Three identical 3.0-kg cubes are placed on a horizontal surface in contact with one another.The cubes are lined up from left to right and an 18-N force is applied to the left side of the left cube causing all three cubes to accelerate to the right.If the cubes are each subject to a frictional force of 3.0 N,what is the magnitude of the force exerted on the middle cube by the left cube in this case?
A) 18 N
B) 6 N
C) 12 N
D) none of the above

Question

Quizplus · Accepted Answer

Since the three cubes are in contact with one another, they form a single object with a total mass of 9.0 kg. The applied force of 18 N causes an acceleration of:
a = F/m = 18 N / 9.0 kg = 2.0 m/s^2

Since the middle cube is in contact with both the left and right cubes, it experiences forces from both of them. The force exerted on the middle cube by the left cube is equal in magnitude to the force exerted on the left cube by the middle cube, but in the opposite direction. Let's call this force F_lm (force exerted by left cube on middle cube). By Newton's third law, the force exerted on the left cube by the middle cube is equal in magnitude but in the opposite direction, thus we have F_ml = - F_lm.

To find F_lm, we can use the equation:
F_lm = ma = (3.0 kg)(2.0 m/s^2) = 6.0 N

Therefore, the magnitude of the force exerted on the middle cube by the left cube is 6.0 N, which is answer choice C.

Three Identical 3