Mechanical properties of Solids Concept

In summary, when the mass is suspended by a long wire, the gravitational potential energy stored is given by 1/2 x Mg x l. This energy is then lost to internal energy, in the form of heat.
  • #1
zorro
1,384
0
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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  • #2
What do you think? Hint: How was the mass lowered from the original position to its final position?
 
  • #3
The mass lowers due to its weight (stress) on the wire, which is stored as elastic potential energy of the rod.
 
  • #4
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?
 
  • #5
Just dropping
 
  • #6
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.
 
  • #7
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?
 
  • #8
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.
 
  • #9
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.
 
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FAQ: Mechanical properties of Solids Concept

What are mechanical properties of solids?

Mechanical properties of solids are the physical characteristics that describe how a solid material reacts under external forces, such as tension, compression, and shear. These properties include strength, stiffness, elasticity, ductility, and toughness.

What is the difference between strength and stiffness?

Strength is a measure of a material's ability to withstand external forces without breaking, while stiffness is a measure of a material's resistance to deformation under stress. In other words, strength describes a material's ability to resist breaking, while stiffness describes its ability to resist bending or changing shape.

How are mechanical properties of solids tested?

Mechanical properties of solids are typically tested using specialized equipment, such as a universal testing machine, which applies forces to a specimen and measures the resulting deformation. These tests can include tension, compression, bending, and torsion tests.

What factors affect the mechanical properties of solids?

The mechanical properties of solids can be affected by various factors, including the material's composition, structure, and processing methods. Other factors, such as temperature, humidity, and external forces, can also impact a material's mechanical properties.

Why are mechanical properties important?

Mechanical properties are important because they determine how a material will behave under different types of stress or load. Understanding a material's mechanical properties is crucial for designing and engineering structures and products that can withstand specific forces and perform as intended.

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