A bundle of bricks is pulled up a ramp to a construction site. The bundle has a mass of 5.1x10^2 kg and the incline of the ramp is 14 degrees. If the minimum force needed to move the bricks up the ramp is 4.1X10^3 N what is the coefficient of static friction between the bricks and the ramp?

To solve this type of problem you need to determine the force needed to (a) overcome the pull of gravity which is trying to pull it down the ramp, and (b) the force of friction, which opposes the attempt to get it to start moving up the ramp. For (a): since gravity acts straight down, you need to determine the component of the object's weight that acts against the pulling force, alomng the direction of the ramp - this is:

.

For (b): friction is assumed to be equal to the component of the weight that is perpendicular to the surface of the ramp times the coefficient of static friction. So the sliding friction is:

,

where is the coefficient of static friction.

Now add these two forces, set the result equal to pulling force that you were given, and solve for the friction coefficient.