Work-Energy: Distance up the Incline, with and without Friction | Symbolic Physics (AP FR C1990M2)
Based on the following AP Free Response question from 1990:
C1990M2. A block of mass m slides up the incline shown above with an initial speed vo in the position shown.
a. If the incline is frictionless, determine the maximum height H to which the block will rise, in terms of the given quantities and appropriate constants.
b. If the incline is rough with coefficient of sliding friction u, the box slides a distance d = h2 / sin θ along the length of the ramp as it reaches a new maximum height h2. Determine the new maximum height h2 in terms of the given quantities.
Other problems these results and methods will be helpful for:
A skier traveling 11.0 ms reaches the foot of a steady upward 19° incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?
A sled is initially given a shove up a frictionless 23.0° incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?
What is the minimum work needed to push a 950-kg car 710 m up along a 9.0° incline? Ignore friction.
A 75.0-kg skier rides a 2830-m-long lift to the top of a mountain. The lift makes an angle of 14.6 degrees with the horizontal. What is the change in the skier’s gravitational potential energy?