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 μk. At the highest point, A) K_A = Fd = K_B. B) K_A = (F − μkMg cosθ)d; K_B = (F − 2μkMg cosθ)d. C) K_A = (F − Mg sinθ)d; K_B = (F − 2Mg sinθ)d. D) K_A = (F − Mg sinθ − μkMg cosθ)d; K_B = (F − Mg sinθ − μkMg cosθ)d. E) K_A = (F − Mg sinθ − μkMg cosθ)d; K_B = (F − 2Mg sinθ − 2μkMg cosθ)d.

Question

Quizplus · Accepted Answer

The work done on each object is equal to the force applied minus the forces opposing motion (gravity component parallel to the incline and friction) times the distance. For object A, the opposing forces are Mg sinθ (gravity component) and μkMg cosθ (friction), and for object B, they are 2Mg sinθ (gravity component, since its mass is 2M) and 2μkMg cosθ (friction, since friction force scales with normal force, which is proportional to mass).

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