Question

A trunk w/ a mass of 100kg is pulled 10m across a floor by a rope making an angle of 30 degree w/ the horizantal.if the coeffient of sliding frictions is 0.2.find
a. the force of the rope
b.the work done

Answer 1

you have to know if the object is accelerating or not... because the force could be anything above the force of kinetic friction and move the object. To calculate the work, you first need to know which work -work done by the rope force or by friction? or both? If the object doesn't accelerate, no net work is done

Answer 2

First off: I am beginning with the assumption that the trunk is to be moving with constant velocity
For a constant force, Work=Force*distance. If there were no friction than no force would be needed to keep it moving.

Then the horizontal portion of the force of the rope needs to be equal and opposite to the frictional force which is = u*N where u is the coefficient of friction and N is the normal force. In this case N= 100kg*g - Fsin(30) since the rope pulls up on the trunk aswell.
then u*N=Fcos(30)
Then we get: 0.2*(100kg*9.8m/s^2 - F/2)=root(3)*F/2
Solving for F we get, F= 196/(root(3)/2 +0.1) Newtons
or F~202.9 newtons
Then the work done is F*10 meters
so W=2.029 kilojoules