Help me solve my dilema.Kinematics and dynamics of Rigid body problem.

[CICCI_2011]

Homework Statement

Find acceleration-x ̈ of the load. Force F=10G, friction μ=1/3, mass of he body is G.

I tried two ways of solving this problem but not sure if any is good. I think second is good. But wondering if first is also good?

Homework Equations

Ek=1/2 G/g x ̇^2

Fμ=G μ

The Attempt at a Solution

Please look at the picture.There you can see my effort in solving this problem. Thanks for any help.

http://s1198.photobucket.com/albums/aa453/nikola5210/?action=view&current=Load-Copy.png

 

[ideasrule]

I think you mean that the weight of the block is G, not the mass.

The first approach is correct, but not the second. It's not true that the rate at which work is being done is equal to the increase in kinetic energy, because friction takes away some of that energy.

 

[CICCI_2011]

Work would be dA=Fdx-Gμdx

dA=10Gdx-G/3dx
dA=(10-1/3)Gdx
dA=29/3 Gdx

from which acceleration is x=29/3 g

For first approach I don't see how to get G μ+G/g x ̈ =F from Newton's second law?

Thanks for your help