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

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SUMMARY

The minimum mass required to initiate movement in a pulley system with a block of mass m1 = 5.5 kg on a table with a static friction coefficient of μs = 0.52 is calculated to be 2.86 kg. The system's tension force must equal the static friction force for movement to commence. When the mass m2 exceeds 2.86 kg, the block will begin to move due to the gravitational force acting on m2. This conclusion is derived from the equation m2 = F_t/(g-a), assuming acceleration a is zero at the moment of impending motion.

PREREQUISITES
  • Understanding of Newton's second law (f_sum=ma)
  • Knowledge of static friction and its coefficient (μs = 0.52)
  • Familiarity with pulley systems and tension forces
  • Basic grasp of gravitational force (g)
NEXT STEPS
  • Study the dynamics of pulley systems and their applications
  • Learn about calculating forces in static and kinetic friction scenarios
  • Explore advanced problems involving multiple blocks and pulleys
  • Investigate the effects of varying coefficients of friction on motion
USEFUL FOR

Students in physics, particularly those studying mechanics, as well as educators looking for practical examples of static friction and pulley systems.

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.
 
Last edited:

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