Question

Jennifer lifts a 2.4 kg carton of cat litter from the floor to a height of 0.81 m.

(a) How much total work is done on the carton during this operation?

___________J

b) Jennifer then pours 0.7 kg of the litter into the cat's litter box on the floor. How much work is done by gravity on the 0.7 kg of litter as it falls into the litter box?

____________J

Answer 1

A)
This can be solved two ways.
First you can look at the change in energy of the box, only potential in this case, and then determine how much work is done. Potential energy is mass * gravity * height(to some relative point, usually the ground). The work done is then equal to the final energy - initial energy. Taking the ground as the reference point, the initial energy is equal to zero. You are left with
W = mass * gravity * height, or W = 2.4 * 9.8 * .81. This totals 19.05 Joules.

B)
This portion can be solved in the same manner, but I will show the second method. Work is equal to the parallel force * the distance. Since the litter is traveling downward, the force of gravity is completely parallel to the distance traveled. To determine the force of gravity, use F = m * a. You can then use the equation W = F * d. Substituting the previous equation, the equation is identical to the equation used in part A, W = m * a * d.
This results in W = 0.7 * 9.8 * .81 = 5.56 Joules.