Discover Physics GCE ‘O’ Level Science

1. Discover PhysicsGCE ‘O’ Level Science Unit 6: Energy, Work and Power

2. 6.1 Energy In this section, you’ll be able to: • identify different forms of energy – kinetic energy, elastic potential energy, gravitational potential energy, chemical potential energy and thermal energy • state the Principle of Conservation of Energy • solve problems using the Principle of Conversation of Energy

3. 6.1 Energy What is Energy? • Energy is the capacity to do work. • The SI unit of energy is the joule (J).

4. 6.1 Energy Different forms of energy and energy conversions There are many forms of energy. Examples include: • Kinetic energy • Potential energy • Sound energy • Electrical energy • Thermal energy • Light energy

5. 6.1 Energy Kinetic Energy • Moving objects have kinetic energy. • Kinetic energy can be used to do work. In windy places, wind is used to turn turbines that convert kinetic energy to electrical energy.

6. 6.1 Energy Potential Energy • Energy that is stored is known as potential energy. • Potential energy can be converted to kinetic energy and vice versa. • Potential energy exists in many forms.

7. How energy is transferred from the sun to humans and animals. 6.1 Energy Chemical Potential Energy • Food contains chemical potential energy which is converted from solar energy via photosynthesis. • These can be converted to kinetic energy.

8. 6.1 Energy Chemical Potential Energy • Chemical potential energy is also stored in fossil fuels like coal and oil. • A battery also stores chemical potential energy that can be converted to electricity.

9. An archer makes use of the elastic potential energy stored in the bow to propel the arrows. A fully flexed bow stores about 300 J of energy. 6.1 Energy Elastic Potential Energy • A spring or rubber band possesses elastic potential energy when it is compressed or stretched. • This energy is converted to kinetic energy when the spring or rubber band is released.

10. When a ball is being dropped from a height, it falls and the gravitational potential energy it has is converted to kinetic energy. 6.1 Energy Gravitational Potential Energy • An object has gravitational potential energy when it is raised to a certain height above the ground. • When released, it falls and gravitational potential energy is converted to kinetic energy.

11. 20 J energy in another form 20 J energy in one form When energy is converted from one form to another, the total amount remains constant. 6.1 Energy Principle of Conservation of Energy Energy can neither be created nor destroyed in any process. It can be converted from one form to another or transferred from one body to another, but the total amount remains constant.

12. Elastic potential energy is converted to kinetic energy, helping to push the boy upwards. 6.1 Energy Conversion of Energy Diver on a diving board Stored chemical energy in the body of a diver allows him to exert a push to bend the diving board. This causes the bent diving board to store elastic potential energy which is then converted to kinetic energy that helps push the diver upwards.

13. When the hammer falls, gravitational potential energy is converted to kinetic energy. 6.1 Energy Conversion of Energy Hammering a nail A raised hammer possesses gravitational potential energy. When it falls, this energy is converted to kinetic energy which is used to do work in driving the nail into the wood block. Sound and thermal energy are also produced and released by the block, nail and hammer.

14. Burning charcoal in a barbecue pit emits a lot of thermal energy to cook food. 6.1 Energy Conversion of Energy Burning of Fuels By burning fuels, the stored chemical energy in these fuels is converted to thermal and light energy.

15. 6.1 Energy Conversion of Energy In real life, energy is easily dissipated into the surroundings. This makes it difficult for us to compare the amount of energy before and after conversion in order to study the Principle of Conservation of Energy effectively.

16. 6.1 Energy Principle of Conservation of Energy and the ideal pendulum

17. 6.1 Energy Principle of Conservation of Energy and the ideal pendulum

18. 6.1 Energy Principle of Conservation of Energy and the non-ideal pendulum In the real world, frictional forces convert some of the total energy of a swinging pendulum to thermal energy. This thermal energy is dissipated to the surroundings and cannot be converted back into kinetic or gravitational potential energy of the pendulum.

19. Height gained is lower than the original because some of the energy has been converted to thermal energy. 6.1 Energy Principle of Conservation of Energy and the non-ideal pendulum The pendulum eventually comes to a stop.

