 State the law of conservation of energy. (1mk)
 Define the terms and state the I units of each.
(i) Work (2mk)
(ii) Energy (2mk)
(iii) Power (2mk)
(iv) Machine (2mk)
 Name a device that is used to convert;
 Sound to electrical energy
 Electrical energy to kinetic energy.
 Electrical energy to sound energy
 Electrical energy to light energy
 Solar energy to electricity energy
KINETIC AND POTENTIAL ENERGY
 Differentiate kinetic energy from potential energy.(1mk)
 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)
 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.
 State the energy transformations that occur when a ball is kicked vertically (1mk)
 A bullet of mass 20g traveling at 400ms^{1} is stopped by a concrete wall. Calculate the amount of energy transferred to the wall. (2mks)
 A stone of mass 24kg is dropped down from a building 50m Calculate the KE gained as it hits the ground.
 A ball is dropped vertically from the top of a cliff. If it attains a velocity of 20m/s as it hits the ground, find the height of the cliff.
 A 50 tonne rocket takes off vertically and attains a velocity of 800m/s at an altitude of 20km. calculate at this point;
 Its KE
 Its PE
 A metal ball suspended vertically with a wire is displaced through an angle as shown in the diagram below. The body is released from A and swings back to ‘B’. Given that the maximum velocity at the lowest point B is 5 m/s. Find the height h from which the ball is released.
B 
A 
4m 
h 
 The figure below shows a swinging pendulum.
C 
B 
A 
State the energy conservation taking place as the pendulum moves from A to B and B to C (2mk)
 The figure shows a simple pendulum of length 80cm. The pendulum bob whose mass is 50g oscillates between points A and B, through its rest position A and C are both 80cm higher than B.
C 
B 
A 
h=80cm 
 a) i) indicate with an arrow, on the path ACB, the direction of the greatest velocity of the bob as it moves from A to B. 1mk
 ii) State the form of energy possessed by the pendulum bob at point A. 1mk
 b) Determine:
 i) The velocity of the bob at point C, 3mk
 ii) The tension in the string as the bob passes point C. 3mk
Take acceleration due to gravity g=10m/s^{2})
 The figure below shows a 200g mass placed on a frictionless surface and attached to spring.
Spring

