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Friction: Blocks and Pulley

  • Thread starter ArticMage
  • Start date
12
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1. 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).


3. 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 [tex]\Sigma[/tex] Fy = N1-m1*g=0

for m2 [tex]\Sigma[/tex] Fy= N2-N1-m2*g=0
and [tex]\Sigma[/tex] Fx= T-[tex]\mu[/tex]s*N2=0

and for m3 [tex]\Sigma[/tex] Fy= T-m3*g=0

From there i solve the m3 for T then m2 Fx for N2 then Fy2 for N1 and finally the first for m1. But that doesnt work at all. So if anyone can point out what goes wrong id be glad to hear it.
 
Last edited by a moderator:

ideasrule

Homework Helper
2,266
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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?
 

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