How do I find the maximum force when one block is held tight against a wall?

Jun 2017
218
6
Lima, Peru
The problem is as follows:

Two bodies are shown in the figure shown below. These are at rest. It is known that the coefficients of friction between the surfaces in contact are $0.5$ and $0.3$. Find the magnitude of the maximum force $\vec{F}$ in $N$ so that the bodies are at rest. The blocks masses are follows $m=6\,kg$ and you may use $g=9.8\frac{m}{s^2}$.​



The alternatives on my book are as follows:

$\begin{array}{ll}
1.&147\,N\\
2.&176\,N\\
3.&187\,N\\
4.&206\,N\\
5.&217\,N\\
\end{array}$

For this problem I'm totally lost at. How am I supposed to use the information given. I find it confusing at what are those values of the coefficients refer?. Are these the static and kinetic friction for the surface between $m$ and $3m$?. Or is it the static friction between $m$ and $3m$. If the latter is the case, which is which?. $0.5$ for between $m$ and $3m$ and $0.3$ for the block $3m$ and the floor, or is it viceversa?. Can somebody help me with a FBD for this problem?!!. I really need help with this one. :help:
 

skeeter

Math Team
Jul 2011
3,129
1,695
Texas
I can only get one of the answer choices if the coefficient of static friction between the m & 3m masses and the 3m mass & floor are identically 0.5

FBD attached
 

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