Work-energy theorem: A worker lifts a 20.0-kg bucket of concrete from the ground up to the top of a 20.0-m tall building. The bucket is initially at rest, but is traveling at 4.0 m/s when it reaches the top of the building. What is the minimum amount of work that the worker did in lifting the bucket?

Question

Quizplus · Accepted Answer

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this problem, the net work done on the bucket is the work done by the worker in lifting it against gravity. Using the equation for gravitational potential energy, we can find the initial potential energy of the bucket:
PE_initial = mgh = (20.0 kg)(9.81 m/s^2)(0 m) = 0 J
At the top of the building, the bucket has both gravitational potential energy and kinetic energy:
PE_final = mgh = (20.0 kg)(9.81 m/s^2)(20.0 m) = 3,924 J
KE_final = (1/2)mv^2 = (1/2)(20.0 kg)(4.0 m/s)^2 = 160 J
The net work done on the bucket is therefore: 
W_net = PE_final + KE_final - PE_initial = 3,924 J + 160 J - 0 J = 4,084 J
Therefore, the minimum amount of work that the worker did in lifting the bucket is 4.08 kJ, which is choice D.

Work-Energy Theorem: a Worker Lifts a 20