- #1
Maximusw47
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Homework Statement
A block of mass m1 is on top of a block of mass m2. Block 2 is connected by an ideal rope passing through a pulley to a block of unknown mass m3 as shown. The pulley is massless and frictionless. There is friction between block 1 and 2 and between the horizontal surface and block 2. Assume that the coefficient of kinetic friction between block 2 and the surface, μ, is equal to the coefficient of static friction between blocks 1 and 2.
What is the minimum value of m3 for which block 1 will start to move relative to block 2?
Homework Equations
F=ma
f= mu*N
The Attempt at a Solution
I've taken a couple of approaches. The one I think is most valid is this: The point just before block 2 slips relative to block 1 is where the static friction between m1 and m2 reaches its maximum value. At this point the magnitude of acceleration between all the blocks is the same. I'm then solving for:
m1*a = mu*m1*g
m2*a = T-mu*m1*g-mu*(m1+m2)*g
m3*a=T-m3*g
Which gives me:
m3=2*mu*(m1+m2)/(1+mu)
Which is wrong. Am I making a math error or taking the wrong approach entirely?
Thanks in advance for any help!