Conquering the Physics GRE Section 1.1 Prob. 3

[coca-cola]

Homework Statement

Two blocks of masses M and m are oriented as shown in the diagram. The block M moves on a surface with coefficient of kinetic friction μ_1, and the coefficient of static friction between two blocks is μ_2. What is the minimum force F which must be applied to M such that m remains stationary relative to M?

The diagram essentially looks like Utah rotated 90 degrees clockwise.

Homework Equations

∑F=ma
F_f = F_N * μ

The Attempt at a Solution

I drew force diagrams for both objects and summed up the forces, as is standard with these problems. My answer was:

g * (μ_1 * M + (m / μ_2))

The book tells you the correct answer and this is not it. I have triple checked my diagrams but I can't find my error.

Any help is greatly appreciated!

 

[Nathanael]

The diagram essentially looks like Utah rotated 90 degrees clockwise.

What is the minimum force F ...

Did you mean to say "What is the maximum force ...?" (Or am I misunderstanding the problem?)
Edit:

Does the attached diagram correctly show the configuration?

Ahh, that diagram makes more sense as to why they asked for the minimum (I was imagining utah rotated 90 degrees in the other direction)

 

[TSny]

Hello, coca-cola.

To help you find your error, we'll need to see the details of your work. You might start by describing the force diagrams.

How many forces do you have acting on M? Can you describe the nature of each force and the direction of each force?

Same questions for the forces acting on m.

Does the attached diagram correctly show the configuration?

 

[coca-cola]

The attached diagram is a correct representation and it states "...minimum force F..." in the problem. I have three forces on the smaller block:

Force to the right exerted by the bigger block
Gravity downwards
The frictional force that keeps the block up upwards

On the larger block, 5 forces:

Gravity downwards
Normal force upwards
Applied force to the right
Force from the smaller block to the left
Frictional force to the left

 

[TSny]

The attached diagram is a correct representation and it states "...minimum force F..." in the problem. I have three forces on the smaller block:

Force to the right exerted by the bigger block
Gravity downwards
The frictional force that keeps the block up upwards

Good

On the larger block, 5 forces:

Gravity downwards
Normal force upwards
Applied force to the right
Force from the smaller block to the left
Frictional force to the left

I think there is one more force on the larger block. Can you identify it?

 

[coca-cola]

The only one that I can think of is a frictional force exerted downward on the larger block. Is this correct?

 

[TSny]

Yes. Good.

 

[coca-cola]

Haha yes! Thank you very much!

 

[TSny]

You're welcome. That's a nice exercise.