A 0.75-kg sphere is released from rest and is moving 5.0 m/s after falling 2.0 m in a viscous medium.What is the change in mechanical energy caused by the force the viscous medium exerts on the sphere during this descent?
A)-6.1 J
B)-4.6 J
C)-5.3 J
D)-6.8 J
E)-2.7 J

Question

Quizplus · Accepted Answer

The change in mechanical energy is equal to the work done by the viscous force on the sphere during its descent. This work is equal to the force multiplied by the distance over which it acts. Since the speed of the sphere is constant, the net force acting on the sphere is zero. Therefore, the viscous force must be equal in magnitude and opposite in direction to the force due to gravity.

Using the work-energy principle, we have:

Change in mechanical energy = Work done by viscous force
= Force due to viscous drag x distance
= Force due to gravity x distance  (since the two forces are equal in magnitude and opposite in direction)
= mgh
= (0.75 kg)(9.81 m/s^2)(2.0 m)
= 14.72 J

Therefore, the change in mechanical energy is -14.72 J (negative because the work done by the viscous force is negative). The closest answer choice is C, which is 5.3 J off from the correct answer.

A 075-Kg Sphere Is Released from Rest and Is Moving 5