Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μ_k. At the highest point, A) K_A K_B. B) K_A = K_B. C) K_A

Question

Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μ_k. At the highest point, A) K_A > K_B. B) K_A = K_B. C) K_A < K_B. D) The work done by F on A is greater than the work done by F on B. E) The work done by F on A is less than the work done by F on B.

Quizplus · Accepted Answer

At the highest point, both objects A and B will have the same potential energy as they have been lifted to the same height. However, the work done by the force F on each object will be different as it depends on both the force and the distance through which it is applied. Object B has twice the mass of object A, so it requires twice the work to be lifted to the same height. Therefore, the force F must do more work on object B than on object A. Since both objects are moving up the incline, the force of kinetic friction acts in the opposite direction to the force F. As the coefficient of friction is the same for both objects, the force of friction acting on object B is greater than the force of friction acting on object A. Therefore, the net force acting on object B is smaller than the net force on object A. This means that the force F must be greater for object B than for object A to achieve the same displacement d up the incline plane, as per the equation Fnet = F - fk = ma. Since the force F is greater for object B and it requires more work to be lifted to the same height as object A, the coefficient of kinetic friction for object B must be greater than that for object A to balance the forces and achieve the same displacement d. Therefore, we have K_A > K_B.

Objects a and B, of Mass M and 2M Respectively