science

A 100 kg crate is pushed at constant speed up the frictionless 30 degree ramp by a horizontal force vector F. What are the magnitudes of a) vector F and b) the force on the crate from the ramp?

I am not sure how to find part a. What would I need to do to find it? for part b would one of the forces be a normal force, and others (which I am not sure of). How would I find the normal force and others.

(a) The component of the horizontal force F in the direction UP the ramp must be equal and opposite to the component of the weight along the same direction.

F cos 30 = M g sin 30
F = M g tan 30

(b) The ramp exerts both a vertical and horizontal force on the crate. The force vector must be perpendicular to the ramp since ther is no friction.

Let F' be the force you want.
Its vertical component, F' sin 30 must equal the weight, Mg.
Solve for F'

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