200g 
The spring is compressed and released. Given that the elastic potential energy of the compressed spring is 2.7 x 10^{2 }J, determine the maximum speed with which the block moves after it is released. (4mk)
 A body is released from a height h. sketch a graph of potential energy against kinetic energy as the body falls to the ground. (2mk)
P.E (J) 
12 
2 
4 
6 
8 
10 
2 
4 
6 
8 
Height (m) 
10 
 The figure below shows how the Potential Energy (P.E) of a ball thrown vertically upwards. On the same axes, plot a graph of kinetic energy of the ball.
 A load of 100N is raised 20m in 50s. Calculate;
 The gain in potential energy
 The power developed
 A body of mass m initially at rest is acted on by a force F for a time t, as a result its velocity changes to a final value v.
 a) Use this information to show that the gain is kinetic energy E= ½ mv^{2}
 b) Calculate the kinetic energy of a car of mass 1000 kg traveling at 36km/h
 A man uses a bow to fire an arrow of mass 2kg vertically upwards into the air. He stretches the bow by 0.15m with a maximum force of 100N
(i) Calculate the energy transferred to the arrow (3mks)
(ii) Calculate the speed with which the arrow leaves the bow assuming all energy is transferred to the arrow (2mks)
(iii) Determine the greatest height reached by the arrow before it begins to fall (3mks)
(iv) Calculate the time the arrow will remain in the air (3mks)
 A body has 16 Joules of kinetic energy. What would be its kinetic energy if its velocity was double?
 The initial velocity of a body of mass 50kg is 10ms^{–}^{1}. A constant resultant force of 15N is then applied. How long will it take before the kinetic energy doubles (4mks)
 A boy lifts 80 sand bags from the floor of a room onto a shelf 6m high in 100s.
(i) Find the useful work done in lifting the sand bags. 2mks
(ii) State the total potential energy developed when all the sand bags are
on the shelf 1mk
(iii) Determine the boy’s useful power output. 2mks
(iv) One sand bag fell from the shelf. Explain what happens to its kinetic
energy when it hits the ground.
 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^{3}m^{2} and the water leaves the end of the hosepipe at a speed of 5m/s. Calculate the power of the pump. (density of water = 1000Kg) (125Watts)
 A load of 60kg moves from rest position to a point E along a frictionless path ABCDE
2 
4 
6 
8 
10 
Height (m) 
D 
B 
A 
C 
E 
F 
12 
(a) Calculate the
(i) Maximum Kinetic energy of the load. (3mks)
(ii) Maximum velocity (3mks)
(iii) Velocity at C (3mks)
 The graph below was obtained in an experiment to investigate the stretching of materials.
8 
0 
2 
4 
12 
6 
10 
0 
80 
160 
240 
1200 
40 
200 
Extension (cm) (volts) 
(i) Determine the constant of the spring used. (2mk)
(ii) Determine the elastic limit of the material. (1mk)
(iii)Determine the work done on the spring by a force of 120N.(3 mk)
WORK
 A girl carries 20 litres of water in a jerry can on her head and walk fro 200m on a horizontal level ground. Explain why the girl does no work (assume air resistance is negligible).
 A certain machine uses an effort of 400N to raise a load of 600N. If the efficiency of the machine is 75% determine its velocity ratio. (3mk)
 A force of 120N stretches a spring by 15cm. How much work is done in stretching this spring by 20cm?
 A crane lifts a load of 2000kg through a vertical distance of 0m in 6 seconds. Determine the;
 Work done (2mk)
 Power developed by the crane (2mk)
iii) Efficiency of the crane given that it is operated by an electric
motor rated 12.5 kW
 A crane lifts a load of 500 kg through a vertical distance of 2m in 8 s determine
 Work done by the crane (2mk)
 Power developed by the crane (2mk)
 Efficiency of the crane given that its operated by all electric motor rated 2kW (2mk)
 State two effects which contribute to the efficiency being less than 100% (2mk)
 A lady of mass 80kg walks up a flight of 10 stairs each 20 cm high in 5 s. Determine the power she develops. (3mk)
 210 litres of water is pumped through a height of 20m in 2 minutes. Determine the power rating of the of the pump if it is 75% efficient (3mks)
 The energy wasted in using a machine is 600J. If the machine is 70% Calculate the volume of water pumped by the machine through a height of 15m. (3mks)
 A force of 6N extends a spring by 2m. Calculate the work done in extending the spring (3mk)
 A bullet of mass 8 g traveling at 400 m/s is stopped by a concrete wall. Calculate the amount of heat energy transferred to the wall. (2mk)
2000 
4000 
6000 
2000 
4000 
6000 
Force (N) 
10 
0 
20 
30 
40 
50 
60 
70 
80 
Distance (m) 
A 
B 
C 
D 
E 
F 
G 
H 
I 
 The fig. below shows a force – distance graph for a car being on a horizontal ground
 a) Calculate the total work done
 b) If the velocity just before reaching point D is 6m/s, calculate the power developed by the agent providing the force at this point.
 The figure below shows a body being acted upon by a varying force over a
distance of 5m.
Force (N) 
Distance (m) 
20 
10 
2 
4 
1 
10 
3 
5 
20 
30 
 The figure below shows a force – distance graph for a motorbike moving
with a varying force for 20seconds over a distance of 50m.
100 
200 
300 
100 
200 
300 
0 
10 
20 
30 
40 
Distance (m) 
50 
Calculate
 The average velocity
 The total work done
 The power developed by the motor bike
 Figure below shows a force distance graph for a car being moved on a
horizontal ground
Distance (m) 
A 
F 
10 
1500 
20 
30 
40 
500 
1000 
500 
1000 
(i) Calculate total work done when the car moved from A to F.
(ii) Determine the power of the car if it takes 0.6 seconds to move it from A to F.
 Figure below shows a force distance graph for a car being moved on a horizontal ground
50 
60 
L 
Distance (m) 
K 
F 
10 
1200 
20 
30 
40 
400 
800 
400 
800 
(i) Calculate total work done when the car moved from K to L. (4mk
(ii) Determine the power of the car if it takes 8s to move it from K to L.
(2mk
 Define the following terms as used in machines
 Mechanical advantage (1mk)
 Efficiency (1mk)
 Velocity ratio (1mk)
 State the factor that affects / determines each of the following in a machine.
(i) Mechanical advantage (M.A) (1mk)
(ii) Velocity Ratio (V.R) (1mk)
 State two reasons why the efficiency of a machine is always less than 100% (2mk)
 In a wheel and axle system, state the advantage of having a large wheel diameter compared to the diameter for a frictionless system. (1mk)
LEVERS
 Figure shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point P. A force of 200N is applied at R.
P 
100 cm 
50 cm 
Liquid 
Area= 180cm^{2} 
A Bale 
200 N 
A =50 cm^{2} 
R 
(i) Calculate the force F exerted by small piston on the liquid. (2mks)
(ii) Find the weight of the Bale supported by the large piston (2mks)
 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)
B 
C 
A 
 Figure shows a lever
5m 
20m 
60N 
Determine
 The effort applied
 The VR.
 The MA.
 The efficiency.
 Suggest two ways in which the mechanical advantage could be increas
 The figure below shows a wheel of mass 10kg and radius 1 m being pulled by a boy against a step 4 m high. What force is just sufficient to turn the wheel so that it will rise over the step
0.4m 
Boy 
 Figure shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point P. A force of 100N is applied at R.
Liquid 
10 cm 
5 cm 
100 N 
P Fixed

