A ball is set in motion at P on a frictionless surface. It moves up slope PQ, along the horizontal surface QR and finally descends slope RS.

Question 24

A ball is set in motion at P on a frictionless surface. It moves up slope PQ, along the horizontal surface QR and finally descends slope RS.

Which graph could represent the variation with time t of the ball’s speed v as the ball moves from P to S?

Reference: Past Exam Paper – June 2017 Paper 12 Q6

Solution:

Answer: A.

The ball moves on a frictionless surface. That is, no frictional force acts on the ball and thus, no energy is wasted against friction.

From P to Q, the ball can be considered to have 2 components: a horizontal component and a vertical component.

The horizontal component remains unaffected (as there is no friction) while the vertical component is affected by the acceleration due to gravity which is downwards.

From P to Q, the vertical component of speed is upwards while the acceleration due to gravity g is downwards. This causes the speed of the ball to decrease. Since g is constant, the decrease in speed is also uniform [gradient is constant – a straight line in the graph]. [D is incorrect]

From Q to R, the ball moves horizontally. It does not have a vertical component. Since the horizontal component is constant, the speed is also constant from Q to R. [B is incorrect]

From R to S, the vertical component is downward and g is also downward. So, the speed increases uniformly.

In terms of energy,

From P to Q, KE - - > GPE    (KE and speed decrease)

From Q to R, GPE remains constant (constant height – KE and v does not change)

From R to S, GPE - - > KE    (KE and speed increase)

 

Since S is at the same level as P. the GPE is the same. And thus, the KE is also the same as before (and so, speed is also the same as before). So, because the ball ends up at the original level, it cannot be travelling faster at the end than it was travelling at the start. [C is incorrect].