Two blocks rest on a horizontal frictionless surface as shown. The surface between the top and bottom blocks is roughened so that there is no slipping between the two blocks. A 30-N force is applied to the bottom block as suggested in the figure.
-What is the minimum coefficient of static friction necessary to keep the top block from slipping on the bottom block?
A)0.05
B)0.10
C)0.20
D)0.30
E)0.40

Question

Two blocks rest on a horizontal frictionless surface as shown. The surface between the top and bottom blocks is roughened so that there is no slipping between the two blocks. A 30-N force is applied to the bottom block as suggested in the figure. 
-What is the minimum coefficient of static friction necessary to keep the top block from slipping on the bottom block?
A)0.05 
B)0.10 
C)0.20 
D)0.30 
E)0.40

Quizplus · Accepted Answer

To find the minimum coefficient of static friction necessary to keep the top block from slipping on the bottom block, we need to use the equation:
Ffriction = μs*Fn
where Ffriction is the force of friction, μs is the coefficient of static friction, and Fn is the normal force.

In this case, the 30-N force applied to the bottom block is balanced by the force of friction between the blocks and by the weight of the top block. Therefore:
Ffriction = 30 N
Fn = m*g = 5 kg * 9.8 m/s^2 = 49 N

Substituting the values in the equation, we get:
30 N = μs*49 N
μs = 30 N / 49 N ≈ 0.61

However, this is not the minimum coefficient of static friction necessary. The top block will start slipping if the force of friction is less than the 30-N force applied to the bottom block. Therefore, the minimum coefficient of static friction necessary is:
μs(min) = 30 N / (5 kg * 9.8 m/s^2) ≈ 0.61
Therefore, the best choice is C) 0.20, which is the closest to the calculated value of 0.61.

Two Blocks Rest on a Horizontal Frictionless Surface as Shown