Figure shows a block of mass m resting on a 20 ? slope. The block has coefficien

Question

Figure shows a block of mass m resting on a 20? slope. The block has coefficients of friction 0.81 and 0.45 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.
(Figure 1)

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?

shows a block of mass m resting on a 20? slope. The block has coefficients of friction 0.81 and 0.45 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.

Explanation / Answer

fro minimum mass

tension in rope = 2kg*g= 2*10 = 20N

for mass to be minimum static fiction shoudl act

0.81*m*gcos20 = 20

m= 20/10cs(20)/.081

i

if slighty pushed kinectic friction comes in to play

20 - mg sin 20 - .45 mg cos20 = (2+m)*a

we get a subtstituting m from obtained above

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