The horizontal surface on which the objects slide is frictionless. If M = 1.0 kg and the magnitude of the force of the small block on the large block is 5.2 N, determine F.
A) 6.0 N
B) 9.0 N
C) 7.8 N
D) 4.8 N
E) 4.1 N

Question

The horizontal surface on which the objects slide is frictionless. If M = 1.0 kg and the magnitude of the force of the small block on the large block is 5.2 N, determine F. 
A) 6.0 N 
B) 9.0 N 
C) 7.8 N 
D) 4.8 N 
E) 4.1 N

Quizplus · Accepted Answer

Using Newton's Second Law, we can write two equations of motion for the two blocks involved:
For the large block: 
F - f = Ma where f is the force of friction between the blocks and "a" is the acceleration of the system. Since the surface is frictionless, f = 0. Hence, 
F = Ma = 1a
For the small block: 
f = ma where "m" is the mass of the small block. Since f = 5.2 N, we have
5.2 = 0.5a (since m = 0.5 kg)
Solving for "a" in the second equation, we get
a = 10.4 m/s^2
Substituting this value of "a" in the first equation, we get
F = Ma = (1 kg)(10.4 m/s^2) = 10.4 N
Therefore, the answer is C) 7.8 N.

The Horizontal Surface on Which the Objects Slide Is Frictionless