This horrible hill!
You end up pushing the 50-pound (222-Newton) box of potatoes up the hill for 30 meters. You know that the vertical height of the hill (up to your Uncle's place) is 10 meters. The entire time you are pushing the box of potatoes at a constant speed and with a force of 40 pounds (178 Newtons). How much work did the force of friction do as you pushed the box up the hill?
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1 solution
Since the kinetic energy of the box of potatoes has not changed, the net amount of work done to the box of potatoes must be zero. The amount of work done by the applied force is simply 178 Newtons times the displacement of 30 meters. The amount of work done by the gravitational force can be found by multiplying the vertical displacement of 10 meters by the weight of the box which is 222 Newtons (the vertical force). (You can also find the work done by the gravitational force by finding the component of the weight of the box parallel to the side of the hill and multiplying that by 30 meters.)
You are working against gravity and friction in order to move the box. So, the amount of work done by friction is the amount of work you did less the amount of work gravity did.