1. State the law of conservation of energy.                                                                                      (1mk)

2. Define the terms and state the I units of each.

         (i)    Work                                                                               (2mk)

         (ii)   Energy                                                                               (2mk)

         (iii)  Power                                                                             (2mk)

         (iv)   Machine                                                                          (2mk)

3. 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

1. Differentiate kinetic energy from potential energy.(1mk)

2. 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)

3. 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.

4. State the energy transformations that occur when a ball is kicked vertically                                                                             (1mk)
5. 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)

6. A stone of mass 24kg is dropped down from a building 50m Calculate the KE gained as it hits the ground.

7. 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.

8. 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

9. 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.

10. The figure below shows a swinging pendulum.

State the energy conservation taking place as the pendulum moves from A to B and B to C                                                                      (2mk)

11. 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.

1. 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
2. ii) State the form of energy possessed by the pendulum bob at point A. 1mk

1. b) Determine:
2. i) The velocity of the bob at point C, 3mk
3. ii) The tension in the string as the bob passes point C. 3mk

Take acceleration due to gravity g=10m/s²)

12. The figure below shows a 200g mass placed on a frictionless surface and attached to spring.

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)

13. 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)

• 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.

15. A load of 100N is raised 20m in 50s. Calculate;

• The gain in potential energy
• The power developed

16. 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.
17. a) Use this information to show that the gain is kinetic energy E= ½ mv²
18. b) Calculate the kinetic energy of a car of mass 1000 kg traveling at 36km/h

17. 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)

18. A body has 16 Joules of kinetic energy. What would be its kinetic energy if its velocity was double?

19. 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)

20. 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.

21. 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^-3m² 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)

22. A load of 60kg moves from rest  position to a point E along a frictionless path ABCDE

(a) Calculate the

(i)  Maximum Kinetic energy of the load.                           (3mks)

(ii)  Maximum velocity                                                      (3mks)

(iii) Velocity at C                                                              (3mks)

23. The graph below was obtained in an experiment to investigate the stretching of materials.

(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

1. 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).

2. 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)

3. A force of 120N stretches a spring by 15cm. How much work is done in stretching this spring by 20cm?
4. A crane lifts a load of 2000kg through a vertical distance of 0m in 6 seconds. Determine the;
5. Work done         (2mk)
6. Power developed by the crane (2mk)

          iii)   Efficiency of the crane given that it is operated by an electric

motor rated 12.5 kW

5. A crane lifts a load of 500 kg through a vertical distance of 2m in 8 s determine
6. Work done by the crane                                        (2mk)
7. Power developed by the crane                               (2mk)

• Efficiency of the crane given that its operated by all  electric motor rated  2kW                                                         (2mk)

1. State two effects which  contribute to the efficiency  being less  than 100%                                                                   (2mk)

6. 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)

7. 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)
8. 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)

9. A force of 6N extends a spring by 2m. Calculate the work done in extending the spring                                               (3mk)

10. 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)

• The fig. below shows a force – distance graph for a car being on a horizontal ground

1. a) Calculate the total work done
2. 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.

12. The figure below shows a body being acted upon by a varying force over a

distance of 5m.

13. The figure below shows a force – distance graph for a motorbike moving

with a varying force for 20seconds over a distance of 50m.

Calculate

1. The average velocity
2. The total work done
3. The power developed by the motor bike

14. Figure below shows a force distance graph for a car being moved on a

horizontal ground

(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.

15. Figure below shows a force distance graph for a car being moved on a horizontal ground

(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

1. Define the following terms as used in machines

• Mechanical advantage (1mk)
• Efficiency (1mk)
• Velocity ratio (1mk)

2. 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)

3. State two reasons why the efficiency of a machine is always less than 100%                                                    (2mk)
4. 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

1. 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.

(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)

2. 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)

3. Figure shows a lever

Determine

• The effort applied
• The VR.
• The MA.
• The efficiency.
• Suggest two ways in which the mechanical advantage could be increas

4. 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

5. 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.

