How Does Deformation Affect the Net Force Between Two Masses?

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SUMMARY

The discussion centers on the effects of deformation on the net force between two masses, specifically when one mass (m2) is placed on top of another (m1). It is established that the normal force acting on m1 is the sum of the weights of both masses (m1g + m2g), while the normal force on m2 is simply m2g. When m1 deforms under the weight of m2, there is an initial net force that causes deformation, but once deformation ceases, forces become balanced. This indicates that a scale beneath m1 would not register less weight once the deformation stabilizes.

PREREQUISITES
  • Understanding of Newton's laws of motion, specifically ΣF=ma
  • Knowledge of normal force and gravitational force concepts
  • Familiarity with elastic and plastic deformation in materials
  • Basic principles of force balance in static and dynamic systems
NEXT STEPS
  • Research the principles of elastic and plastic deformation in materials
  • Study the implications of Newton's second law in real-world applications
  • Explore the concept of normal force in different contexts, such as inclined planes
  • Investigate the behavior of forces in systems involving springs and trampolines
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This discussion is beneficial for physics students, educators, and engineers interested in mechanics, particularly those studying force interactions and material properties under load.

anonymous99
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Homework Statement
Suppose you have two masses m1 and m2 with m2 on top of m1. I understand the normal force acting on m1 will be m1g+m2g and normal force on m2 will just be m2g but wanted to know, is this only true for rigid masses? If m1 was able to deform from the weight of m2 above it (like a trampoline for example), would a scale underneath m1 register less weight now?
Relevant Equations
Thanks
S
 
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John781049 said:
Homework Statement:: Suppose you have two masses m1 and m2 with m2 on top of m1. I understand the normal force acting on m1 will be m1g+m2g and normal force on m2 will just be m2g but wanted to know, is this only true for rigid masses? If m1 was able to deform from the weight of m2 above it (like a trampoline for example), would a scale underneath m1 register less weight now?
Relevant Equations:: Thanks

S
Consider the vertical balance of forces on each mass. Can there be a net force on either?
 
I think there is for m1 because it wouldn't deform otherwise.
 
John781049 said:
I think there is for m1 because it wouldn't deform otherwise.
Equal and opposite forces are quite able to deform objects.
What does ΣF=ma tell you about the consequences of a net force?
 
haruspex said:
Equal and opposite forces are quite able to deform objects.
What does ΣF=ma tell you about the consequences of a net force?
Well, there is a net force initially then while m1 deforms but once it's stopped deforming forces are balanced? I think it would be like with a trampoline. If someone stands on the trampoline, there's a net force that causes the ropes to sag downwards when you land from each jump and once the trampoline doesn't sag anymore, it will propel you back up.
 
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Even if mass 1 is not elastic and suffers a plastic deformation under the weight of mass 2, would a scale underneath mass 1 and 2 register less weight?

Tip: Weight force is only the result of the combination of mass and the acceleration of gravity.
Have any of those changed for mass 1?
 
John781049 said:
there is a net force initially then while m1 deforms but once it's stopped deforming forces are balanced?
Yes.
Does that answer your original question?
 

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