Figure shows a block of mass m resting on a 20degree slope. The block has coeffi

Question

Figure shows a block of mass m resting on a 20degree slope. The block has coefficients of friction mu_s = 0.82 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. (Figure 1) What is the minimum mass m that will stick and not slip? Express your answer to three significant figures and include the appropriate units. If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

this is being pulled by the block with T = T of the hanging block,

that T = m1g or 2* 9.8 = 19.6 N

force of friction is ƒ = N

N = Fgcos20 so ƒ = N = mgcos20

here f = T

mgcos20 = m1g

mcos20 = m1

m = m/cos20

m = 2/(0.50*cos20)

mass m = 4.25 kg

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accelration a = F/m

a = 19.6/4.25

a = 4.61 m/s^2

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