Question

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?

Answer 1

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)