Question

You push a crate of mass m up a ramp inclined at an angle A with a force parallel to the ramp but of varying magnitude. The coefficient of friction between the crate and ramp is u, and the speed of the crate, which starts from rest, is v at the end of the ramp of length d.

a) Use the work-energy theorem to find the work done by the non-constant force in moving the crate up the ramp.

b) Find the magnitude of the average force applied.

Answer 1

A) Total energy is conserved

At bottom potential energy is zero and also starting from rest so the kinetic energy is also zero.

At top, it has velocity and its at a height. Therefore, it possesses both K.E and P.E

K. E = 1/2 m v^2

P. E = mgh = m g d sin A sin A = h /d

Work done = 1/2 m v^2 + m g d sin A

(B) work done = force * distance

1/2 m v^2 + m g d sin A = force * d ----- I

force = Fapplied - m g sin A - u m g cos A

Now I becomes,

     1/2 m v^2 + m g d sin A = Fapplied * d - m g d sin A - u m g cos A

solve and write the expression for F applied