A heavy box is kept on a smooth inclined plane and is pushed up by a force F acting parallel to the plane. Does the work done by the force F as the box goes from A to B depend on how fast the box was moving at A and B? Does the work by the force of gravity depend on this?

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Solution

(i) No. As the surface is smooth and the friction is zero, work done by the force will only depend on the force and the displacement.

(ii) No, because gravitational force is a conservative force and work done by a conservative force will depend only on the force and the displacement.

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Q. A block of mass 2 kg kept at rest on an inclined plane of inclination 37° is pulled up the plane by applying a constant force of 20 N parallel to the incline. The force acts for one second. (a) Show that the work done by the applied force does not exceed 40 J. (b) Find the work done by the force of gravity in that one second if the work done by the applied force is 40 J. (c) Find the kinetic energy of the block at the instant the force ceases to act. Take g = 10 m/s².

Q. A man pushes a

15 kg

box of books

2.0 m

up a

37^{\circ}

incline into the back of a moving van. The box moves at a constant velocity if you push it with a force of

95 N

. Find the work done by gravity on the box. Take

(g = 10 {m/s}^{2})