### Elastic Potential Energy

- Energy in the
**elastic potential store**of an object is defined as:

**The energy stored in an elastic object when work is done on the object**

- This means that any object that can
**change shape**by stretching, bending or compressing (eg. springs, rubber bands)- When a spring is
**stretched**(or**compressed**), work is done on the spring which results in energy being**transferred to**the**elastic potential store**of the spring - When the spring is
**released**, energy is**transferred away from**its elastic potential store

- When a spring is

**How to determine the extension, e, of a stretched spring**

- The amount of elastic potential energy stored in a stretched spring can be calculated using the equation:

*E _{e}* = ½ ×

*k*×

*e*

^{2}- Where:
*E*= elastic potential energy in joules (J)_{e}*k*= spring constant in newtons per metre (N/m)*e*= extension in metres (m)

- The above equation assumes that the spring has not been stretched beyond its
**limit of proportionality**

**The spring on the right has been stretched beyond the limit of proportionality**

#### Worked Example

A mass is attached to the bottom of a hanging spring with a spring constant of 250 N/m. It stretches from 10.0 cm to 11.4 cm.Calculate the elastic energy stored by the stretched spring.

**Step 1: Determine the extension of the spring**

**Step 2: List the known quantities**

- Spring constant,
*k*= 250 N/m - Extension,
*e*= 1.4 cm = 0.014 m

- Spring constant,

**Step 3: Write out the elastic potential energy equation**

*E _{e}* = ½

*k*

*e*

^{2}**Step 4: Calculate the elastic potential energy**

*E _{e}* = ½ × 250 × (0.014)

^{2}= 0.0245 J

**Step 5: Round the answer to 2 significant figures**

*E _{e}* = 0.025 J

#### Exam Tip

Look out for units! If the question gives you units of cm for the length you **MUST** convert this into metres for the calculation to be correct.