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
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
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 mStep 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 kgKE 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, vMultiply 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, 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
Multiply both sides by 2: ke2 = 2 x Ee
Divide both sides by e2:
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