• Physics 9702 Doubts | Help Page 244

Question 1127: [Deformation > Hooke’s law]

For a wire, Hooke’s law is obeyed for a tension F and extension x. The Young modulus for the material of the wire is E.

Which expression represents the elastic strain energy stored in the wire?

A ½ Ex                        B Ex                C ½ Fx                                    D Fx

Reference: Past Exam Paper – November 2008 Paper 1 Q23

Solution 1127:

Answer: C.

As Hooke’s law is obeyed, a graph of tension against extension would be a straight line passing through the origin.

The elastic strain energy is given by the area under the graph. This would correspond to that of a triangle.

Elastic strain energy = ½ Fx

Question 1128: [Work, Energy and Power]

Which statement is correct?

A A ball lands on the ground and bounces. The kinetic energy changes sign, because the ball changes direction.

B A car drives up a slope at a steady speed. The power generated by the engine equals the potential energy gained per unit time.

C An electric heater can be 100% efficient.

D It is impossible for momentum to be conserved in a collision.

Reference: Past Exam Paper – June 2015 Paper 11 Q17

Solution 1128:

Answer: C.

Choice A: Kinetic energy is a scalar and does not have a direction.

Choice B: The power from the engine does not just increase the potential energy of the car. It is also providing for the kinetic energy – even if it is constant, it is not created in its own. The KE comes from the fuel. Additionally, there would be a frictional drag on the car and energy is required to overcome this. This energy comes from the engine.

Choice C: This is correct. Usually, energy is dissipated as heat in systems but for an electric heater this heat is useful. So, all the output power is useful in this situation.

Choice D. This is obviously wrong.

Question 1129: [Kinematics > Terminal velocity]

A stone of mass m is dropped from a tall building. There is significant air resistance. The acceleration of free fall is g.

When the stone reaches its terminal velocity, which information is correct?

Reference: Past Exam Paper – November 2011 Paper 12 Q7

Solution 1129:

Answer: B.

At terminal velocity, the speed is constant. So, there is no acceleration and the resultant force on the stone is zero.

The force of gravity always acts on the stone and is equal to mg.

For the resultant force to be zero, the air resistance should be of the same magnitude (= mg).