Physics 581 Homework #3
Due Friday 4 p.m.
1. Suppose you take a ball weighing 0.5kg and holding your hand above your head swing the ball around in a circle on the end of a piece of light string one meter long. Assume that in this steady circular motion the string makes an angle of sixty degrees with the vertical.
(a) What is the tension in the string?
(b) How long does the ball take to go once around?
(c) In real life, the ball must feel some air resistance. How come it isn’t slowing down, even though you’re only pulling it towards you? Draw a force diagram and explain what’s going on.
2. You are driving a loaded truck, weighing a total of eleven tons, towards a bridge that arches over a river. The mid part of the bridge—the weakest part—is like the top of a roller coaster, an arc of a (vertical) circle, of radius 400 meters. You suddenly see a warning sign: Bridge cannot carry over ten tons." Assuming that is literally true, with no safety factor, how fast should you drive to be safe?
3. As a variant on the "executive toy" problem, imagine a set of five frictionless cars, each weighing 0.5kg, at rest on a long track, with a space of 0.1 meters between neighboring cars. Now suppose a 1 kg car comes down the track traveling at 1 meter per second. Assume all subsequent collisions are perfectly elastic. Describe the sequence of events that takes place, and give the speeds of all the cars long after the last collision occurs.
4.(a) Suppose you are standing on a spring bathroom scale in an elevator which is at rest. What is your acceleration? What forces are acting on you? What is the reading on the bathroom scale?
(b) Suppose now you push the button for a higher floor, and the elevator begins to move. After three seconds it is going up at a steady one meter per second. Did you accelerate? Are you still accelerating? How do you think the reading on the scale will vary as the elevator begins to move then settles to a steady speed? (Just answer qualitatively - no numbers expected.)
(c) Now imagine disaster—the rope holding the elevator snaps, there are no safety features, and the elevator plunges down the shaft in free fall. You avail yourself of this golden opportunity to check Newton's Laws further, since it is unlikely to be repeated, at least for you personally. You stay calmly on the spring scale. What does it read?