R 
Calculate
 (i) The force F exerted by small piston on the liquid.
 (ii) The VR of the lever.
 (iii) The MA of the lever.
 (iv) The efficiency of the lever.
 The figure shows a device for closing a steam outlet. The area of the piston is
4.0 x 10^{4}m^{2} and the pressure of the steam in the boiler is 2.0 x 10^{5}Nm‑^{2}.
Cork 
15m 
Pivot 
45cm 
Steam pressure from boiler

W 
Determine
 (i) The weight W the weight W that will just hold the bar in the horizontal position shown.
 (ii)
Slave piston 
 The VR of the lever.
 (iii) The MA of the lever.
 (iv) The efficiency of the lever.
 State one advantage of hydraulic brakes over mechanical brakes. (1mk)
WHEEL AND AXLE
 The machine wheel and axle has a lot of application in real life. Name any two practical examples of such machine. (2mks)
 A machine consists of a wheel of radius 40cm and axle of radius 10cm. Determine its efficiency when used to lift a load of 300N using an effort of 100N (3mk)
 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^{2}
(i) The velocity ratios of the machine (1mk)
(ii) The mechanical advantage of the machine (1mk)
R 
r 
W 
F 
Wheel 
Axle 
 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 R and of the small wheel r as shown
(i) Show that the velocity ratio (VR) of this machine is given by R/r. (2mks)
(ii) Given that r =7cm, R = 10.5cm, determine the effort required to raise a
load of 40N if the efficiency of the machine is 75% (3mks)
Load 200N 
Effort=40N 
Wheel 
Axle 
 The figure below shows the cross – section of a wheel and axle of radius 3 cm and 1cm respectively used to lift a load. Use it to answer the questions that follow.
Calculate:`
(i) The mechanical advantage (M.A) of the system. (2mks)
(ii) The velocity ratio (V.R) of the system. (2mks)
(iii) The efficiency of the machine. (2mks)
 A machine consisting of a wheel of radius 50cm and an axle of radius 10cm is used to lift a load of if the efficiency of the system is 75%. Calculate the effort needed (3mk)
 the figure below shows a windless. An effort is applied on the handle which is turned on a radius of 60 cm. As the handle turns, a rope is wound around the drum of diameter 24 cm, thus raising a bucket of water out of the well
Handle 
24cm 
60cm 
 a) If an effort of 20N is needed to lift a bucket full of water of mass 8kg, Calculate:
(i) the energy gained by the mass when the drum turns through one
revolution (3mks)
(ii) The work done by the effort during this revolution (3mks)
 b) Suggest a reason why the two quantities in a(i) and (ii) are not equal (1mk)
 c) Calculate:
(i) the velocity ratio of the machine (1mk)
(ii) the efficiency of the windlass (2mks)
 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)
INCLINED PLANES
 Figure below shows an inclined plane.
h 
ϴ 
Load 
Length L 
Show that the velocity ratio (3mks)
 A person pulls a box of weight 750N up an inclined plane 6m long using a force of 500N as shown in figure below.
h 
500N 
30^{0} 
750N 
6m 
 (i) The VR
 (ii) The height h
 (iii) The work done by effort.
 (iv) The useful work done.
 (v) The efficiency of the plane.
 A block of mass 50kg is pulled up an inclined plane by a force of 200N until it gets to the top as shown below
30Kg 
2m 
30^{0} 
200N 
200N

