Hints for Problem Set 4

Last revised 1997/09/22

HRW pp. 72-80 # 69, 91; sheet # V, VI, VII;

69. Where is the center of the circular path of the person on the surface of the earth? It is not at the center of the earth.

91. Be careful to keep track of what is measured by what observer.

V. Make sure you draw a diagram. The man can, of course, head partly up- or down-stream while he is rowing. How do you find the minimum of a function?

You might want to review the solution of problem IV.

VI. There are two different kinds of problems hidden here. What are they, and what kind of physical problem is each one? How do you handle the effects of tangential acceleration?

VII. What is the magnitude of r as a function of time?

Math notes

d f(at)/dt = a df/dt, special case of chain rule d f( g(t) )/dt = (df/dg)(dg/dt)

d cos(wt)/dt = -w sin(wt)
d sin(wt)/dt = w cos(wt)

d (xy)/dt = dx/dt y + x dy/dt

A vector written in terms of unchanging unit vectors may be differentiated using the product rule and

di / dt = 0 (etc.)

Hence if

v = v_y j

then

dv / dt = ( dv_y/dt ) j

You might also find it useful to use

d w² /dt = 2 w dw/dt

in seeking places where dw/dt vanishes, especially if w involves a square root.

HRW pp. 99-107 # 10, 11

10. No hint, except to remember that forces are vectors.

11. (a) and (b) are pretty easy. In (c), you should be able to achieve a = 0.