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