Question

1. Based on the centripetal force law, explain why specific speed limit sign is posted on the banked curves of the roads

2. Is it more difficult to do a sit-up with your hands stretched in front of you or with them behind your head? Explain.

3. When would a ball hitting a wall have a greater change in momentum: when it hits the wall and bounces back at the same speed or when it hits and sticks to the wall? Explain.

Answer 1

(1) The centripetal force that is exerted on a car when it is negotiating a curve of radius r is given as

For the given amount of frictional force that can be provided by the surface, these two forces must be balanced as you see this force is also a function of velocity so if the velocity is very large, the frictional force might not be able to support the car and it will slip away. So for this reason, the speed limit is mentioned at the post.

(B) When doing a situp, you are rotating the upper half of your body from laying down position to the sitting posture. So larger is the radius or rotational inertia, we would require more torque so it becomes harder to do the situp. If we hold them behind the head, the rotational inertia becomes smaller and the situp becomes easier to be done.

(C) Change of momentum measures by the change in the velocity before and after it hits the wall.

So when it hits and gets back at the same speed the change of momentum is v-(-v) = 2v ,

if it gets stick, then it is v-0 = v so it is the greatest when it reverses at the same speed.