Mass on incline will it slip or stick?

[charan1]

Homework Statement

Figure shows a block of mass m resting on a 20* slope. The block has coefficients of friction uS=0.80 and uK=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.

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

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

Homework Equations

Fnet=ma
us=F/N

The Attempt at a Solution

I really have no idea how to do Part B, but I tried part A and was real confident with my answer but it turned out wrong. This is what I did.

(2kg)(9.8)=19.6N for the hanging mass

assuming that the Hanging mass = to the tension force on the block with mass m I then did this...

19.6N=m(9.8)cos20*(.8)
m=2.66kg and this is wrong

Were did I go wrong?

Thanks

 

[tiny-tim]

Welcome to PF!

Figure shows a block of mass m resting on a 20* slope. The block has coefficients of friction uS=0.80 and uK=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.

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

Part B:
If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?
…
(2kg)(9.8)=19.6N for the hanging mass
…
19.6N=m(9.8)cos20*(.8)
m=2.66kg and this is wrong

Hi charan1! Welcome to PF!

(Useful tip: don't bother to multiply everything by 9.8 … all the terms have 9.8, so just call it g, and cancel it at the end. )

(oh … and have a mu: µ )

I take it you were applying Newton's second law in the direction of the slope.

That means that you must include all the forces … you left out the force due to gravity.

(For part B, use µ_K instead of µ_S)