# 1.1.6 KE, GPE & EPE

### KE, GPE & EPE

• When a vertical spring is extended and contracted, its energy is converted into other forms
• Although the total energy of the spring will remain constant, it will have changing amounts of:
• Elastic potential energy (EPE)
• Kinetic energy (KE)
• Gravitational potential energy (GPE)
• When a vertical mass is hanging on a spring and it moves up and down, its energy will convert between the three in various amounts Energy changes when a spring is stretched

• At position A:
• The spring has some EPE since it is slightly compressed
• Its KE is zero since it is stationary
• Its GPE is at a maximum because the mass is at its highest point
• At position B:
• The spring has some EPE since it is slightly stretched
• Its KE is at a maximum as it passes through its resting position at its maximum speed
• It has some GPE since the mass is still above the ground
• At position C:
• The spring has its maximum EPE because it is at its maximum extension
• Its KE is zero since it is stationary
• Its GPE is at a minimum because it is at its lowest point above the Earth’s surface

#### Worked Example

The diagram below shows a student before and after a bungee jump. The bungee cord has an unstretched length of 30.0 m. The mass of the student is 60.0 kg. The gravitational field strength is 9.8 N / kg.

Calculate:

a) The change in GPE at 30.0 m

b) The maximum change in GPE

c) The speed of the student after falling 30.0 m if 90% of the GPE is transferred to the student’s KE store

d) The spring constant of the bungee cord if all the GPE is transferred to the bungee cord’s elastic store

Part (a)

Step 1: List the known quantities

• Mass of the student, m = 60.0 kg
• Gravitational field strength, g = 9.8 N/kg
• Change in height, h = 30.0 m

Step 2: Write out the equation for GPE

GPE = mgh

Step 3: Calculate the change in GPE

GPE = 60 × 9.8 × 30 = 17 640 J

Part (b)

Step 1: List the known quantities

• Mass of the student, m = 60.0 kg
• Gravitational field strength, g = 9.8 N/kg
• Maximum change in height, h = 75.0 m

Step 2: Calculate the maximum change in GPE

Max. GPE = 60 × 9.8 × 75 = 44 100 J

Part (c)

Step 1: List the known quantities

• Mass of the student, m = 60.0 kg
• KE at 30.0 m = 90% change in GPE = 0.9 × 17 640 = 15 876 J

Step 2: Write out the equation for KE

KE = ½ mv2

Step 3: Rearrange for speed, v Step 4: Calculate the speed Part (d)

Step 1: List the known quantities

• EPE at 75.0 m, Ee = Max. GPE = 44 100 J
• Extension of the bungee cord, e = 75.0 – 30.0 = 45.0 m

Step 2: Write out the equation for EPE

Ee = ½ ke2

Step 3: Rearrange for spring constant, k Step 4: Calculate the spring constant #### Exam Tip

If a question asks you to “state” a value, you do not need to carry out a calculation: The answer will almost certainly be a number either from a previous answer or which was given somewhere in the question.

For example, if you have just calculated the gravitational potential energy of an object and are then asked to state the kinetic energy a moment later, the answers are very likely to be the same.

The terms “gravitational store” and “gravitational potential energy” mean the same thing and are interchangeable. Likewise for “kinetic store” and “kinetic energy”, and “elastic store” and “elastic potential energy ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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