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.

6. The figure shows a device for closing a steam outlet. The area of the piston is

4.0 x 10^-4m² and the pressure of the steam in the boiler is 2.0 x 10⁵Nm‑².

Determine

• (i) The weight W the weight W that will just hold the bar in the horizontal position shown.
• (ii)

• The VR of the lever.
• (iii) The MA of the lever.
• (iv) The efficiency of the lever.

7. State one advantage of hydraulic brakes over mechanical brakes. (1mk)

WHEEL AND AXLE

1. The machine wheel and axle has a lot of application in real life. Name any two practical examples of such machine. (2mks)

2. 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)

3. 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/s²

(i)     The velocity ratios of the machine                                          (1mk)

(ii)     The mechanical advantage of the machine                (1mk)

• 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)

• 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)

6. 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)

7. 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

1. 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)

1. b) Suggest a reason why the two quantities in a(i) and (ii) are not equal (1mk)
2. c) Calculate:

(i) the velocity ratio of the machine                                           (1mk)

(ii) the efficiency of the windlass                                      (2mks)

1. 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

1. Figure below shows an inclined plane.

Show that the velocity ratio                                             (3mks)

2. A person pulls a box of weight 750N up an inclined plane 6m long using a force of 500N as shown in figure below.

• (i) The VR
• (ii) The height h
• (iii) The work done by effort.
• (iv) The useful work done.
• (v) The efficiency of the plane.

3. 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

(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)

4. 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 30⁰ with the horizontal, calculate;

• The VR
• The effort needed
• The work output
• The work input.
• The work done against friction.

5. 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.

6. A person pulls a box of mass 30kg up an inclined plane 5m long at a constant speed as shown in figure below.

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

7. 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.

1. (i) State the value of the force acting downwards along the inclined plan                                                                    (1mk)
2. ii) Explain how the value in part (a) (i) is obtained            (2mk)
3. b) For the system, determine the:
4. i) Mechanical advantage:                                                                                                                           (2mk)
5. ii) Velocity ratio;                                                                                                                                        (2mk)

iii)  Efficiency.                                                                            (2mk)

8. The following diagram shows a load of 50N being raised by pulling it along an Inclined plane of length 0m.

Determine

1. i) The work done by the 22 N force
2. ii) The work done against the load

iii)  The efficiency of the system

1. iv) Why is the efficiency less than 100%

9. The figure below shows an inclined plane placed at 30⁰ to the horizontal so that it can be used to raise a load through a height ‘h’. The efficiency is 96%.

(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)

10. A girl of mass 50 kg climbs up a ramp 200m long inclined at an angle 10⁰ to the horizontal. Calculate the minimum work done by the girl. (3mk)

11. 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 30⁰ to the ground.

(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

1. A screw advances 1mm when the screw is turned through two What is the pitch of the screw?

2. The figure below shows a cross-section of a handle of a screw jack 70 cm long and pitch of the screw is 8 cm.

Given that the efficiency is 60%, calculate:

1.  i) The velocity ratio of the system.                                            (2mk)
2. ii) If an effort of 50N is applied calculate the load that can be lifted.     (3mk)

• 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)

4. 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 

1. The fore gear of bicycle has 48 teeth while the rear one has 24 teeth. Find its VR.
2. Calculate the VR of the gears below

3. Calculate the combined VR of the gears below.

4. Figure shows part of a bicycle

Determine;

1. i) The velocity ratio                                                      (4mk)
2. ii) Efficiency of the bicycle if its mechanical advantage is 15     (3mk)

THE BELT AND THE GEARS 

1. Calculate the VR of the pulley belt below

2. 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.

