Two masses on an inclined plane with a massless pulley

[JefeNorte]

Homework Statement

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?

Homework Equations

T-f_k-(mg*sin(theta))=m*a
f_k=u_k*(mg*cos(theta))

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?

 

[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.

 

[JefeNorte]

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

 

[Dick]

I mean something exactly like that.