With reference to the figure above, a mass *m* hangs at the end of a rope which is attached to a support fixed on a trolley moving to the right with a speed *v* on a horizontal track. The angle, *θ*, is the angle the rope makes with the vertical.

Are the following statements true or false? Explain your answer.

- The angle
*θ*is zero when the trolley moves with a uniform speed. - When the trolley moves with a constant acceleration
*a*, the magnitude of angle*θ*is only determined by*a*and*g*. - The ball swings to the right when the trolley decelerates.
- The tension
*T*in the rope is larger when the trolley moves with a uniform speed than when it moves with a constant acceleration.

### Suggested answer:

1. TRUE.

At the uniform speed, the rope does not experience any horizontal acceleration. Hence the angle is zero.

2. TRUE.

T sin *θ* = ma

T cos *θ* = W = Mg

tan *θ* = a/g

3. TRUE. When the car decelerates, the net horizontal force is leftwards, which swings the rope to the right.

4. FALSE.

When it accelerates, T = W / sin *θ*

When it moves at a uniform seed, T = W

Hence, W / sin *θ* > W

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