By principle of conservation of energy, in an ideal world, when an object move from a higher position to a lower position, the loss in gravitational potential energy equals gain in kinetic energy. However, in a real world where there is friction, some energies are converted to other forms of energies such as heat and sound as the object overcome friction. Hence the loss of gravitational potential energy may not be exactly equal to the gain in kinetic energy. The following is a suggested solution to GCE O Level Physics Year 2011, Paper 2, Section A, Question 2, illustrating such a scenario.
GCE O Level Physics 2011, Paper 2, Question A2
For this question, you are given the following information:
The cyclist starts from rest at A and rolls down the hill to B, through a vertical distance of 60m. He does not brake or use the pedals. The speed of the cyclist at B is 12 m/s. The total mass of the cyclist and bicyle is 90kg. The acceleration of free fall g is 10 m/s.
The student is required to:
(a) State the principle of conservation of energy:
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.
(b)((i) Calculate the loss in gravitational potential energy Ep between A and B.
At point A, gravitational potential energy:
Ep = mgh = 90 x 10 x 60 = 54,000 J
At point B, gravitational potential energy is zero.
Hence, loss in gravitational potential energy = 54,000
(Note that as the cyclist travels from A to B, the distance that we will use to calculate the loss in gravitational potential energy is the vertical distance between the gravitational potential energy is a result of the vertical downward pull of the the force of gravity towards the center of the earth.)
(b)(ii) Calculate the increase in kinetic energy Ek as the cyclist travels from A to B.
At point A, since the cyclist starts from rest, kinetic energy is zero.
At point B, kinetic energy = ½ mv2 = ½ x 90 x 122 =6,480J
Hence, increase in kinetic energy= 6480
(c) Suggest why the loss in gravitational potential energy and increase in kinetic energy are different and explain how the law of conservation of energy applies to this situation.
Part of the gravitational potential energy has been converted to heat and sound energy as the bicycle has to overcome resistive frictional force when it goes down the slope.