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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
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
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