A 9.0 kg box is sliding down a smooth flat ramp which makes an angle of 24° with the horizontal. If the coefficient of kinetic friction between the box and the ramp is 0.25, how long will it take the box to slide 2.0 m down the ramp from a standing start?

Question

A 9.0 kg box is sliding down a smooth flat ramp which makes an angle of 24° with the  horizontal. If the coefficient of kinetic friction between the box and the ramp is 0.25, how  long will it take the box to slide 2.0 m down the ramp from a standing start?

anonymous · Answer

First determine the acceleration by summing up the forces in the x-direction, along the ramp, and setting it equal to ma.
Using down the ramp as the positive direction:
Fx = mgsin(theta) - uk mgcos(theta) = ma      uk is the coefficient of kinetic friction

With the acceleration, you can use the equations of motion with constant acceleration to determine the time:
x2 = x1 + v1t + 1/2 a t^2        where x1 = 0   and  v1 = 0

anonymous · Answer

Excellent! 
Thank you! :D