# Calculate the minimum force

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1. Jan 6, 2017

### doktorwho

1. The problem statement, all variables and given/known data

$m=1[kg]$, $M=5[kg]$, $u=0.6$
Calculate the minimum force required for the blocks to remain in the same position thourought the motion. For the part a) there is no friction between block 2 and the floor, for the part b there is and its $u_f$
2. Relevant equations
3. The attempt at a solution

For the part a) the frictional force between the blocks must be equal to $mg$. The frictional force is proportional to the force on the block.
$mg=F_{fr}$
$mg=uN$ $\Rightarrow$ $N=ma$ $\Rightarrow$ $F=(m+M)a$
$mg=um\frac{F}{m+M}$ $\Rightarrow$ $F=g\frac{m+M}{u}$
The book solution is: $F=mg\frac{m+M}{uM}$
I was certain i got this right and then i see a different answer in the book. What is wrong?
For the part b)
$mg=F_{fr}$
$mg=uN$ $\Rightarrow$ $N=ma$ $\Rightarrow$ $(m+M)a=F-u_pMg$ $\Rightarrow$ $a=\frac{F-u_pMg}{m+M}$
Is this right so far?

2. Jan 6, 2017

### Staff: Mentor

You are assuming that the force between the blocks equals the force applied to the first block. Not so.

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