3. 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 cog-wheel system determine

(i)  Velocity ratio.                                                                                                           (2mks)

(ii)  The efficiency.                                                                                                         (3mks)

4. 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 cog-wheel system determine

(i)  Velocity ratio.                                                                              (2mk)

(ii)  The efficiency.                                                                             (3mk)

PULLEYS

1. 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)

2. 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
3. The effort distance. (2mk)
4. The work done by the effort (mechanic) (2mk)

• The useful work done by the pulley machine. (2mk)

1. The mechanical advantage of the machine. (2mk)
2. The efficiency of the machine.          (2mk)
3. State two reasons why the efficiency of a machine is always less than 100%  (2mk)
4. 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)

4. 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

5. The figure below shows a single fixed pulley being used to lift a load.

State;

• The mechanical advantage of the pulley            (1mk
• The velocity ratio of the pulley     (1mk)

6. A man used the pulley system shown below to raise a 3kg load through a height of 5m using an effort of 25N

(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)

• 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)

8. 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)

• Figure shows the relationship between the efficiency and the load for a pulley system

Explain the shape of the curve                                                   (1mk

• 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)

11. Figure shows a pulley system

(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)

16. 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)

17. Figure shows a block and tackle pulley system lifting a load of 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)

12. The Figure below shows a machine being used to raise a load.

1. 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)

13. A block and tackle is made up of three pulley wheels on top and two pulley wheels at the bottom as shown below.

(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)

(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)

14. The pulley system in the diagram has two wheels in each block.

1. a) Complete the diagram to show the string as the pulley is being used to lift the load L.          (1 mk)
2. 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)

• The figure below shows a pulley used to raise a load of 50N.

1. a) What is the velocity ratio of the system?                   (1mk
2. b) Determine the mechanical advantage.                      (1mk)

16. 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.

(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.

17. Figure shows a pulley system being used to raise a load.

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)

18. 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.

1. a)     Calculate the value of the unknown mass.
2. b)       State the assumptions you make in calculating the value (a) above
3. 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.

20. 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

1. 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

2. 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.

(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

3. 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 4cm² and that of the load piston D is 400cm².

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

4. 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.

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)

5. The diagram below represents a motor car hydraulic braking system

(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

• 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)

21. The diagram below represents a motor car hydraulic braking system

(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)

22. The figure below shows a hydraulic lift used to lift a load.

Calculate

1. The effort exerted at the smaller piston Q          (2mk)
2. Calculate the load that can be supported by the above machine at P (2mk)
3. TheR of the system                                            (3mk)
4. The A of the system                                            (3mk)
5. The efficiency of the system          (2mk)

23. The figure below shows an effort of 100N being on a single moving pulley to exert a pressure on a gas in a cylinder.

The area of the piston is 10cm² and the volume of the gas is 20cm³.The

weight of the pulley, beam and frictional forces at the moveable part are taken

zero. If the beam is equilibrium:

1. i) Calculate the force acting on the piston. (2mk)     (300N)
2. 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 (3-x))=                                             0.6m

1. 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 5×10⁷ Pa and the cross section area of the new piston is 5cm². What is the amount of force acting on the piston? (2mk) (= 7.5 x 10³N)

24. 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.

Determine the:

(i)     Maximum load that can be lifted.                                               (3mk)

(ii)     Efficiency of the system.                                                            (3mk)

THE PUMP

1. An electric pump can raise water from a lower-level reservoir to the high level reservoir at the rate of 0 x 10⁵ 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.

2. 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?

3. 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

1. 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

iii) Explain  the shape of the graph.                                   1mk

2. 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.

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

3. In an efficiency test carried out on this machine, the following results

were obtained.

1. i) Plot a graph showing how the efficiency varies with the load on the graph

paper provided.                                                                   (7mk)

1. ii) Comment on the variation of the efficiency with the load and give a reason

for this variation.                                                                  (1mk)

4. 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.

         (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.

(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. P₁

CHAPTER SIX

WAVES II                          

Properties of waves

Waves exhibit various properties which can be conveniently demonstrated using the ripple tank. It consists of a transparent tray filled with water and a white screen as the bottom. On top we have a source of light. A small electric motor (vibrator) is connected to cause the disturbance which produces waves.

