AUTUMN 2012 PHYSICS 7601 DUE Never

Most of these will be undergraduate problems; some may be much harder. I will

try to keep adding problems in the coming weeks.

0.1 For two-dimensional motion the force is given in polar coordinates by ~F = Ar

where A is a constant. Is the force conservative? An important result you should

remember: a force is conservative if ~F = ~U and thus if ~ ~F = 0.

0.2 Two spacecraft are coasting in exactly the same circular orbit around the earth

but one is a few hundred meters behind the other. Astronaut Jack in the rear satellite

wants to throw a ham sandwich to Jill his fellow-astronaut in the other craft. What is

the best way of doing this? This is a well-known problem from the 1960s.

0.3 A plank of length 2L (of negligible width and thickness) leans against a wall.

It starts to slip downward without friction on both surfaces. Show that the top of the

plank loses contact with the wall when it is at two-thirds of its initial height. This is a

very instructive problem and you should do this both with Newtonian and Lagrangian

methods.

0.4 You are riding on a flat railroad car that has a linear acceleration a in the

direction of motion. At what angle to the vertical should you throw a ball so that you

can catch it without moving? Make sure you can explain this to a sophomore.

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