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

For the larger block:
The force of friction opposing its motion is F_friction = 0.20 * M * g
The net force on the larger block is F - F_friction = M * a (where a is its acceleration)
So, a = (F - F_friction) / M = (14 N - 0.20*1.0 kg*9.81 m/s^2) / 1.0 kg = 11.24 m/s^2
For the smaller block:
The force of friction opposing its motion is F_friction = 0.30 * (M/2) * g (since it is half the mass of the larger block)
The net force on the smaller block is F_friction - T = (M/2) * a (where T is the tension in the string connecting the two blocks and a is the acceleration of both blocks)
Since the two blocks are connected by a string, their acceleration is the same. 
Substituting the value of F_friction and rearranging the equation, we get:
a = (F_friction - T) / (M/2) = (0.30 * 0.5 kg * 9.81 m/s^2 - T) / 0.5 kg = (1.4715 N - T) / 0.5 kg
Now, using Newton's second law for the combined system of blocks, we have:
F - F_friction - T = (M + M/2) * a (where M + M/2 is the total mass of the system)
Substituting the values and solving for T, we get:
T = 2.938 N
Substituting the value of T in the equation for the acceleration of the smaller block, we get:
a = (1.4715 N - 2.938 N) / 0.5 kg = -3.932 m/s^2 (negative sign indicates that its direction is opposite to that of the applied force)
Since the two blocks are connected by a string, their acceleration must be the same. Therefore, the acceleration of both blocks is 1.966 m/s^2 (the magnitude being 1.966 m/s^2). 
So, the best choice is B.

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