# A friction problem containing a frictionless pulley

1. Mar 19, 2013

### Amurri9030

1. The problem statement, all variables and given/known data

Two masses are connected by an inelastic string over a frictionless pulley. M1 is 4 kg and the coefficient of static friction between M1 and the inclined plane Us = 0.25. What minimum and maximum amount of mass can M2 have so that M1 remains stationary on the plane? (In the given picture θ equals 30 degrees.

2. Relevant equations
F1y = F1 Sin 30
F1y = F1 sin 30 = mg
F1 = mg / sin30

3. The attempt at a solution

Im having an extremely difficult time understanding the concept of pulleys with forces. Am i simply taking the 4kg / cos 30 degrees = 5.0N and then taking 5.0N Sin 30 Degrees? Im very lost and dont understand where the coefficient of friction plays a role! Please help!

2. Mar 19, 2013

### haruspex

I assume M2 is suspended, whereas M1 sits on the slope.
The key thing about pulleys in statics is that if the pulley is frictionless and the string weightless then the tension is the same everywhere. (In kinetics, you might need to worry about the mass of the pulley.)
Consider the forces on each mass separately. For M1, you need to consider which way it would move if there were no friction. This will depend on the mass of M2. The force of friction will always act so as to oppose that movement, so if M1 would slide up then friction acts down the plane.
So there are two cases to consider: max friction acting down the plane; max friction acting up the plane. For each case, you need to determine M2.
Do the FBD for M1. What are all the forces and which way do they act? What equations does that give you? You will need to choose two directions in which to resolve forces to get these equations. You can choose any two of vertical, horizontal, normal to the plane, parallel to the plane - whichever are the most convenient.