Question

SPH4U Physics 12 Communication 3. (4 marks)Two identical balls, A and B, are released from rest on inclines that have the same vertical drop and the same horizontal distance from one end to the other. The inclines differ in detail as illustrated in Figure 3. (Note that very little energy is lost due to rolling friction.) A А (a) Which ball arrives at the end first? Explain your answer. B OD Figure 3 (b) Racing cyclists apply this principle on inclined oval tracks. Explain how.​

Answer 1

Acceleration of an object down a slope increases as the angle of the slope is increased

(a) The ball that arrives at the end first is ball A

(b) Racing cyclist select areas having a steeper slope on a hill that gives them a velocity boost

Reason:

A drawing to clarify the explanation and to represent the possible drawing of figure 3 in the question is attached

The acceleration of the balls on the inclined plane is given by the following formula;

Force, F = m·g·sin(θ)

Therefore, the acceleration, a, of ball A and ball B at the part having the same slope are equal

The acceleration of ball A at the part of its track that is almost vertical is approximately, g, (acceleration due to gravity). The velocity at the end of the drop is u' = v + g·Δt, therefore;

• The velocity of ball A at the recessed sections given by v' = u' + a·t are higher than the velocities of ball B, which is v

• At the higher velocity of ball A, the time it takes ball A to arrive at the end is much lesser, and therefore, ball A arrives at the end first.

(b) The principle is applied by racing cyclist by selecting a steeper path that gives them a velocity boost much larger than what is being normally applied, by the force applied by pedaling

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