20. 6.1 Energy Efficiency From the Principle of Conservation of Energy, the total energy output by a machine must be equal to its energy input. In real life, energy output is always less than energy input as energy is dissipated, due to friction, or as a form of sound and thermal energy. This energy lost is considered wasted energy output.

21. useful energy output  100% = Efficiency energy input 6.1 Energy Efficiency Energy input = useful energy output + wasted energy

22. 6.1 Energy Key Ideas • Energy is the capacity to do work. • Energy can be converted from one form to another. • The Principle of Conservation of Energy states that energy can neither be created nor destroyed in any process. It can be converted from one form to another or transferred from one body to another but the total amount remains constant.

23. 1 2 = E m v and E m g h = k p 2 6.2 Work Learning Outcomes In this section, you will be able to: • Understand the concept of work and apply the relationship W = F s to solve problems • Apply the relationships to solve problems

24. 6.2 Work Work Done Definition: Work done by a constant force on an object is given by the product of the force and the distance moved by the object in the direction of the force. W = Fs where W = the work done (in J), F = the constant force (in N) s = the distance moved in the direction of the force (in m)

25. 6.2 Work The SI unit of work is the joule (J). Definition: One joule (J) is defined as the work done by a force of one newton (N) which moves an object through a distance of one metre (m) in the direction of the force. one joule = one newton  one metre 1 J = 1 N m

26. 6.2 Work Example of work being done: Lady pushing a pram

27. A man carrying a load while walking. No work is done on the load in the upward direction as the load is only moving horizontally. 6.2 Work No work is being done when: 1. The direction of the applied force and the direction in which the object moves are perpendicular to each other.

28. Boy pushing against a solid wall. A girl holding a heavy pile of books in a stationary position does no work. 6.2 Work No work being is being done when: 2. The force is applied on the object (such as the wall or the pile of books) but the object does not move.

29. 6.2 Work How is energy related to work and force? We need energy to move an object, run and climb stairs. To move a stationary object, we need to apply force to them. For a moving object, we also need to apply force to increase its speed. Hence, work is done when we move a stationary object or make a moving object move faster.

30. 6.2 Work

31. A roller coaster uses a motor-and-chain system to pull the riders up the first hill before letting gravity take over the rest of the ride. 6.2 Work Mechanical Energy There are two types of mechanical energy: 1. Kinetic energy 2. Gravitational potential energy

32. 1 2 E mv = k 2 where E = kinetic energy (in J), k m = mass of the body (in kg) and – 1 = speed of the body (in m s ) v 6.2 Work Kinetic energy and work done A moving body has kinetic energy. When a force moves an object, it does work and the object gains kinetic energy. Kinetic energy is defined as:

33. An object of mass m raised to a height h above ground level possesses G.P.E. of mgh. 6.2 Work Gravitational potential energy and work done Potential energy is stored energy • Gravitational potential energy (G.P.E) is the energy a body has due to its position • To find G.P.E. of an object near surface of Earth, we need to consider its mass and its height above the ground.

34. = g m h E p where E = gravitatio nal potential energy (in J), p = mass of the body (in kg) m – 1 = gravitatio nal field strength (in N kg ) g = height (in m) h 6.2 Work Gravitational potential energy and work done Gravitational potential energy is defined as:

35. 6.2 Work WORKED EXAMPLE 6.4

36. Figure 6.23 6.2 Energy, Work and Power

37. 6.2 Work Key Ideas 1. Force, work and energy are interrelated. 2. Work done W by a constant force F is given by the product of the force F and the distance moved in the direction of the force, i.e. W = Fs. 3. The SI unit of work is the joule (J), which is the same as the SI unit of energy.