The wave fronts represent wave patterns as they move along.

Rectilinear propagation

This is the property of the waves travelling in straight lines and perpendicular to the wave front. The following diagrams represent rectilinear propagation of water waves.

Refraction

This is the change of direction of waves at a boundary when they move from one medium to another. This occurs when an obstacle is placed in the path of the waves. The change of direction occurs at the boundary between deep and shallow waters and only when the waves hit the boundary at an angle.

Diffraction of waves

This occurs when waves pass an edge of an obstacle or a narrow gap, they tend to bend around the corner and spread out beyond the obstacle or gap.

Interference of waves

This occurs when two waves merge and the result can be a much larger wave, smaller wave or no wave at all. When the waves are in phase they add up and reinforce each other. This is called a constructive interference and when out of phase they cancel each other out and this is known as destructive interference.

A ripple tank can be used to produce both constructive and destructive waves as shown below in the following diagram.

Interference in sound

Two loud speakers L₁ and L₂ are connected to the same signal generator so that sound waves from each of them are in phase. The two speakers are separated by a distance of the order of wavelengths i.e. 0.5 m apart for sound frequency of 1,000 Hz.

If you walk along line AB about 2m away from the speakers, the intensity of sound rises and falls alternately hence both destructive and constructive interference will be experienced.

Stationary waves

They are also known as standing waves and are formed when two equal progressive waves travelling in opposite direction are superposed on each other. When the two speakers are placed facing each other they produce standing waves. A rope tied at one end will still produce stationary waves.

CHAPTER SEVEN

ELECTROSTATICS II

Electric fields

An electric field is the space around a charged body where another charged body would be acted on by a force. These fields are represented by lines of force. This line of force also called an electric flux line points in the direction of the force.

Electric field patterns

Just like in magnetic fields, the closeness of the electric field-lines of force is the measure of the field strength. Their direction is always from the north or positive to the south or negative.

Charge distribution on conductors’ surface

A proof plane is used to determine charge distribution on spherical or pear-shaped conductors. For an isolated sphere it is found that the effect is the same for all points on the surface meaning that the charge is evenly distributed on all points on the spherical surface. For appear-shaped conductor the charge is found to be denser in the regions of large curvature (small radius). The density of charge is greatest where curvature is greatest.

Charges on or action at sharp points

A moving mass of air forms a body with sharp points. The loss of electrons by molecules (ionization) makes the molecules positively charged ions. These ions tend to move in different directions and collide producing more charged particles and this makes the air highly ionized. When two positively charged bodies are placed close to each other, the air around them may cause a spark discharge which is a rush of electrons across the ionized gap, producing heat, light and sound in the process which lasts for a short time. Ionization at sharp projections of isolated charged bodies may sometimes be sufficient to cause a discharge. This discharge produces a glow called corona discharge observed at night on masts of ships moving on oceans. The same glow is observed on the trailing edges of aircrafts. This glow in aircrafts and ships is called St. Elmo’s fire. Aircrafts are fitted with ‘pig tails’ on the wings to discharge easily.

The lightning arrestors

Lightning is a huge discharge where a large amount of charge rushes to meet the opposite charge. It can occur between clouds or the cloud and the earth. Lightning may not be prevented but protection from its destruction may be done through arrestors. An arrestor consists of a thick copper strip fixed to the outside wall of a building with sharp spikes.

Capacitors and capacitance

A capacitor is a device used for storing charge. It consists of two or more plates separated by either a vacuum or air. The insulating material is called ‘dielectric’. They are symbolized as shown below,

Capacitance C = Q / V where Q- charge and V – voltage.

The units for capacitance are coulombs per volt (Coul /volt) and are called farads.

