Work and energy

A hand is moving a book vertically. The initial velocity of the book is zero, as is the final velocity. Assume no air resistance. Make no assumption about the motion, other than these conditions. During the motion,

1. the total energy is conserved.
2. the work done by the gravity is equal and opposite to the work done by hand.
3. the force of gravity is equal and opposite to the force by hand.
4. all of the above.

Stopping a compass needle

A compass needle, as one of the homework problems shows, is a simple harmonic oscillator. Clearly, an ever oscillating compass needle would be useless, and so a frictional damping becomes very handy.

—Insecure URL transclusion is not allowed.— In order to make the compass needle indicate the magnetic north as quickly as possible, the friction must be

1. as little as possible.
2. not too much, not too little -- just right.
3. as much as possible.