# Pulling masses in different ways on a rough surface

1. Sep 12, 2016

### Karol

1. The problem statement, all variables and given/known data
The coefficient of friction between the each mass and the floor are μM and μm respectively. which system accelerates faster under the same F in case:
1) μM = μm
2) μM < μm
3) μM > μm

2. Relevant equations
Friction force: $f=mg\mu$

3. 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.

2. Sep 12, 2016

### BvU

Helllo Karol,

And what is it you need assistance with ?

3. Sep 12, 2016

### Karol

Nothing.... i thank you BvU