This is a problem about pushing a packing crate up a ramp. The worker pushing th

Question

This is a problem about pushing a packing crate up a ramp. The worker pushing the crate plans to push parallel to the surface of the ramp (NOT horizontally, which is parallel to the surface of the Earth). The problem begins with the crate lying on the ramp (the crate is at rest), not being touched by the worker. For reporting component directions in this problem, use a coordinate system which is parallel or perpendicular to the surface of the ramp. The possible parallel directions are "Up the Ramp" or "Down the Ramp", and the possible perpendicular directions are "Into the Ramp" and "Away from the Ramp".

The mass of the crate is 115 kg. The ramp makes an angle of 7 degrees with the horizontal.

I need to find:

(a) What is the force of gravity on the crate by the Earth?
(b) What is the "parallel-to-ramp" component of the force of gravity on the crate by the Earth?
(c) What is the "perpendicular-to-ramp" component of the force of gravity on the crate by the Earth?
(d) If the worker is not touching the crate, with how many objects is the crate in contact?
(e) What is the normal component of the contact force on the crate by the ramp?
(f) What is the frictional component of the contact force on the crate by the ramp?

Explanation / Answer

a) mg = 115 x 9.8 = 11128.15 N

b) mg sin7 = 1356.18 N

c) mgcos7 = 11045.2 N

d) with the ramp

e) N = mgcos7 = 11045.2 N

f) f = u(N)= umg cos7 = u x 11045.2 N

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