A block of mass m resting on a 20° slope. The block has coefficients of friction and 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?
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Expert's answer
2011-06-23T17:46:20-0400
Let T be the unknown tension of the string. Then for hanging mass will be T - m2g=0 => T=m2g, m2=2.0 kg
For the first mass T - μ*m1g*cos(θ)=0 Hence m1=m2g/(μ*g*cos(20))=m2/(μ*cos(20))=2.13/μ - its minimal value of mass m1=m of the block when it doesn't slip, where μ is the coef. of friction with the surface(the value of it isn't given in the task)
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