KE, GPE & EPE | Physics for Grade 10 PDF Download

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

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

Multiply both sides by 2: mv² = 2 x KE

Divide both sides by m:

Take the square root of both sides:

Step 4: Calculate the speed

Part (d)
Step 1: List the known quantities

• EPE at 75.0 m, E_e = 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

E_e = ½ ke²

Step 3: Rearrange for spring constant, k
Multiply both sides by 2: ke² = 2 x E_e
Divide both sides by e²: