A ball is released from rest at the point shown on an incline. It then rolls ont

Question

A ball is released from rest at the point shown on an incline. It then rolls onto a level section of track, and then on to a second incline with the same slope as the first the diagram below shows the location of the ball at several instants of time. Determine the magnitude of the acceleration of the ball at point A (halfway up the second incline). Show your work (I.e. the algebra!). On the diagram above, draw an arrow indicating the direction of the acceleration of the ball at point A. On the diagram above, draw an arrow indicating the direction of the acceleration of the ball at t = 4.0 s (the turnaround point). If the acceleration at the turnaround point is zero, state that explicitly, (i.e. Say so in so many words.) Explain why you drew the arrow as you did.

Explanation / Answer

3. (A) suppose velocity at t=2.8s

vi = v0

and at t = 4s

vf = 0

Applying vf = vi + a t

0 = v0 + a(4- 2.8)

1.2a + v0 = 0 .... (i)

and vf^2 - vi^2 =2 a d

0^2 - v0^2 = 2 a (1.8)

- (-1.2a)^2 = 3.6a

1.44a^2 + 3.6a = 0

a = - 2.5 m/s^2

magnitude of a = 2.5 m/s^2

(B) at A:

along the incline downwards.

(C) acceleration is constant throughout the incline.

hence at t = 4s

a will be along down the incline.

(at t = 4s, velocity will be zero not the acceleration)

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