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.

  1. The angle θ is zero when the trolley moves with a uniform speed.
  2. When the trolley moves with a constant acceleration a, the magnitude of angle θ is only determined by a and g.
  3. The ball swings to the right when the trolley decelerates.
  4. 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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