A block of mass M1 = 160.0 kg sits on an inclined plane and is connected to a bucket with a massless string over a massless and frictionless pulley. The coefficient of static friction between the block and the plane is ms = 0.52, and the angle between the plane and the horizontal is q = 47°. Mass M2 (mass of the bucket) can be changed by adding or taking away sand from the bucket. What is the maximum value of M2 for which the system will remain at rest?

Question

Can someone please give me a little help?

Answer 1

First, break the forces on M1 into normal and down the plane forces.

Down the plane is mgSinTheta, and friction down the plane of -mg*mu*CosTheta.

A system equations: To stop the bucket from going up, the weight of the bucket must equal the forces down the plane.

M2*g=mgSinTheta-mg*mu*CosTheta

check my thinking.

Answer 2

That's right.
Now it asks for the minimum value of M2 for which the system will remain at rest. Do I still use mgSinTheta-mg*mu*CosTheta?

Answer 3

In the first case, maximum M2, both the component of weight down the plane and friction are in the down plane direction. They add, no minus sign.
If the thing is to move the other way, down the ramp, the friction is opposite in direction, up the ramp. So you change the sign of that second term, the friction one. NOW you have a minus sign

Answer 4

Ok I got it, thanks.
The last part is this: Suppose the coefficient of kinetic friction between the block and the inclined plane is muk = 0.36. If M2 = 217.1 kg, what is the magnitude of the acceleration of M1?

Which equation am I using for this?