strong>. The vertical height of the water is raised <strong>360m</strong>. If the rate of energy loss in form of heat is<strong> 200</strong> <strong>kW</strong>, determine the efficiency of the pump.</li>
</ol>
<p> ;</p>
<ol start="2">
<li>When an electric pump whose efficiency is <strong>70%</strong> raises water to a height of <strong>15m</strong>, water is delivered at the rate of <strong>350</strong> litres per minute.</li>
</ol>
<p>(i) What is the power rating of the pump?</p>
<p>(ii) What is the energy lost by the pump per second?</p>
<p> ;</p>
<ol start="3">
<li>A pump is used to spray water from a pool to form fountain.</li>
</ol>
<p><strong> (i) </strong> Determine the minimum power of the pump if it ejects <strong>50 litres</strong> of water per minutes and spray reached a height of <strong>5 m</strong>. (3mk)</p>
<p><strong> (ii) </strong> Give a reason why water often returning to the pool has a different temperature from that which left the pump. (2mk)</p>
<p> ;</p>
<p> ;</p>
<p><strong><u>GRAPH</u></strong></p>
<ol>
<li>In an experiment using a pulley system, results collected were used to plot the graph below. From the graph, determine the velocity ratio of the system.3mk</li>
</ol>
<table width="100%">
<tbody>
<tr>
<td><strong>0</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.2</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>EFFICINCY (</strong><strong>%</strong><strong>)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.7</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.4</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>30</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>20</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>40</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>60</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>80</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>100</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>50</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>70</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>10</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>90</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.5</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.3</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.1</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>0.8</strong></td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td width="101"></td>
</tr>
<tr>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>iii) Explain the shape of the graph. 1mk</p>
<p> ;</p>
<ol start="2">
<li>The pulley system in <strong>(a)</strong> above was used to find the relation between load and minimum effort required to raise the loads. The results obtained are shown below.</li>
</ol>
<table>
<tbody>
<tr>
<td width="128"><strong>Load (N)</strong></td>
<td width="70"><strong>1.0</strong></td>
<td width="121"><strong>2.0</strong></td>
<td width="106"><strong>3.0</strong></td>
<td width="68"><strong>4.0</strong></td>
<td width="98"><strong>5.0</strong></td>
<td width="98"><strong>6.0</strong></td>
</tr>
<tr>
<td width="128"><strong>Effort(N)</strong></td>
<td width="70"><strong>1.0</strong></td>
<td width="121"><strong>1.5</strong></td>
<td width="106"><strong>2.0</strong></td>
<td width="68"><strong>2.5</strong></td>
<td width="98"><strong>3.0</strong></td>
<td width="98"><strong>3.5</strong></td>
</tr>
<tr>
<td width="128"><strong>Mechanical advantage</strong></td>
<td width="70"><strong> </strong></td>
<td width="121"><strong>1.33</strong></td>
<td width="106"><strong> </strong></td>
<td width="68"><strong> </strong></td>
<td width="98"><strong>1.67</strong></td>
<td width="98"><strong>1.71</strong></td>
</tr>
<tr>
<td width="128"><strong>Efficiency %</strong></td>
<td width="70"><strong> </strong></td>
<td width="121"><strong>66.5</strong></td>
<td width="106"><strong> </strong></td>
<td width="68"><strong> </strong></td>
<td width="98"><strong>83.5</strong></td>
<td width="98"><strong>85.5</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p>Complete the table above (2mk)</p>
<ul>
<li>Plot a graph of efficiency ( y- axis) against load on the graph paper</li>
</ul>
<p>provided on the next page. (4mk)</p>
<ul>
<li>Estimate the maximum useful efficiency from the graph for large load.</li>
</ul>
<p>(1mk)</p>
<ul>
<li>State one reason for pulley system being less than <strong>100%</strong></li>
</ul>
<p>(1mk</p>
<ol start="3">
<li>In an efficiency test carried out on this machine, the following results</li>
</ol>
<p>were obtained.</p>
<table width="782">
<tbody>
<tr>
<td width="364"><strong>Load in Newton’s</strong></td>
<td width="91"><strong>20</strong></td>
<td width="91"><strong>80</strong></td>
<td width="76"><strong>140</strong></td>
<td width="76"><strong>220</strong></td>
<td width="84"><strong>300</strong></td>
</tr>
<tr>
<td width="364"><strong>Effort in Newton’s</strong></td>
<td width="91"><strong>10</strong></td>
<td width="91"><strong>25</strong></td>
<td width="76"><strong>40</strong></td>
<td width="76"><strong>60</strong></td>
<td width="84"><strong>80</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<ol>
<li>i) Plot a graph showing how the efficiency varies with the load on the graph</li>
</ol>
<p>paper provided. (7mk)</p>
<ol>
<li>ii) Comment on the variation of the efficiency with the load and give a reason</li>
</ol>
<p>for this variation. (1mk)</p>
<ol start="4">
<li>The table below shows the results obtained in an experiment to determine the performance of a single string pulley system with a velocity ratio of five.</li>
</ol>
<table>
<tbody>
<tr>
<td width="150"><strong>Load (N)</strong></td>
<td width="60"><strong>50</strong></td>
<td width="66"><strong>100</strong></td>
<td width="80"><strong>200</strong></td>
<td width="80"><strong>300</strong></td>
<td width="80"><strong>400</strong></td>
<td width="80"><strong>500</strong></td>
<td width="80"><strong>600</strong></td>
</tr>
<tr>
<td width="150"><strong>Effort (N)</strong></td>
<td width="60"><strong>30</strong></td>
<td width="66"><strong>45</strong></td>
<td width="80"><strong>65</strong></td>
<td width="80"><strong>85</strong></td>
<td width="80"><strong>105</strong></td>
<td width="80"><strong>125</strong></td>
<td width="80"><strong>145</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p><strong> (i)</strong> Plot a graph of load against effort (5mk)</p>
<p><strong>(ii)</strong> Use your graph to determine the mechanical advantage and</p>
<p>efficiency corresponding to a load of <strong>450 N</strong> (4mk</p>
<p> ;</p>
<p> ;</p>
<p><strong><u>SCHEEM</u></strong></p>
<p>State <strong>one</strong> advantage of hydraulic brakes over mechanical brakes. (1mk)</p>
<p><strong><em>Hydraulic brakes are more efficient hence require less effort than mechanical ones. </em></strong><strong><em>P</em></strong><strong><em> (1mk)</em></strong></p>
<p> ;</p>
<p>A load was raised using the system shown below as in figure (a). The system was then modified as shown in figure (b) and used to raise the same load.</p>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></p>
<p> ;</td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>(b)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>E</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>(a)</strong></td>
</tr>
</tbody>
</table>
<table width="100%">
<tbody>
<tr>
<td><strong>L</strong></td>
</tr>
</tbody>
</table>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p> ;</p>
<p>(i) The block and tackle system in <strong>(b)</strong> above was used to lift a load of <strong>80kg</strong>. Given that its efficiency is <strong>80%.</strong> Calculate the effort applied to lift the load. 4mk)</p>
<p>(ii) Explain the change in efficiency.</p>
<p><strong><em>Since the velocity ratio has increased, the efficiency has also increased. </em></strong><strong><em>P</em></strong><strong><em><sub>1</sub></em></strong></p>

