In the figure,the coefficient of kinetic friction between the surface and the larger block is 0.20,and the coefficient of kinetic friction between the surface and the smaller block is 0.30.If F = 14 N and M = 1.0 kg,what is the magnitude of the acceleration of either block? A)2.0 m/s² B)1.3 m/s² C)1.5 m/s² D)1.8 m/s² E)3.5 m/s²

Question

Quizplus · Accepted Answer

We will calculate the acceleration of both blocks separately.

For the smaller block, the net force acting on it is F - f_k, where f_k is the kinetic friction force. Thus, we have:

F - f_k = m*a
a = (F - f_k) / m
a = (14 - 0.3*6) / 1
a = 1.3 m/s^2

For the larger block, the net force is the force applied minus the friction force. The friction force is equal to the weight of the smaller block plus the force applied to it, multiplied by the coefficient of kinetic friction between the surface and the larger block. Thus, we have:

F - f_k = m*a
F - (0.2*(6 + 14)) = 1*a
a = (F - 2.8) / m
a = (14 - 2.8) / 1
a = 11.2 m/s^2

Since the two blocks are connected, they must have the same acceleration, and the smaller acceleration (1.3 m/s^2) is the limiting factor. Therefore, the answer is B, 1.3 m/s^2.

In the Figure,the Coefficient of Kinetic Friction Between the Surface