How Does Mass Affect Friction in a Pulley System?

[ArticMage]

Homework Statement

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Masses m1 and m2 rest on a table 1.2 meters above the floor and are attached to m3 via a very light string and a frictionless pulley as shown above. The coefficient of static friction between the m2 and the table is μs = 0.21 and their coefficient of kinetic friction is μk = 0.14. m2 = 56 kg and m3 = 28 kg.
a) What is the minimum mass that m1 can have to keep the two blocks from sliding off the table?
b) m1 is completely removed. What will be the acceleration of m3? (assume up to be the positive direction).

The Attempt at a Solution

I havn't gotten to b yet only attempted a so far.

a) i make the free body diagram and end up with the following equations.
for m1 \Sigma F_y = N₁-m₁*g=0

for m₂ \Sigma F_y= N₂-N₁-m₂*g=0
and \Sigma F_x= T-\mu_s*N₂=0

and for m₃ \Sigma F_y= T-m₃*g=0

From there i solve the m₃ for T then m₂ F_x for N₂ then F_y2 for N₁ and finally the first for m₁. But that doesn't work at all. So if anyone can point out what goes wrong id be glad to hear it.

 

[ideasrule]

For part a, I think it's easier to solve the problem intuitively rather than mathematically. Let's first assume that m1 is large enough to keep the two blocks stationary. m2 is then pressing down on the table with a force of (m1+m2)g. Now let's reduce the mass of m1. At some point, the table can no longer provide enough static friction to hold m3 still. At what point does this happen?