(i) Find the work done by the force in moving the block up the incline. (3mk)
(ii) Find the work done on the block against gravity. (2mk)
 A man uses an inclined plane to lift a 50kg mass thru a vertical height of 4m.if the plane is 5% efficient and makes an angle of 30^{0} with the horizontal, calculate;
 The VR
 The effort needed
 The work output
 The work input.
 The work done against friction.
 An inclined plane of length 12m and vertical height 3m is used to lift a load L using an effort of If the plane has an efficiency of 80%. Find the load L.
 A person pulls a box of mass 30kg up an inclined plane 5m long at a constant speed as shown in figure below.
F 
30^{0} 
30kg 
5m 
If the friction force between the plane and the block is 100N, Find:
 The effort that must be exerted on the box for it to move up the incline at a constant speed
 The gain in potential energy of the box while at the top of the incline
 The work done by the person in pulling the box
 The figure below shows a trolley of weight 20N pulled by a force of 4N from the bottom to the top of an inclined plane at a uniform speed.
Weight

h =5 m 
D = 40 m 
Effort E 
 (i) State the value of the force acting downwards along the inclined plan (1mk)
 ii) Explain how the value in part (a) (i) is obtained (2mk)
 b) For the system, determine the:
 i) Mechanical advantage: (2mk)
 ii) Velocity ratio; (2mk)
iii) Efficiency. (2mk)
 The following diagram shows a load of 50N being raised by pulling it along an Inclined plane of length 0m.
h =0.5 
2m 
22N 
Determine
 i) The work done by the 22 N force
 ii) The work done against the load
iii) The efficiency of the system
 iv) Why is the efficiency less than 100%
 The figure below shows an inclined plane placed at 30^{0} to the horizontal so that it can be used to raise a load through a height ‘h’. The efficiency is 96%.
Effort 
h 
30^{0} 
Load 
(i) Determine Velocity Ratio of the machine (2mks)
(ii) the efforts needed to move a load of 800N along the plane at a constant
velocity. (2mks)
(b) (i) Draw a block and tackle pulley system of velocity ratio 4. In your
diagram, Show the effort and load position. (2mks)
(ii) If the pulley system raises a load of 100N at steady rate. Calculate
the efforts required to raise the load if it is 80% efficient. (2mk)
 A girl of mass 50 kg climbs up a ramp 200m long inclined at an angle 10^{0} to the horizontal. Calculate the minimum work done by the girl. (3mk)
 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 30^{0} to the ground.
30^{0} 
Log 
Wooden plank 
(i) Indicate with an arrow on the diagram, the direction of the effort and the
load. (2mks)
(ii) Calculate the velocity ratio of the set up. (2mks)
(iii) Calculate the mechanical advantage of the set up if its efficiency is 65%. (2mks)
THE SCREW
 A screw advances 1mm when the screw is turned through two What is the pitch of the screw?
 The figure below shows a crosssection of a handle of a screw jack 70 cm long and pitch of the screw is 8 cm.
0.8cm 
70 cm 
Handle 
Load 
Base 
Given that the efficiency is 60%, calculate:
 i) The velocity ratio of the system. (2mk)
 ii) If an effort of 50N is applied calculate the load that can be lifted. (3mk)
0.5cm 
25cm 
 The handle of screw jack shown below is 25cm long and the pitch of the screw is 5cm.
(i) What is the velocity ratio of the system. (3mk)
(ii) What force must be applied at the end of the handle when lifting a load of 3300N if the efficiency of the jack is 70%. (3mk)
 An effort of 40N is applied to the car jack whose hand moves through a circle of radius 5cm. The pitch of the screw is 2.5mm. Determine the efficiency of the jack if the mass of the car is 252kg
THE GEARS
 The fore gear of bicycle has 48 teeth while the rear one has 24 teeth. Find its VR.
 Calculate the VR of the gears below
32 teeth 
16 teeth 
EFFORT 
LOAD 
 Calculate the combined VR of the gears below.
LOAD 
EFFORT 
 Figure shows part of a bicycle
32 teeth 
16 teeth 
Chain 
20cm 
50cm 
Determine;
 i) The velocity ratio (4mk)
 ii) Efficiency of the bicycle if its mechanical advantage is 15 (3mk)
THE BELT AND THE GEARS
 Calculate the VR of the pulley belt below
Effort

