How Is Extra Energy Calculated in a Stretched Wire?

In summary: T>0). why not use the max and min values?The Attempt at a Solution Extra energy= E(n)-E(m) = 1/2 x (T'n-Tm)The left side is the energy difference , the right side is the average work done by the tension force [average force times the distance]this is what i can say ,,:)Extra energy= E(n)-E(m) = 1/2 x (T'n-Tm)
  • #1
Tulatalu
29
1

Homework Statement


Under tension T the wire has lenghth of m, its length becomes n when the tension is increase to T'. What is the extra energy stored in the wire as a result of this process?

Homework Equations


E=1/2 Fe[/B]

The Attempt at a Solution


Extra energy= E(n)-E(m) = 1/2 x (T'n-Tm)

There is no such answer in the multiple choices. Am I wrong when I subtracted the two energy?[/B]
 
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  • #2
I might be wrong but is that the right equation for the energy stored in a "spring"?


 
  • #3
CWatters said:
I might be wrong but is that the right equation for the energy stored in a "spring"?
It is applicable to any specimens when they are extended or compressed within their limits.
 
  • #4
E=1/2 Fe looks like some average force times extension when starting at zero force. $$\int_n^m T\; ds$$ would be a lot better. See what that gives. (What are the multiple choice options to choose from ?)
 
  • #5
I don't think they require the exact energy. The right answer is 1/2(T'+T)(n-m) but I have no idea why.
 
  • #6
Well, that IS average force times extension
 
  • #7
But I just don't understand why i was wrong. Could you please explain how they get the result physically?
 
  • #8
Anybody explain the result for me please ?
 
  • #9
Tulatalu said:
1/2(T'+T)(n-m)

If I'm not mistaken ,, I think this is related a work-energy theorem
the energy is equal to the external work

So
$$E_f-E_i = 0.5 (T'_n-T_m)(n-m)$$

the left side is the energy difference , the right side is the average work done by the tension force [average force times the distance]
this is what i can say ,,
:)
 
  • #10
Tulatalu said:
Extra energy= E(n)-E(m) = 1/2 x (T'n-Tm)

I think that is not the right answer ,,

the left side is an energy , while the right side is a force ,,,

Check the units of each side ,,,

Are they equal ??
 
  • #11
the left side is an energy , while the right side is a force
I thought the same thought at first, until I realized it (the n and the m) was a multiplication, not a subscript.

The formula stems from inserting T = k x and ds = dx in $$\int_0^n T\; ds = \int_0^n kx\; dx = \left [{1\over 2} k x^2 \right ]^n_0 = {1\over 2} kx\; x = {1\over 2} Tx$$

(I strongly prefer and recommend ## {1\over 2} kx^2 ## !)

Numerically there isn't much difference between the 'absent' and the 'right' multiple choice

[edit] the integral bounds look a bit stupid. lower bound is equilibrium position (T=0)
 
Last edited:

What is energy stored in a wire?

Energy stored in a wire refers to the potential energy that is stored within the atoms and molecules of the wire. This energy is stored in the form of electrical potential energy, as the electrons within the wire are held in place by the electric field created by the wire's voltage.

How is energy stored in a wire?

Energy is stored in a wire through the movement of electrons. When a voltage is applied to a wire, the electrons within the wire begin to move and create an electric current. As the electrons move, they build up potential energy due to their position in the electric field created by the wire's voltage.

What factors affect the amount of energy stored in a wire?

The amount of energy stored in a wire is affected by the voltage applied to the wire and the material properties of the wire, such as its resistance and capacitance. The length and thickness of the wire also play a role in determining the amount of energy stored.

How can energy stored in a wire be released?

The energy stored in a wire can be released by completing an electrical circuit. This allows the electrons to flow through the wire and use their potential energy to do work, such as powering a lightbulb or electronic device.

What are some practical applications of energy stored in wires?

The energy stored in wires is essential for many everyday technologies, including electricity and electronics. It allows us to power our homes, charge our phones, and run appliances. It is also used in more advanced applications, such as in medical devices and renewable energy systems.

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