A 22.6-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?

work done = 79.825 J

Explanation:

given,

mass of box = 22.6 Kg

energy = 58 J

speed = 1.5 m/s

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

U = work done - K

box is moving with constant velocity hence no change in kinetic energy.

so, K is equal to zero.

U = work done

U = 58.0 J

work done by pushing force = K + U

now, work done when box reaches to the speed of 1.5 m/s

work done = final kinetic energy - initial kinetic energy + U

work done = 0.5 m v² - 0 + U

work done = 0.5 x 19.4 x 1.5² + 58.0

work done = 79.825 J