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A 10.2 kg crate is pulled up a rough incline
with an initial speed of 1.5 m/s. The pulling
force is 123.0 N parallel to the incline, which
makes an angle of 14.6◦ with the horizontal.
The coecient of kinetic friction is 0.39 and
the crate is pulled a distance of 8.1 m.
The acceleration of gravity is 9.81 m/s2 .

a) Find the work done by Earth’s gravity
on the crate. Answer in units of J.

You don't need to worry about friction to know how much work was done by, or against, gravity. It equals the change in potential energy, which is
M g * (change in elevation).
Put a minus sign in front of it to get the work done BY gravity.
The change in elevation is
H = 8.1 sin 14.6 meters

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