We want to slide a 12 kg crate up a 2.5 m long ramp inclined at 30o. A worker, ignoring friction, calculates that he can do this by giving it an initial speed of 5.0 m/s at the bottom and letting it go. But friction is not negligible; the crateslides only 1.6 m up the ramp, stops, and slides back down.

Find the magnitude of the friction force acting on the crate, assuming that it is constant.

33.72N

Explanation:

To find the magnitude of the friction force you take into account all forces over the object:

   (1)

where Mgsin0 is the gravitational force, Ff is the friction force F is the force of the worker, m is the mass and a is the acceleration of the object while it is going up the ramp.

it is necessary to find the acceleration of the crate:

with this value and the values for m, g, the angle and d you obtain, by using (1)  you obtain:

(3)

For the calculation of F:

If the surface would be frictionless you have:

with these values you can calculate the force F:

BY replacing this values in the expression (3) you get:

hence, the magnitude of the friction force is 33.72N