Physics, 28.01.2020 13:49 cxttiemsp021

How far must you compress a spring with twice the spring constant to store the same amount of energy?

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Answer from: misk980

The spring with twice spring constant has to compress $\boxed{\frac{1}{{\sqrt 2 }}}$ or $\boxed{0.707}$ times the compression of spring of the given spring constant.

Further explanation:

Consider a spring of spring constant k is compressed by length .

Then amount of energy stored in the spring 1 can be calculated as.

${E_1}=\dfrac{1}{2}k{x^2}$ …… (1)

Here, ${E_1}$ is the amount of energy store in spring 1 due to its compression.

Now, another spring with spring constant as given is compressed by length .

Then the energy stored in the spring due to its compression can be calculated as.

${E_2}=\dfrac{1}{2}\left( {2k}\right){y^2}$ …… (2)

Here, ${E_2}$ is the amount of energy store in spring 2 due to its compression.

As given in the question energy store in both the spring is same. So, equate equation (1) and equation (2).

$\begin{aligned}\frac{1}{2}k{x^2}&=\frac{1}{2}\left( {2k} \right){y^2}\\k{x^2}&=\left( {2k}\right){y^2}\\\frac{1}{2}{x^2}&={y^2}\\\end{aligned}$

Taking square root both the sides in above equation,

$\begin{gathered}\sqrt {\frac{1}{2}{x^2}}=\sqrt {{y^2}}\\\frac{x}{{\sqrt 2 }} = y \\ \end{gathered}$

The above equation can be written as,

$\boxed{y=\frac{x}{{\sqrt 2 }}}$

So, spring of spring constant is compressed $\dfrac{1}{{\sqrt 2 }}$ times the compression of spring of spring constant .

Learn more:

1. Conservation of energy: link.

2. Motion under friction link.

3. Conservation of momentum link.

Answer detail:

Grade: Senior school

Chapter: Work and Energy

Subject: Physics

Keywords:

Compression, expansion, spring, twice the spring constant, same amount of energy, spring constant, energy, potential energy, kinetic energy, force, Hook’s law.

Answer from: Quest

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electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia

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