# Two masses on an inclined plane with a massless pulley

1. Oct 3, 2007

### JefeNorte

1. The problem statement, all variables and given/known data
A block of mass m resting on a 20 degree slope. The block has coefficients of friction mu_s =0.80 and mu_k =0.50 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.

What is the minimum mass m that will stick and not slip?

If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?

2. Relevant equations
T-f_k-(mg*sin(theta))=m*a
f_k=u_k*(mg*cos(theta))

3. The attempt at a solution
I completed the first part of the problem and determined that the minimum mass is 1.829 kg. I calculated the tension on the rope by multiplying the mass of the hanging block by 9.8. But when I plug these values into the equation I keep getting 2.76 m/s^2 which is not the correct answer. Is there something wrong with my equations or the tension value?

2. Oct 3, 2007

### Dick

The tension in the rope is only equal to the weight of the hanging block if the objects aren't accelerating. You need to write the sum of the forces = ma for each object, where the sum of the forces includes the unknown tension T. Then you have two equations and two unknowns and you solve for T and a.

3. Oct 3, 2007

### JefeNorte

Do you mean like T-(u_k*(mg*cos(theta)))-(mg*sin(theta))=m*a?

4. Oct 4, 2007

### Dick

I mean something exactly like that.