(3 points) A block of mass m is pushed up an inclined plane with an initial velocity v0. The coefficient of sliding friction between the block and the plane is µ = 0.1. The angle of the inclined plane is q = 30°.
How far up the plane does the block slide?
How much time does it take for the block to slide up and back down to where it started from. Note that the time to slide down does not equal the time to slide up.
(3 points) Given an object of mass m constrained to move in one dimension, and acted on by a force F(t) = F0 e-t/t . If the position and velocity are zero at time t=0, determine the position and velocity for later times.
(4 points) For each of the following force functions, determine the potential energy function, V(x).
F(x) = F0 + cx
F(x) = F0 + cx2
F(x) = F0 e-cx
F(x) = F0 cos(cx)
where F0 and c are positive constants. For each, sketch the potential and comment on whether any regions exist where the motion of a particle could be bounded if the particle has sufficiently little energy.