Work-energy theorem: A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

Question

Quizplus · Accepted Answer

According to the work-energy theorem, the work done by the braking force on each object is equal to the initial kinetic energy of that object. As the initial speeds of the two objects are different, their initial kinetic energies will be different. However, both objects will be brought to rest, meaning their final speed is 0 m/s. Therefore, their final kinetic energy is also 0. The work done by the braking force is given by the equation: 
Work done = change in kinetic energy = final kinetic energy - initial kinetic energy

Since the final kinetic energy is 0, the work done by the braking force on each object is equal to its initial kinetic energy.

The initial kinetic energy of the 4.0-kg object is given by: 
KE = (1/2)mv^2 = (1/2)(4.0 kg)(2.0 m/s)^2 = 8.0 J

The initial kinetic energy of the 1.0-kg object is given by: 
KE = (1/2)mv^2 = (1/2)(1.0 kg)(4.0 m/s)^2 = 8.0 J

Thus, both objects have equal initial kinetic energies and therefore experience equal work done by the braking force. This means they will travel the same distance before stopping.

Work-Energy Theorem: a 4