What Is the Minimum Force Needed to Keep Two Blocks Stationary?

[doktorwho]

Homework Statement

##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##

Homework Equations

3. The Attempt at a Solution [/B]
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?

 

[Doc Al]

I was certain i got this right and then i see a different answer in the book. What is wrong?

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