What maximum force can be exerted by the string on the top block without causing the top block to slip?

Question

A block of mass m = 5.00 kg rides on top of a second block of mass M = 10.0 kg. A person attaches a string to the top block and pulls the system horizontally across a horizontal, frictionless surface, as shown in the Figure in attachment. If the coefficient of static friction between the two blocks is 0.350, what maximum force can be exerted by the string on the top block without causing the top block to slip?

Answer 1

The maximum force that can be exerted by the string on the top block without causing slippage would be a force equal to the static friction force pulling in the other direction. So, if you find the static friction force, you find your answer.

The friction force formula is the following:

F_f = μ_sF_N

Where μ_s is the coefficient of static friction and F_N is the normal force. The normal force is the force pointing up on the block, and is usually equal to the gravity force pulling the object down. In this case, that is true, therefore:

F_N = mg

We can plug that back into the friction force equation and solve for friction force.

F_f = μ_smg = 0.35*5*9.81 = 17.17N