# Extremely frustrated - inclined plane problem w/ friction

1. Feb 25, 2012

### iJamJL

1. The problem statement, all variables and given/known data
Mass M1 (6.58 kg) is on a rough inclined plane that makes an angle θ = 59o with the horizontal. The coefficient of kinetic friction between M1 and the incline is μk = 0.18. A rope is attached to M1, passes over a frictionless pulley, and is attached to mass M2 = 7.30 kg which hangs freely.
(a) If M1 is initially moving up the incline: find the magnitude of the acceleration of the masses.
(b) If M1 is initially moving down the incline: find the magnitude of the acceleration of the masses.

2. Relevant equations
Frictional force = μk * N
F=mg
Components

3. The attempt at a solution
I drew the inclined plane and labeled all of the forces. To solve part (a), M1 is moving up the incline, making the frictional force in the direction of the bottom of the plane, parallel to the plane. The total frictional force should be (μ*N) + (mg*sin(59)), if I am correct. The net force on M1 would be (M2*g) - [(μ*N) + (mg*sin(59))] = (Ʃm)*a

We then divide by Ʃm to get the acceleration.

For part (b), it's the same idea. I would solve it like this:

(mg*sin(59)) - [(M2*g) + (μ*N)] = (Ʃm)*a

We divide by Ʃm again to find the acceleration.

Am I taking the wrong approach? Also, if I'm not being clear on any part, let me know.

2. Feb 26, 2012

### ehild

If you mean M1 on m your equations are correct. Explain the chosen direction of acceleration in both cases, what direction you take positive.

ehild