For a translating block with slipping find the maximum force F

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SUMMARY

The discussion centers on calculating the maximum force F for a translating block problem, specifically addressing the moment about the center of gravity G. The equation derived is F = (-μ_k mg (h/2) + mg(b/2)) / d, where μ_k represents the coefficient of kinetic friction, mg is the weight of the block, h is the height, b is the width, and d is the distance from the pivot. A critical error identified was the incorrect distance used for the moment calculation, which should be d - h/2 instead of d.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with concepts of torque and moments
  • Knowledge of friction coefficients, specifically kinetic friction (μ_k)
  • Basic principles of static equilibrium
NEXT STEPS
  • Study the derivation of torque in rigid body dynamics
  • Learn about the application of Newton's laws in translating systems
  • Explore the effects of varying friction coefficients on motion
  • Investigate the principles of static and dynamic equilibrium in mechanical systems
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Mechanical engineers, physics students, and anyone involved in analyzing forces and moments in translating systems will benefit from this discussion.

annamal
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Homework Statement
For a translating block with slipping find the maximum force F to cause no tipping
Relevant Equations
Ig*alpha = sum of moments
For this translating block problem, below is the solution. I was wondering why if I took the moment about the center of gravity G, the answer for F would no longer be the same because ##I_G \alpha = -\mu_k N (h/2) + N (b/2) - F*d = 0## because ##\alpha = 0##
$$F = \frac{-\mu_k mg (h/2) + mg(b/2)}{d}$$
What am I doing wrong by taking the moment about G though?
Screenshot 2024-03-19 at 9.15.09 PM.png
 
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annamal said:
## -\mu_k N (h/2) + N (b/2) - F*d = 0##
Is ##d## the correct distance for the last term on the left-hand side?
 
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TSny said:
Is ##d## the correct distance for the last term on the left-hand side?
Resolved, that was my mistake. The distance is d - h/2.
 
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