Rectangular box tips over (or not)

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SUMMARY

The discussion focuses on determining the conditions under which a uniform rectangular wood block of mass M will tip over rather than slip down an incline as the angle θ increases. The critical relationship involves the dimensions of the block (length b and height a) and the coefficient of static friction (μs). The key equations referenced include the static friction force (Fs ≤ μs * F_n) and the torque equation (τ = Fr * sinθ). Understanding these relationships is essential for solving the problem effectively.

PREREQUISITES
  • Understanding of static friction and its coefficient (μs)
  • Basic principles of torque and rotational dynamics
  • Knowledge of forces acting on inclined planes
  • Ability to analyze free-body diagrams
NEXT STEPS
  • Study the effects of varying the coefficient of static friction (μs) on tipping and slipping scenarios
  • Learn how to construct and analyze free-body diagrams for inclined planes
  • Explore the relationship between torque and angular motion in rigid bodies
  • Investigate the critical angle calculations for different shapes and materials
USEFUL FOR

This discussion is beneficial for physics students, engineers, and anyone interested in mechanics, particularly those studying the behavior of objects on inclined surfaces and the principles of static equilibrium.

usamo42j
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Homework Statement


A uniform rectangular wood block of mass M, with length b and height a, rests on an incline as shown. The incline and the wood block have a coefficient of static friction, μs. The incline is moved upwards from an angle of zero through an angle θ. At some critical angle the block will either tip over or slip down the plane. Determine the relationship between a, b, and μs such that the block will tip over (and not slip) at the critical angle. The box is rectangular, and a ̸= b.


Homework Equations



Fs≤μs*F_n
τ=Fr*sinθ



The Attempt at a Solution



I'm assuming this has to do with torque. There is the normal force doing torque (right?) but that's all I could see. Perhaps gravity also does torque but I'm having trouble seeing how much the radius in the torque formula would be and where does the static friction coefficient come in?
 
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Hi usamo,

Start with a picture, showing all the forces and torques.

ehild
 

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