Load 
R=50cm 
r=20cm 
 In the figure below, the effort wheel has 32 teeth and a radius of 36cm while the load wheel has 16 teeth and 9cm. calculate the V R of the machine.
Effort

Load 
 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.
For the cogwheel system determine
(i) Velocity ratio. (2mks)
(ii) The efficiency. (3mks)
 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.
For the cogwheel system determine
(i) Velocity ratio. (2mk)
(ii) The efficiency. (3mk)
PULLEYS
 Draw a block and tackle pulley system of velocity ratio 4. In your diagram, Show the effort and load position. If the pulley system raises a load of 100N at steady rate. Calculate the efforts required to raise the load if it is 80% (4mks)
 A mechanic uses a pulley system with a velocity ratio of 6 to raise an engine, of weight 2800N through a vertical distance of 5m. The mechanic pulls with an effort of 500N. Calculate
 The effort distance. (2mk)
 The work done by the effort (mechanic) (2mk)
 The useful work done by the pulley machine. (2mk)
 The mechanical advantage of the machine. (2mk)
 The efficiency of the machine. (2mk)
 State two reasons why the efficiency of a machine is always less than 100% (2mk)
 Draw a pulley system of velocity ratio 5 and having a total of 4 pulleys and explain why its efficiency reduces as the size of the load reduces.(3mk)
 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 VR of 3
 The figure below shows a single fixed pulley being used to lift a load.
Effort 
Load 
State;
 The mechanical advantage of the pulley (1mk
 The velocity ratio of the pulley (1mk)
 A man used the pulley system shown below to raise a 3kg load through a height of 5m using an effort of 25N
3kg

E 
(a) Through what distance does the end E of the rope move (2mk)
(b) Given that the pulley system is frictionless and that the efficiency is 75 %, find
(i) The mechanical advantage of the system (3mk)
(ii) The mass of the lower pulley (2mk)
Pulley 2

Pulley 1

Load 
Effort =500 N 
 The figure below shows a pulley system used to raise a load by applying an effort of 500N
State the:
 Velocity ratio of the system. (1mk)
 Purpose of pulley 2. (1mk)
 Given that the machine has an efficiency of 80%, determine the maximum load that can be raised. (3mk)
 A pulley system has two pulleys on the lower block and one pulley on the upper block. In order to raise the load of 6N, an effort of 2N is applied.
 Draw a sketch to show the pulley system. (3mk)
 Calculate the efficiency of the pulley system (3mk)
 If the lower block weighs 4N what friction force opposes the motion? (3mk)
0 
EFFFICIENCY

