Question

Kenny pulls with a force of 850 N. Justin pushes with a force of 650 N. The crate weighs 1250 N and sits on a ramp that is 40 degrees from the horizontal. Tyler is pushing at an angle of 35 degrees with respect to the crate. There is an angle of 50 degrees between Tanner's rope and the crate. What is the highest that mu (ì) can be in order for them to get the crate up the ramp?

Answer 1

Friction is parallel to the surface of the ramp, and in the opposite direction of motion.

The easiest way is to shift the coordinate axes so that x is parallel to the surface of the ramp. Then draw a free body diagram, splitting each force up into x and y components. Don't forget the force of weight.

The sum of the forces in the y direction should be 0. For them to move the crate up the ramp, the force in the x direction must be >= 0. Through that you should be able to find the maximum frictional force.