# Thread: mass, friction and equilibrium in a system

1. ## mass, friction and equilibrium in a system

A particle of mass m is placed on a rough track which goes up at an angle A to the horizontal, where sinA=0.6 and cosA=0.8. The coefficient of friction is 0.5. A string is attached to the particle, and a particle of mass M is attached to the other end of the string. The string runs up the track, passes over a smooth bar at the top of the track, and then hangs vertically. Find the interval of values of M for which the system can rest in equilibrium.

I thought this would be easy but I think I started with the wrong idea and it messed me up. So the particle with mass M has a vertical downward force of 10M. Thats going to be constant. However the force exerted by the first particle is going to depend on the direction of motion, right? I.e. against which force the friction will work. So first of all I took 10M>(10m)(sinA)(µ) which makes M>0.3m which I already know is wrong. And then for the other possibility I'm not even sure which equations to use, and I'm getting all mixed up with the tension in the string...any help appreciated.

2. Members are, of course, welcome to posts comments here, but this question has been addressed here on PHF.

-Dan