Problems
Problem 1.1:
Air resistance is a force with magnitude proportional to v2, and always acts
in the opposite direction of the velocity of the particle. Is air resistance a
conservative force?
[Solution]
Problem 1.2:
A small disk of mass 4 kg moves in a circle of radius 1 m on a horizontal
surface, with coefficient of kinetic friction of .25. How much work is done by
friction during the completion of one revolution?
A disc moving with friction in a circle
[Solution]
Problem 1.3:
Consider the last problem, a small disk traveling in circle. In this case,
however, there is no friction and the centripetal force is provided by a string
tied to the center of the circle, and the disk. Is the force provided by the
string conservative?
[Solution]
Problem 1.4:
Consider a ball being thrown horizontally, bouncing against a wall, then
returning to its original position. Clearly gravity exerts a net downward force
on the ball during the entire trip. Defend the fact that gravity is a
conservative force against this fact.
[Solution]
Problem 1.5:
Calculus Based Problem Given that the force of a mass on a spring is
given by Fs = - kx, calculate the net work done by the spring over one complete
oscillation: from an initial displacement of d, to -d, then back to its original
displacement of d. In this way confirm the fact that the spring force is
conservative.
a) initial position of mass. b) position of mass halfway through oscillation. c)
final position of mass
[Solution]
[Solution]
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