it takes 12.0j to stretch a spring 3.00cm. what is the force necessary to do this?

Spring Potential Energy (Rubberband Potential Energy)

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Definition of Leap Potential Free energy (Rubberband Potential Energy)

If you pull on a leap and stretch information technology, then you do work . That is because you are applying a force over a displacement. Your pull is the force and the amount that y'all stretch the spring is the displacement.

Since work is the transfer of energy , we must understand where the energy was transferred. We say that the free energy was transferred into the bound. The work becomes stored free energy in the spring. The piece of work becomes potential energy in the leap.

A spring can be stretched or compressed. The aforementioned mathematics holds for stretching every bit for compressing springs. We will exist primarily discussing free energy equally it is stored in a spring when it is stretched here; withal, the aforementioned physics would apply for a leap when it is compressed.

Equally yous have probably noticed from the above header, bound potential energy is also chosen elastic potential energy.

Linear Springs

This word will be about linear springs, the simplest type of spring.

A linear spring is a spring where the forcefulness that stretches the leap is in direct proportion to the amount of stretch. That is, the force vs. extension graph forms a directly, positively sloped line that passes through the origin, similar this:

The slope of this graph is called the leap constant and is symbolized by the letter thousand . The spring constant in the higher up graph is 20 Newtons per meter, or xx Due north/m. This means that you lot would need 20 Newtons of force to stretch the jump one meter, or 2 Newtons of force to stretch the spring 0.1 meter, and so on.

Work Washed Stretching The Bound

Allow us say that in this discussion a forcefulness of F is necessary to stretch the leap to an extension of x.

We meet below that this force F and the related extension 10 take been marked on the graph. Also detailed is the expanse under the graph for this state of affairs.

The expanse under this graph of force vs. extension is in Joules, units of energy. This is because the area is in units of Newtons (vertically) times meters (horizontally).

Practise not forget that units of work are units of force times units of displacement, or units of Newtons times units of meters. And units of work are units of the transfer of energy, that is, they are units of energy, or Joules.

So, the surface area under this graph symbolizes free energy. This area is the work done to stretch the leap.

At present, piece of work is the transfer of energy. Afterward the spring has been stretched, and work has been done, to where has the energy been transferred? We say that it has become potential energy in the bound. That is, the energy has been stored in the leap. Therefore, the amount of energy symbolized past the area under the to a higher place graph is the energy that has been stored in the spring. It is the potential energy of the spring.

This area can be calculated. It is shaped like a triangle; so, its expanse is one half times its superlative times its base. Nosotros have:

Area nether graph = (0.5)(F)(10)

This expanse is the energy stored in the jump. The symbol for the free energy stored in the spring could be U_{due south}. The 'U' stands for potential energy and the subscript 's' stands for spring. Then, now we have:

U_southward= (0.5)(F)(x)

The spring is a linear leap where the stretching force is directly proportional to the extension, equally mentioned to a higher place. This, again, tin exist stated every bit:

F = kx

Placing this commutation for F in the above formula for U_s we get:

U_s= (0.5)(kx)(10)

Removing the parentheses and noticing that ten times x is 10^two, we have:

U_s= 0.5kx ⁱⁱ

This concluding formula reads: The potential energy of a spring, or the energy stored in a bound, equals one half times the spring constant times the square of the extension. This is how to calculate how much energy is stored in a spring.

Work Done Compressing The Spring

Some linear springs store free energy through compression, rather than extension. For example, when you lot compress the leap in a mutual jack-in-the-box toy, you do work on the spring, and that work is stored every bit energy in the spring. Later, when the jack-in-the-box pops, that energy comes out of storage.

The formula for the amount of energy stored in a linear spring due to pinch is the aforementioned every bit the 1 for extension:

U_south= 0.5kx ²

Questions virtually Spring Potential Energy

Here are a few issues over the above equations.

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Run into also:

Mass on a Leap

Scramble Puzzle

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