Question

1. 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?

2. Now, consider the same situation – you’re standing on a subway carrying a stone hanging from a rock – but now the train is moving at a constant speed while turning to the right. When you do this, you will see the stone hang to the left. Suppose that it hangs at an angle θ from the vertical, and that you know the train is moving at a speed v.

(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?

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

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

(e) Calculate the radius of the curve in terms of θ and v (and g).

Answer 1