Why Does a Force Greater Than 4µW Cause Sliding Between Stacked Boxes?

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SUMMARY

The discussion centers on the mechanics of three stacked boxes against a wall, specifically addressing the conditions under which sliding occurs between the upper and middle boxes when a horizontal force P is applied. It is established that if P exceeds 4µW, where µ represents the coefficient of friction, sliding will occur due to insufficient frictional force to keep the upper box moving with the middle box. The confusion arises from the calculations of frictional forces, with participants questioning why the threshold is set at 4µW instead of lower values like 2µW or 3µW.

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  • Understanding of Newton's laws of motion
  • Knowledge of frictional forces and coefficients of friction
  • Ability to construct and analyze free body diagrams
  • Familiarity with basic mechanics concepts such as normal force and acceleration
NEXT STEPS
  • Study the derivation of frictional force equations in stacked systems
  • Learn about the implications of static versus kinetic friction
  • Explore the concept of normal force in multi-body systems
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of friction and motion in stacked objects. It is particularly relevant for those studying mechanics or preparing for physics examinations.

furor celtica
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Homework Statement



three identical boxes, each of weight W, are to be stacked one on top of another against a vertical wall. The lowermost box is in contact with the wall, and the other two boxes are positioned as shown in the diagram. The middle box is pushed into position by the application of a horizontal force of magnitude P.
Show that if P>4µW (where µ is coefficient of friction between any two boxes), sliding takes place between the upper and middle boxes (i.e. friction is not strong enough for the upper box to follow the middle box in its movement).

Homework Equations





The Attempt at a Solution



I don't understand why it is 4µW, shouldn't it be 3µW or 2µW? I'm not sure.
Firstly the middle box must be able to move, i.e. P>(friction from lowermost box), P>(normal reaction) x µ, P> 2µW. However, the frictional force between the upper and middle boxes is only Wµ, os shouldn't the 2µW force be enough? Or 3µW if both frictional forces are added, I'm not even sure, but any way i can't get to 4µW.
 

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The question is if the middle or upper boxes move together or not if a force P>4µW is applied. Just draw the free body diagram and solve for the accelerations of both blocks. Take care to the normal forces acting on the middle box.

ehild
 

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