Mechanical properties of Solids Concept

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Discussion Overview

The discussion revolves around the mechanical properties of solids, specifically focusing on the elastic potential energy in a wire when a mass is suspended from it. Participants explore the relationship between gravitational potential energy, elastic potential energy, and kinetic energy during the lowering of the mass.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the fate of the additional gravitational potential energy that does not convert to elastic potential energy when a mass is dropped.
  • Another suggests that the mass's lowering is influenced by its weight, which is converted into elastic potential energy and kinetic energy.
  • There is a discussion about whether the mass is dropped or lowered gently, with implications for energy transformation.
  • Some participants propose that the kinetic energy lost during the drop is converted to internal energy, possibly as heat, due to internal friction.
  • One participant introduces the idea that the wire experiences both longitudinal elongation and a decrease in cross-sectional radius, complicating the energy dynamics.
  • A later reply suggests a different approach to understanding the energy transformations, emphasizing the need to consider both elastic and gravitational forces in the analysis.

Areas of Agreement / Disagreement

Participants express differing views on the energy transformations involved when the mass is dropped versus lowered, and there is no consensus on the complete understanding of energy distribution in this scenario.

Contextual Notes

Some assumptions about the behavior of the wire and the nature of energy transformations remain unresolved, particularly regarding the elastic and inelastic properties of the wire and the effects of internal friction.

zorro
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When a block of mass M is suspended by a long wire of length L, the elastic potential energy stored is given by 1/2 x Mg x l, where l is the elongation produced.
The loss in gravitational potential energy of the mass-earth system is Mgl. I wonder where does the other Mgl/2 go?
 
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What do you think? Hint: How was the mass lowered from the original position to its final position?
 
The mass lowers due to its weight (stress) on the wire, which is stored as elastic potential energy of the rod.
 
Abdul Quadeer said:
The mass lowers due to its weight (stress) on the wire, which is stored as elastic potential energy of the rod.
Are you just dropping the mass or are you lowering it gently?
 
Just dropping
 
Abdul Quadeer said:
Just dropping
OK. The gravitational PE goes into both elastic PE and KE. Eventually, that KE will be 'lost' to internal energy.
 
So the elastic PE includes 2 quantities- PE due to elongation and PE due to shrinking of wire?
How is the KE lost to internal energy - You mean by the production of heat etc?
 
Abdul Quadeer said:
So the elastic PE includes 2 quantities- PE due to elongation and PE due to shrinking of wire?
:confused:
How is the KE lost to internal energy - You mean by the production of heat etc?
Yes. If you just drop the load, the mass will oscillate about the equilibrium point. Due to internal friction, eventually it will come to rest.
 
When the wire is stretched, there is some longitudinal elongation produced as well as decrease in cross sectional radius (shrinking in that sense).
Here the wire in not completely elastic to execute oscillations.
 
  • #10
You only mentioned elastic PE in your original post, so I thought that's what you were asking about. The 'additional energy' can go into various other forms, including inelastic deformation.
 
  • #11
Thanks!
 
  • #12
Let me suggest a solution without ad hoc energy losses.
The mass m is moving under the influence of the force f = g - kx (k is the spring constant of the wire). So you can´t apply
Epot = mgh here the way you do it. If you work it out keeping this in mind, all will be ok.

Edit:
A different view of the situation: Energy has a sign (you can put energy into a system or you can take energy from it). Don´t forget you have two forces (elastic/gravity) here. Take a look at their directions.
 
Last edited:

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