Question

You are riding on a subway carrying a 500 g stone hanging from a short rope.1

Suppose that the train is in the process of decelerating from 20 m/s to a stop over 10 seconds. Instead of hanging straight down, the stone is observed to hang at an angle θ away from the vertical. Explain why this happens. Calculate/answer:

(a) Draw a force diagram (free-body diagram) for the stone. Make sure you clearly label which direction is which, using labels like “front of train”, “left of train”, “up”, etc.

(b) In what direction does the stone appear to swing? What is its swing angle?

(c) Is there a force pushing it in that direction?

(d) If yes, calculate its magnitude. If no, why does the stone appear to swing even though no force is applied to it?

(e) Suppose the mass of the stone were doubled. Does this affect anything? Why or why not?

Answer 1

Part (a): The free body diagram can be shown as,

Part (b): The stone will swing in forward direction of train as shown in figure. By equating horizontal and vertical forces we can calculate the swinging angle,

and

Divide both equations,

Here a is acceleration of stone in forward direction which is equal to deceleration of train and can be calculated as,

  

Thus the swinging angle is,

Part (c): No, there is no pushing force in that direction.

Part (d): The stone swings because the stone is free to move and which was is in motion with initial speed 20 m/s. After the deceleration of train the stone will tend to remain in same state. So the stone will move in forward direction where as the fixed end of the string will decelerate with train.

Part (e): If the mass of the stone is doubled, then it will not affect the swinging angle of the stone as can be seen in the expression.

Swinging angle doesn't depend on mass of the stone.