Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done by the two forces are related by A) W_A = 4 W_B. B) W_A = 2 W_B. C) W_A = W_B. D) W_B = 2 W_A. E) W_B = 4 W_A.

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Quizplus · Accepted Answer

The work done by a force is given by the formula W = F•d•cosθ, where F is the magnitude of the force, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion. Since the tracks are frictionless, the angle between the direction of motion and the applied force is 0 degrees. Thus, the work done by both forces is simply W = F•d, where F is the magnitude of the force and d is the distance over which it is applied. Since the masses and distances traveled are equal for carts A and B, the work done by the forces is directly proportional to their magnitudes. Therefore, if one force is twice as large as the other, it does twice the work. Thus, the relative amounts of work done by the forces on A and B are related by the equation: W_A = 2 W_B or, equivalently, W_B = 2 W_A. Therefore, the correct answer is D.

Carts a and B Have Equal Masses and Travel Equal