Question

A 19.4-kg box is being pushed from the bottom to the top of a frictionless ramp. When the box is pushed at a constant velocity, the nonconservative pushing force does 58.0 J of work. How much work is done by the pushing force when the box starts from rest at the bottom and reaches the top of the same ramp with a speed of 1.50 m/s?

Answer 1

for box and the earth system the only external force is the pushing force

work done by external force = change of energy of the system

work done by pushing force = change in kinetic energy K + change in potential energy U

U = work done - K

box moves with constant velocity so there will be no change in kinetic energy-

so,

K = 0, and

U = work

U = 58.0 J

work done by pushing force = K + U

change in kinetic energy K = final kinetic energy - initial kinetic energy

work done by pushing force = final kinetic energy - initial kinetic energy + 58.0

work done by pushing force = 0.5 * 19.4 * 1.5^2 - 0 + 58.0 (initial kinetic energy is zero since the box starts from rest)

work done = 79.825 J