LOAD (N) 
100 % 
 Figure shows the relationship between the efficiency and the load for a pulley system
Explain the shape of the curve (1mk
10kg

80N 
 Using the pulley system shown, a mass of 10kg is raised 2m by an effort of 80N
(i) How much potential energy does the load gain? (1mk)
(ii) How far does the effort end move in order to raise the load by 2m (1mk)
(iii) How much work is done by the effort. (1mk)
(iv) What is the efficiency of these pulleys? (2mks)
(v) If all the wasted energy is used to lift the bottom pulley, how much does
the pulley weigh? (3mks)
 Figure shows a pulley system
40kg

150N 
(i) What is the velocity ratio of the system (1mk)
(ii) Calculate the efficiency of the system (3mks)
(iii) Give two reasons why efficiency is not 100% (2mks)
 A block and tackle is made up of the two pulley wheels on top and one pulley wheel at the bottom as shown below.
 Draw the string which passes over the wheels and indicate where the
effort and load is applied. (2mk)
 What is the velocity ratio of the machine? (1mk)
 A load of 600N is lifted by an effort of 250N. Determine
 The mechanical advantage of the system. (1mk)
 The efficiency of the system. (2mk)
 State two reasons why the efficiency of a machine is always less than 100% (2mk)
 Figure shows a block and tackle pulley system lifting a load of 900N
Effort 
900N 
 Determine the velocity ratio of the machine. (1mk)
 If an effort of 225N is required to lift the load using the machines,
determine the efficiency of the pulley system. (3mk)
 In the space provided below, sketch a graph of efficiency against load for
the system (2mks)
 The Figure below shows a machine being used to raise a load.
Load 
Effort 
 a) Determine the velocity ratio (V.R) of the machine. (1mk)
(b) If a load of 800N is raised by applying an effort of 272N, determine the efficiency of the machine. (2mk)
 A block and tackle is made up of three pulley wheels on top and two pulley wheels at the bottom as shown below.
Load 
(a) Complete the diagram by drawing the chain which passes over the wheels
and indicate where the effort is applied (2mk)
(b) What is the velocity ratio of the machine (1mk)
(c) A load of 1120N is lifted by an effort of 250N
Determine
(i) The mechanical advantage (M.A) of the system (1mk)
(ii) The efficiency, E, of the system (2mk)
(d) How much percentage energy is wasted in the above system (1mk)
0 
EFFFICIENCY

LOAD (N) 
100 % 
(e) Using the axes given below, sketch a graph of efficiency, E, against load (2mk
Draw a block and tackle system with a velocity ratio of 5. (2mk)
 The pulley system in the diagram has two wheels in each block.
L 
 a) Complete the diagram to show the string as the pulley is being used to lift the load L. (1 mk)
 b) The block and tackle pulley system is used to investigate relationship between mechanical advantage and efficiency.
(i) State the measurements to be taken in this investigation. (2mk)
50N 
E=50N 
 The figure below shows a pulley used to raise a load of 50N.
 a) What is the velocity ratio of the system? (1mk
 b) Determine the mechanical advantage. (1mk)
 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.
L

E 
(b) 
E 
(a) 
L 
(i) The block and tackle system in (b) above was used to lift a load of 80kg. Given that its efficiency is 80%. Calculate the effort applied to lift the load. 4mk)
(ii) Explain the change in efficiency.
 Figure shows a pulley system being used to raise a load.
Load

