Pulling masses in different ways on a rough surface

[Karol]

Homework Statement

[/B]The coefficient of friction between the each mass and the floor are μ_M and μ_m respectively. which system accelerates faster under the same F in case:
1) μ_M = μ_m
2) μ_M < μ_m
3) μ_M > μ_m

Homework Equations

Friction force: ##f=mg\mu##

The Attempt at a Solution

1) Both systems accelerate the same. case A:
$$F-(M+m)g\mu=(M+m)a$$
Case B:
$$F-(Mg+T\sin\alpha+mg-T\sin\alpha)\mu=(M+m)a$$
2)The acceleration is bigger since the net force available for accelerating is bigger. the left side of the inequality corresponds to A:
$$F-[(M\mu_M+m\mu_m)g+(\mu_M-\mu_m)T\sin\alpha>F-(M\mu_M+m\mu_m)g$$
3)The in verse of 2.

 

[BvU]

Helllo Karol,

And what is it you need assistance with ?

 

[Karol]

Nothing... i thank you BvU