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

The spring with twice spring constant has to compress or 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.

                                                                …… (1)

Here, 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.

                           …… (2)

Here, 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).

Taking square root both the sides in above equation,

The above equation can be written as,

So, spring of spring constant is compressed 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.

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