Solve Work Formula Problem: Calculate Force Exerted by Man

[Farm4Life]

I have pretty much figured out the problem, but i am unsure of my work.
the question reads:
a 330kg piano slides 3.6m down a 28degree incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. The effective coefficient of kinetic friction is 0.40. Calculate: (a) the force exerted by the man.

F=mgsin(theta)
=(330kg)(9.81m/s2)sin90
F= 3237.3 N

Is this the correct formula to use to find the force exerted by the man?

 

[berkeman]

Where is the force due to the friction? The man's job is made easier by the help of friction.

 

[kyle8921]

Yes, the formula you have used is correct for finding the force exerted by the man. However, you have used the angle of 90 degrees instead of 28 degrees in the calculation. The correct formula to use in this case would be F = mg(sin(theta) - u*cos(theta)), where u is the coefficient of kinetic friction and theta is the angle of the incline. So the correct calculation would be:

F = (330kg)(9.81m/s^2)(sin(28) - 0.40*cos(28))
= 3237.3 N

Therefore, the force exerted by the man is approximately 3237.3 N.