# Elastic Potential Energy problem

In summary, the spring must be stretched 0.122 meters for its potential energy to be 47 J. This can be found by setting up the equation 47 = 1/2 (30000)(x)^2 and solving for x.

## Homework Statement

A spring has a force constant of 30000 N/m. How far must it be stretched for it's potential energy to be 47 J? Answer in units of m.

Us= 1/2k(∆x)^2

## The Attempt at a Solution

47= 1/2 (30000)(x)^2
47=15000(x)^2
-14953= x^2
√14953= 122.28

## The Attempt at a Solution

47= 1/2 (30000)(x)^2
47=15000(x)^2
So far, so good.
-14953= x^2
Oops... you subtracted instead of divided. Redo this step.

47= 1/2 (30000)(x)^2
47=15000(x)^2
-14953= x^2
√14953= 122.28
You subtracted when you should have divided.

So you are saying to do 47/15000?
that would equal .0031... then would i do the square root of it or leave it at that?

ohhh nvm i did that on one of my attempts but i forgot to put .0 in front of .0557=] Thanks a lot. I apperciate it!

## What is elastic potential energy?

Elastic potential energy is the energy stored in an object when it is stretched or compressed. It is a type of potential energy that is related to an object's elasticity, or its ability to return to its original shape after being deformed.

## How is elastic potential energy calculated?

Elastic potential energy is calculated using the formula PE = 1/2 * k * x^2, where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position. The spring constant is a measure of how stiff the spring is, and it varies depending on the material and design of the spring.

## What factors affect the amount of elastic potential energy in a system?

The amount of elastic potential energy in a system is affected by the spring constant, the amount of stretch or compression, and the distance the spring is stretched or compressed. The type of material the spring is made of and the design of the spring can also impact the amount of elastic potential energy.

## What is the difference between elastic potential energy and elastic potential energy problem?

Elastic potential energy refers to the energy stored in an object due to its elasticity, while elastic potential energy problem refers to a specific type of physics problem that involves calculating the amount of elastic potential energy in a system. These problems often involve springs, but can also involve other elastic materials such as rubber bands or bungee cords.

## How is elastic potential energy used in real life?

Elastic potential energy is used in many applications, including in sports equipment such as trampolines and diving boards, as well as in everyday objects such as door hinges and shock absorbers. It is also used in more advanced technologies, such as in the design of prosthetic limbs and in renewable energy sources such as wind turbines.

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