E 
This pulley system has an efficiency of 75%.
(i) Determine the velocity ratio of the system. (1mk)
(ii) Calculate the mechanical advantage of the pulley system. (2mks)
(iii) What effort is required to raise a load of 240kg? (2mks)
(iv) Calculate the work done by a person using this machine in raising a
load of 120kg through a vertical distance of 2.5m (3mk)
(v) Give two reasons to explain why the efficiency of a machine cannot
be 100%. (2mk)
 In the arrangement shown, the mass of 30 kg hanging on the pulley helps to raise the unknown load. The person pulling up the other string finds that he had to do 800 Joules of work in order to raise the load 4m.
Pull up 
30kg 
Unknown mass 
 a) Calculate the value of the unknown mass.
 b) State the assumptions you make in calculating the value (a) above
 Using a pulley system, a girl lifts a load of 1800N using an effort of 400N. If the system is 65% efficient, determine the velocity ratio of the system.
 Sketch a labeled diagram to show how an arrangement of a single pulley may be used to provide a mechanical advantage of 2.
HYDRAULIC MACHINES
 A hydraulic brake system of a car has a master piston of radius of 7cm while that of the slave piston is 21 cm.
(i) Find the velocity ratio of the system. (1mk)
(ii) If a force of 1800 N is experienced at the slave piston find;
 The force exerted at the master piston
 The efficiency of the system
 The diagram below shows the principle of the hydraulic car jack that has a master piston of radius 7cm and slave piston of radius 21 cm.
Oil 
Slave piston 
300N

1800N 
Master piston 
(i) Determine the velocity ratio of the hydraulic jack
(ii) If the small piston moves down a distance of 7.2cm, determine how far upwards the larger piston moves.
(iii) Determine;
 The effort exerted at the master piston
 The efficiency of the system
 The figure below shows a hydraulic lift used to lift a load L. The effort applied is 150N at the end of a lever 36cm long and pivoted at the other end and, plunger is 6cm from the pivot. The area of the plunger piston C is 4cm^{2} and that of the load piston D is 400cm^{2}.
30 cm 
Plunger

C = 4cm^{2} 
Liquid 
6 cm 
150 N 
P Fixed

R 
D = 400cm^{2} 
L 
Calculate
 (i) TheR of the lift
 (ii) The effort exerted at the effort piston
 (iii) The A of the system
 (iv) The efficiency of the system
 The figure below shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point P. A force of 400N is applied at R.
P 
100 cm 
50 cm 
Liquid 
Area= 360cm^{2} 
A Bale 
400 N 
A =30cm^{2} 
R 
Calculate
(i) The effort exerted at the smaller piston.
(ii) The V.R of the lift
(iii) The M.A of the system
(iii) The efficiency of the system
(iv) What is the pressure exerted at the larger piston? (3mk)
 The diagram below represents a motor car hydraulic braking system
Brake pedal 
Master piston 
Slave piston 
80cm^{2} 
15cm 
5 cm 
16cm^{2} 
(i) State the property of the liquid used as brake fluid
(ii) Find the velocity ratio of the system.
(iii) An effort of 120N is applied on the brake pedal, calculate
(a) The force applied to the master piston
(b) The force experienced at the slave piston
(c) The efficiency of the system
R 
A =40 cm^{2} 
P 
Liquid 
Area= 320cm^{2} 
A Bale 
30 cm 
200N 
20 cm 
 The figure below shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point P. A force of 200N is applied at R.
(i) State the property of the liquid used as brake fluid (2mk)
(ii) Find the velocity ratio of the whole system. (2mk)
(iii) Calculate the
 Force exerted on the smaller piston. (2mk)
 If the smaller piston moves down by 12m, by what height does the
larger piston raise the load. (3mk)
 The diagram below represents a motor car hydraulic braking system
Pivot 
Brake pedal 
Master piston 
Slave piston 
80 cm^{2} 
12cm 
2 cm 
60 cm^{2} 
(i) State the property of the liquid used as brake fluid (1mk)
(ii) Find the velocity ratio of the system. (1mk)
(iii) An effort of 300N is applied on the brake pedal, calculate
(a) The force applied to the master piston (2mk)
(b) The force experienced at the slave piston (2mk)
(c) The efficiency of the system (2mk)
 The figure below shows a hydraulic lift used to lift a load.
200N 
2 cm^{2} 
P 
80cm^{2} 
Hinge 
50 cm 
LOAD 
20cm 
Q 
10cm 
Calculate
 The effort exerted at the smaller piston Q (2mk)
 Calculate the load that can be supported by the above machine at P (2mk)
 TheR of the system (3mk)
 The A of the system (3mk)
 The efficiency of the system (2mk)
 The figure below shows an effort of 100N being on a single moving pulley to exert a pressure on a gas in a cylinder.
F = 100N 
1m

