A block of mass m is at rest on a 20° slope. The coefficient of static friction between the box and the floor is 0.64. The block is connected by 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 to the surface and not rise up the slope?

Question

zephyr141 · Answer

as always draw your Full Body Diagram out. then label the forces acting on each object.

zephyr141 · Answer

|dw:1444245859571:dw|

zephyr141 · Answer

for m2 do this$$y:T-m_2g=0$$$$y:T=m_2g$$then for the block on the incline$$y:n-m_1gsin20=0$$$$y:n=m1gsin20$$and for x$$x:T-f=0$$$$x:T=f$$$$x:T=\mu n$$

zephyr141 · Answer

$$m_2*g=\mu *m_1*g*\sin20$$put in your known values and solve for m1. i think this is how you do it.

zephyr141 · Answer

$$m_2=\mu m_1\sin20$$

zephyr141 · Answer

g could be divided out.

zephyr141 · Answer

damn i forgot one force. hold on.

zephyr141 · Answer

ok it should be this...$$m_1=\frac{m_2}{\mu \sin20+\cos20}$$