If friend pull on a spring and stretch it, then you do work. The is because you are using aforce end a displacement. Her pull is the force and also the amount the you large the spring is the displacement.

You are watching: What is the stretch of the spring?

Since job-related is the transfer that energy, us must understand where the power was transferred.We say that the energy was transferred right into the spring. The work becomes stored energy in the spring. The workbecomes potential energy in the spring.

A spring have the right to be extended or compressed. The same math holds for extending as for compressing springs. We will certainly be mainly discussing energy as that is save in a spring once it is extended here; however, the same physics would apply for a spring when it is compressed.

As you have actually probably noticed from the over header, feather potential power is also called elastic potential energy.

Linear Springs

This conversation will be around linear springs, the simplest type of spring.

A linear spring is a spring wherein the pressure that stretches the feather is in straight proportionto the lot of stretch. The is, the pressure vs. Extension graph creates a straight, positive sloped heat thatpasses with the origin, choose this:


The slope that this graph is called the spring constant and also is symbolized through the letter k. Thespring consistent in the over graph is 20 Newtons per meter, or 20 N/m. This way that girlfriend would require 20 Newtonsof force to large the spring one meter, or 2 Newtons of pressure to stretch the feather 0.1 meter, and also so on.

Work Done extending The Spring

Let us say that in this conversation a force of F is important to big the feather to an expansion of x.

We see listed below that this force F and the relatedextension x have been significant on the graph. Likewise detailed isthe area under the graph for this situation.


The area under this graph of pressure vs. Extension is in Joules, units of energy. This is becausethe area is in units of Newtons (vertically) time meters (horizontally).

Do not forget that systems of occupational are devices of pressure times devices of displacement, or units ofNewtons times units of meters. And also units of work-related are devices of the deliver of energy, the is, they space units ofenergy, or Joules.

So, the area under this graph symbolizes energy. This area is the occupational done come stretch the spring.

Now, occupational is the carry of energy. ~ the spring has actually been stretched, and also work has actually been done,to where has the power been transferred? us say the it has become potential power in the spring. The is, theenergy has been save on computer in the spring. Therefore, the lot of power symbolized through the area under the over graphis the power that has been stored in the spring. That is the potential power of the spring.

This area deserve to be calculated. That is shaped choose a triangle; so, the area is one half times itsheight time its base. We have:

Area under graph = (0.5)(F)(x)

This area is the energy stored in the spring. The symbol because that the power stored in the springcould be Us. The "U" means potential energy and the subscript"s" stands for spring. So, now we have:

Us= (0.5)(F)(x)

The spring is a direct spring where the stretching force is directly proportional come the extension,as stated above. This, again, deserve to be stated as:

F = kx

Placing this substitution because that F in the over formula for us we get:

Us= (0.5)(kx)(x)

Removing the parentheses and noticing that x times x is x2, we have:

Us= 0.5kx2

This last formula reads: The potential energy of a spring, or the energy stored in a spring,equals one fifty percent times the spring constant times the square the the extension. This is just how to calculate how muchenergy is save on computer in a spring.

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Work excellent Compressing The Spring

Some linear springs store power through compression, quite thanextension. Because that example, once you compress the feather in a commonjack-in-the-box toy, you do job-related on the spring, and that occupational is save asenergy in the spring. Later, when the jack-in-the-box pops, the energycomes the end of storage.


The formula for the amount of power stored in a linear spring early tocompression is the exact same as the one because that extension: