What Is the Minimum Mass Needed to Move the Block in a Pulley System?

AI Thread Summary
To determine the minimum mass needed to move the block in a pulley system, the tension force must equal the force of static friction. Given a block mass of 5.5 kg and a static friction coefficient of 0.52, the static friction force is calculated as 28.44 N. The equation m2 = F_t/(g-a) is used, with acceleration set to zero at the moment of impending motion. This results in a minimum mass, m2, of 2.86 kg; exceeding this mass will initiate movement. The discussion emphasizes the balance of forces in the system to find the critical mass for motion.
jorcrobe
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Homework Statement


A block with mass, m1 = 5.5 kg rests on the surface of a horizontal table which has a coefficient of static friction of μs = 0.52. This block is connected to another block by a pulley system and it hangs vertically under the influence of gravity, g. The hanging block has mass m2.

What is the minimum mass, m2, that will cause the system to move?


Homework Equations


f_sum=ma


The Attempt at a Solution


I figured that the tension force must be equal to the force of static friction in order for the block to begin moving. I'm unsure where I should go from here.
 
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I have found that m2 = F_t/(g-a)

I figure that at that instant a = 0?

making m2 = 2.86
 
If m2 exceeds 2.86 kg, motion will occur.
 
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