1 Coul/ volt = 1 farad (F)

1 µF = 10^-6 F and 1pF = 10^-12

Types of capacitors are;

1. Paper capacitors
2. Electrolyte capacitors
3. Variable capacitors
4. Plastic capacitors
5. Ceramic capacitors
6. Mica capacitors

Factors affecting the capacitance of a parallel-plate capacitor

1. Distance between the plates: – reducing separation increases capacitance but the plates should not be very close to avoid ionization which may lead to discharge.
2. Area of plate: – reduction of the effective area leads to reduction in capacitance.
3. Dielectric material between plates: – different materials will produce different capacitance effects.

Charging and discharging a capacitor

When the switch S₁ is closed the capacitor charges through resistor R and discharges through the same resistor when switch S₂ is closed.

Applications of capacitors

1. Variable capacitor: – used in tuning radios to enable it transmit in different frequencies.
2. Paper capacitors: – used in mains supply and high voltage installations.
3. Electrolytic capacitors: – used in transistor circuits where large capacitance values are required.

Other capacitors are used in reducing sparking as a car is ignited, smoothing rectified current and increasing efficiency in a. c. power transmission.

Example

A capacitor of two parallel plates separated by air has a capacitance of 15pF. A potential difference of 24 volts is applied across the plates,

1. Determine the charge on the capacitors.
2. When the space is filled with mica, the capacitance increases to 250pF. How much more charge can be put on the capacitor using a 24 V supply?

Solution

1. C= Q / V then Q = VC, hence Q = (1.5 × 10^-12) × 24 = 3.6 × 10^-10
2. Mica C = 250pF, Q = (250 × 10^-12) × 24 = 6 × 10^-9

Additional charge = (6 × 10^-9) – (3.6 × 10^-10) = 5.64 × 10^-9Coul.

Capacitor combination

1. Parallel combination – for capacitors in parallel the total capacitance is the sum of all the separate capacitances.

C_T = C₁ + C₂ + C₃ + ………..

1. Series combination – for capacitors in series, the reciprocal of the total capacitance is equal to the sum of the reciprocals of all the separate capacitances.

1/ C_T = 1 / C₁ + 1 / C₂ + 1 / C₃

For two capacitors in series then total capacitance becomes,

C_T = (C₁ C₂) / (C₁ + C₂)

Examples

1. Three capacitors of capacitance 1.5µF, 2µF and 3µF are connected to a potential difference of 12 V as shown.

            Find;

1. The combined capacitance
2. The charge on each capacitor
3. The voltage across the 2 µF capacitor

Solution

1. 1 /C_T = 1/ 1.5 + 1 / 3.0 + 1 /20 = 3/2 hence C_T = 0.67 µF
2. Total charge, Q = V C , (2/3 × 10^-6) × 12.0 V = 8 × 10^-6 = 8 µC.
3. The charge is the same for each capacitor because they’re in series hence = 8 µC.
4. V = Q / C, then V = 8 µC / 2 µF = 4 V.

1. Three capacitors of capacitance 3 µF, 4 µF and 5 µF are arranged as shown. Find the effective capacitance.

Solution

Since 4 µF and 5 µF are in parallel then, C_T = 9 µF, then the 9 µF is in series with 3 µF,

Hence C_T = 27/ 12 = 2.25 µF

1. Calculate the charges on the capacitors shown below.

Solution

The 2 µF and 4 µF are in parallel then combined capacitance = 6 µF

The 6 µF is in series with the 3 µF capacitor hence combined capacitance = 18 / 9 = 2 µF

Total charge Q = CV then Q = (2.0 × 10^-6) × 100 = 2.0 × 10^-4 C

The charge on the 3 µF capacitor is also equal to 2.0 × 10^-4 C

The p.d across the 3 µF capacitor => V = Q / C => (2.0 × 10^-4)/ 3.0 × 10^_6

= 2/3 × 10² = 66.7 V

The p.d across the 2 µF and 4 µF is equal to 100 V – 66.7 V = 33.3 V,

Hence Q₁ = CV = 2.0 × 10^-6 × 33.3 = 6.66 × 10^-5 C

Q₂ = CV = 4.0 × 10^-6 × 33.3 = 1.332 × 10^-4 C

N.B