How do I find the maximum value of the force between two blocks?

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

In the figure from below there are two blocks, one over another. The system is at rest. The horizontal surface is frictionless and the coefficient of static friction is $0.45$ Find the maximum value of $F$ in $N$ such as the blocks will not slide between them. (You may use $g=10\frac{m}{s^{2}}$)​



The alternatives given in my book are:

$\begin{array}{ll}
1.&58\,N\\
2.&42\,N\\
3.&30\,N\\
4.&25\,N\\
5.&10\,N\\
\end{array}$

In my attempt to solve this problem I thought that:

For the lighter block:

$F-mg\times \mu_{s}=0$

$F= 5\times 10 \left(0.45\right)=22.5\,N$

But this ain't the case. I don't know how to relate this with what is happening in the block from below. :help:

The answer supposedly is $30\,N$. But I have no idea how to get there. Can somebody offer some help here please?. :)
 
Last edited:

skeeter

Math Team
Jul 2011
3,129
1,695
Texas
net force on the upper block ...
$F - f_s = 5a$

net force on the lower block ...
$f_s = 15a$

combining the two equations term for term yields ...
$F = 20a$

use the second equation to solve for acceleration of the two mass system ...

$a = \dfrac{f_s}{15} = \dfrac{\mu \cdot 5g}{15} = 1.5 \, m/s^2$

$F = 20a = 30 \text{ N}$
 

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