Two blocks are accelerated across a horizontal frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. If F = 1.2 N and M = 1.0 kg, what is the horizontal component (frictional force) of the force of the large block on the small block?
A) 0.40 N to the left
B) 0.80 N to the right
C) 0.40 N to the right
D) 0.80 N to the left
E) 1.20 N to the left

Question

Two blocks are accelerated across a horizontal frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. If F = 1.2 N and M = 1.0 kg, what is the horizontal component (frictional force) of the force of the large block on the small block? 
A) 0.40 N to the left 
B) 0.80 N to the right 
C) 0.40 N to the right 
D) 0.80 N to the left 
E) 1.20 N to the left

Quizplus · Accepted Answer

Since the surface is frictionless, the only force acting on both blocks is the force F applied to the large block. The force of the large block on the small block is equal in magnitude and opposite in direction to the force of the small block on the large block (Newton's third law). Thus, the net force on each block is F/2. Using Newton's second law (F = ma), we have:

F/2 = Ma       (where M is the mass of the small block)

Solving for the acceleration of the two blocks (which is the same for both blocks), we get:

a = F/2M

Substituting the given values, we get:

a = 1.2 N / (2 x 1.0 kg) = 0.60 m/s²

Since the two blocks have the same acceleration, the force of friction acting on the small block is equal in magnitude to the force of friction acting on the large block (since the masses are equal). The force of friction acting on the small block is equal and opposite to the horizontal component of the force of the large block on the small block. Therefore:

frictional force = Fx = Ma = 1.0 kg x 0.60 m/s² = 0.60 N

Since the small block is being pulled to the right, the frictional force exerted by the large block on the small block must be to the left, so the answer is 0.40 N to the right (choice C).

Two Blocks Are Accelerated Across a Horizontal Frictionless Surface as Shown