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

Since the horizontal surface is frictionless, the only forces acting on the system are the force of the small block on the large block and the force of the large block on the small block, which are equal in magnitude and opposite in direction. Using Newton's second law, we can write:
F - 5.2 N = (1.0 kg + 2.0 kg) a
where a is the acceleration of the system. Since the blocks move together, the acceleration is the same for both blocks, and we can write:
a = (F - 5.2 N) / 3.0 kg
Now, we can use the fact that the forces are equal in magnitude to write:
5.2 N = F - 5.2 N
Solving for F, we get:
F = 10.4 N
Substituting this into the equation for acceleration, we get:
a = (10.4 N - 5.2 N) / 3.0 kg = 1.7 m/s^2
Finally, we can use Newton's second law again to find the force on the small block, which is given by:
F_small = m_small a = 1.0 kg × 1.7 m/s^2 = 1.7 N
The magnitude of the force of the small block on the large block is 5.2 N, which is greater than the force on the small block, so the blocks will move together as a single system. The net external force on the system is F - 5.2 N, which is equal to the force required to provide the acceleration. Therefore, we have:
F - 5.2 N = (1.0 kg + 2.0 kg) a = 5.1 N
Solving for F, we get:
F = 5.1 N + 5.2 N = 10.3 N
The closest choice is C, 7.8 N. It is the best choice as it is closest to 10.3 N, which is the exact value of F.

The Horizontal Surface on Which the Objects Slide Is Frictionless