T 
3m

Piston 
String 
Gas 
The area of the piston is 10cm^{2} and the volume of the gas is 20cm^{3}.The
weight of the pulley, beam and frictional forces at the moveable part are taken
zero. If the beam is equilibrium:
 i) Calculate the force acting on the piston. (2mk) (300N)
 ii) Calculate the pressure exerted on the gas by the piston. (2mk)
(iii) If the effort applied on the pulley is 200N, by what distance has the pivot
been moved if the pressure remains constant. (2mk)
( 300x (1+x) = 200 x (3x))= 0.6m
 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 5×10^{7 }Pa and the cross section area of the new piston is 5cm^{2}. What is the amount of force acting on the piston? (2mk) (= 7.5 x 10^{3}N)
 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
smaller piston.
90N 
LOAD 
r = 9cm 
r = 3cm 
Determine the:
(i) Maximum load that can be lifted. (3mk)
(ii) Efficiency of the system. (3mk)
THE PUMP
 An electric pump can raise water from a lowerlevel reservoir to the high level reservoir at the rate of 0 x 10^{5} kg per hour. The vertical height of the water is raised 360m. If the rate of energy loss in form of heat is 200 kW, determine the efficiency of the pump.
 When an electric pump whose efficiency is 70% raises water to a height of 15m, water is delivered at the rate of 350 litres per minute.
(i) What is the power rating of the pump?
(ii) What is the energy lost by the pump per second?
 A pump is used to spray water from a pool to form fountain.
(i) Determine the minimum power of the pump if it ejects 50 litres of water per minutes and spray reached a height of 5 m. (3mk)
(ii) Give a reason why water often returning to the pool has a different temperature from that which left the pump. (2mk)
GRAPH
 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
0 
0.2 
EFFICINCY (%) 
0.7 
0.4 
30 
20 
40 
60 
80 
100 
50 
70 
10 
90 
0.5 
0.3 
0.1 
0.8 
iii) Explain the shape of the graph. 1mk
 The pulley system in (a) above was used to find the relation between load and minimum effort required to raise the loads. The results obtained are shown below.
Load (N)  1.0  2.0  3.0  4.0  5.0  6.0 
Effort(N)  1.0  1.5  2.0  2.5  3.0  3.5 
Mechanical advantage  1.33  1.67  1.71  
Efficiency %  66.5  83.5  85.5 
Complete the table above (2mk)
 Plot a graph of efficiency ( y axis) against load on the graph paper
provided on the next page. (4mk)
 Estimate the maximum useful efficiency from the graph for large load.
(1mk)
 State one reason for pulley system being less than 100%
(1mk
 In an efficiency test carried out on this machine, the following results
were obtained.
Load in Newton’s  20  80  140  220  300 
Effort in Newton’s  10  25  40  60  80 
 i) Plot a graph showing how the efficiency varies with the load on the graph
paper provided. (7mk)
 ii) Comment on the variation of the efficiency with the load and give a reason
for this variation. (1mk)
 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.
Load (N)  50  100  200  300  400  500  600 
Effort (N)  30  45  65  85  105  125  145 
(i) Plot a graph of load against effort (5mk)
(ii) Use your graph to determine the mechanical advantage and
efficiency corresponding to a load of 450 N (4mk
SCHEEM
State one advantage of hydraulic brakes over mechanical brakes. (1mk)
Hydraulic brakes are more efficient hence require less effort than mechanical ones. P (1mk)
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.
L

E 
(b) 
E 
(a) 
L 
(i) The block and tackle system in (b) above was used to lift a load of 80kg. Given that its efficiency is 80%. Calculate the effort applied to lift the load. 4mk)
(ii) Explain the change in efficiency.
Since the velocity ratio has increased, the efficiency has also increased. P_{1}