38. 1 2 E mv = 2 k 6.2 Work Key Ideas 4. No work is done when • The direction of the applied force and the direction in which the object moves are perpendicular to each other • The force is applied on the object but the object does not move. 5. Moving objects have kinetic energy. The kinetic energy of an object of mass m in kilograms and speed v in m s–1 is given in joules by the expression:

39. 1 2 mv mgh = 2 6.2 Work Key Ideas 6. An object of mass m kg at height h has gravitational potential energy given by Ep = mgh where g is the gravitational field strength (10 N kg–1). 7. Potential energy can be converted to kinetic energy and vice versa. The total energy in a system is fixed. If all the gravitational energy is converted to kinetic energy or all the kinetic energy is converted to gravitational potential energy, the equation is true.

40. G.P.E 30 m 5 m K.E 4 kg 6.2 Work Test Yourself 6.2 2. A block of mass 4 kg slides from rest through a distance of 30 m down a frictionless slope, as shown in the diagram. What is the kinetic energy of the block at the bottom of the slope? Answer: At the top, the block has G.P.E G.P.E = mgh = 4  10  5 = 200 J At the bottom, the G.P.E is converted into K.E. Hence, the K.E of the block at the bottom is 200 J.

41. 1 1 2 Initial K.E = mv vf = vi i 2 2 2 v æ ö 1 Final K.E = m i ç ÷ 2 2 è ø 1 æ ö 1 2 = mv ç ÷ i 4 2 è ø 6.2 Work Test Yourself 6.2 3. If the speed of a springboard diver decreases by half on entering the water, by how much will his kinetic energy decrease? Answer: Let the initial speed of the diver just before he hit the water be vi , and the final speed after he entered the water be vf . Since speed is decreased by half, i.e. Hence, the final K.E is now one quarter of the initial K.E.

42. G.P.E 5 kg 10 m 6.2 Work Test Yourself 6.2 4. A package of 5 kg is lifted vertically through a distance of 10 m at a constant speed. Taking acceleration due to gravity to be 10 m s–2, what is the gravitational potential energy gained by the package? Answer: Gravitational P.E = mg h = 5  10  10 = 500 J Hence, the package gained 500 J of gravitational potential energy.

43. work done power = time taken 6.3 Power Learning Outcomes In this section, you will be able to: • Recall and apply the relationship to solve problems.

44. W E P = = t t where P = power W = work done (in J) E = energy converted (in J) and t = time taken (in s) 6.3 Power What is power? Power is defined as the rate of work done or rate of energy conversion.

45. one joule one watt = one second - 1 1 W = 1 J s 6.3 Power The SI unit of power is the watt (W). One watt (W) is defined as the rate of work done or energy conversion of one joule per second.

46. 6.3 Power WORKED EXAMPLE 6.6 A windmill is used to raise water from a well. The depth of the well is 5 m. The windmill raises 200 kg of water everyday. What is the useful power extracted from the wind? (g= 10 N kg-1) Solution Work done in raising 200 kg of water up a height of 5 m = mgh = 200  10 5 = 10 000J There are 24  60  60 seconds in one day. Therefore power = 10 000 / (24  60  60) = 0.12 W

47. 6.3 Power WORKED EXAMPLE 6.7 A man pushes a heavy box across the floor at a constant speed of 0.5 m s-1 by exerting a horizontal force of 120 N on it. (a) Explain why the resultant force on the box is zero. (b) How much work is done by the man in five seconds? (c) At what rate is the man doing work? Solution (a) The resultant force on the box is zero because the box is moving at a constant speed. A resultant force will cause the box to accelerate and the speed would not be constant.

48. (b) In five seconds, the box would have moved a distance of 0.5  5 = 2.5 m Work done = force  distance moved in the direction of the force = 120 N  2.5 m = 300 J (c) Rate of doing work= work done/time taken = 300/5 = 60 W

49. WORKED EXAMPLE 6.8 A 60 W fluorescent lamp transfers half the electrical energy supplied into light energy. How much light energy does it emit in 10 s? Solution Energy used by lamp in 10 s = 60  10 = 600 J Half of this energy is converted to light energy. Therefore, amount of light energy = 600 / 2 = 300 J

50. 6.3 Power Key Ideas • Power is the rate of work done or energy converted. • The SI unit of power is the watt (W). One watt is the rate of work done at 1 joule per second.