Question

1. A proton travels directly (head on) towards a stationary lead nucleus, with an initial speed v0, when the proton is a distance x0 from the nucleus. It undergoes an acceleration of magnitude a = kx−2 directed away from the nucleus, where x is the distance from the proton to the nucleus and k is a positive constant. (Assume the lead nucleus remains stationary throughout.)

(a) Give an expression for how the velocity of the proton depends on x. (It will also depend on k, v0, and x0.)

(b) Find an expression for the distance of closest approach of the proton to the nucleus.

2. Alice and Bob are swimming in a river. They start together at the same point on the bank of a wide stream that flows with a speed v. Both move at the same speed c (where c > v) relative to the water. Alice swims downstream a distance L and then upstream the same distance. Bob swims so that his motion relative to the Earth is perpendicular to the banks of the stream. He swims the distance L and then back the same distance, with both swimmers returning to the starting point. In terms of L, c, and v, find the time intervals required

(a) for Alice’s round trip.

(b) for Bob’s round trip.

(c) Explain which swimmer returns first.

(Refer back to this calculation in physics 4C and 4D when you consider the Michelson interferometer and the Michelson-Morley experiment.)

3. A small child is sitting in a high chair eating and throwing Cheerios. She can launch each Cheerio with a maximum initial speed of 2.00 m/s in any direction and her hand is 1.00 m above the floor as she does so. What is the minimum area of the floor that her father needs to sweep in order to be certain to collect all the Cheerios when she is done eating? (Assume that the Cheerios do not bounce on landing, but rather stick to the juice-covered floor.)

Answer 1