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## Homework Statement

1)What should F be so that m

_{3}accelerates upwards at 1 m/s

^{2}?

## Homework Equations

F = ma

## The Attempt at a Solution

So I start by drawing FBD's for everything:

^^also, there is supposed to be a force of friction to the right on M1, I factored that into my solution but forgot to draw in in the diagram.

Then I proceed to sum the x and y components of the forces where it is relevant.

m

_{3}:

ƩF

_{y}=m

_{3}a

_{1}

T-m

_{3}g=m

_{3}a

_{1}

m

_{2}:

μ

_{k}m

_{2}g-T=m

_{2}a

_{1}

m

_{1}:

F-N

_{m3}+μ

_{k}m

_{2}g=m

_{1}a

_{2}

F=(m

_{1}+m

_{3})(a

_{2}-1)-μ

_{k}m

_{2}g

i got the relationship a

_{2}=a

_{1}-1

(a

_{2}is the acceleration of the big block and a

_{1}is the acceleration of the 2 smaller blocks)

For a final answer I got:

F = (m

_{1}+m

_{3})[(μ

_{k}m

_{2}g-m

_{3}g)/(m

_{2}+m

_{3})-1]-μ

_{k}m

_{2}g

I am not sure if this is correct. May someone verify this solution please. In particular, I was unsure about the contact forces between the large block and the block accelerating vertically.

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