Question #3214

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?

Expert's answer

Let T be the unknown tension of the string. Then for hanging mass will be

T - m_{2}g=0 => T=m_{2}g, m_{2}=2.0 kg

For the first mass T - μ*m_{1}g*cos(θ)=0

Hence

m_{1}=m^{2}g/(μ*g*cos(20))=m2/(μ*cos(20))=2.13/μ

- its minimal value of mass m_{1}=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)

T - m

For the first mass T - μ*m

Hence

m

- its minimal value of mass m

where μ is the coef. of friction with the surface(the value of it isn't given in the task)

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