# How much work does it take to push an object with a mass of #2 kg# up a #3 m# ramp, if the ramp has an incline of #(5pi)/12 # and a kinetic friction coefficient of #2 #?

W = 87.21 J

Since the ramp is angled at a 75-degree angle, the force of gravity dragging it down can be calculated as follows:

In order to determine the opposing friction force's for, we now find:

Only the portion of gravity perpendicular to a ramp constitutes normal force in this scenario, so:

Assuming the minimum amount of work is desired, we can now use F_"net" = ma to find the set up total force, and a (and consequently m) will be set to 0.

W= f*d cos(theta) can now be used to find work; theta will be set to 0 because we are assuming that the force is applied in the ramp's direction.

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The work done to push the object up the ramp would be approximately 29.4 Joules.

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