A trolley rolls along a horizontal surface and then travels up a slope before reaching a second horizontal surface.

Question 20

A trolley rolls along a horizontal surface and then travels up a slope before reaching a second horizontal surface. The slope is of length L. The trolley has mass M. The slope is at an angle α to the horizontal surface. The second horizontal surface is at height h above the first surface.

Assume negligible frictional forces. The acceleration of free fall is known.

In order to determine the minimum initial velocity of the trolley for it to reach the top of the slope, which additional values are needed?

A h and M                   B M, L and h               C α, L, M                     D h only

Reference: Past Exam Paper – November 2017 Paper 13 Q18

Solution:

Answer: D.

At the bottom, the trolley needs to have a minimum amount of kinetic energy as a result of its initial velocity.

As the trolleys moves up the slope, it gains gravitational potential energy.

From the conservation of energy,

KE at bottom = GPE at top + Work done against resistive (frictional) force

But since the question tells us that frictional forces are negligible, the work done against resistive forces is zero.

So,

KE at bottom = GPE at top

½ Mv² = Mgh

The mass M can be eliminated on both sides.

v² = 2gh

 
Thus, form the above equation, to obtain the speed v we only need the values of ‘g’ and ‘h’. ‘g’ is already known, so we only need to know the value of ‘h’.