2. What energy is propelling these teenagers into the air?
Forces and energy in springs
Quick Starter
What energy is propelling these teenagers into the air?
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3. What energy is propelling these teenagers into the air?
Forces and energy in springs
Quick Starter
What energy is propelling these teenagers into the air?
The trampoline is an elastic canvas suspended from a frame by lots of springs
Hint X
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4. What energy is propelling these teenagers into the air?
Forces and energy in springs
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What energy is propelling these teenagers into the air?
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5. Elastic potential energy
Forces and energy in springs
Quick Starter
Elastic potential energy
The teenagers supply the original energy by jumping from a standing start
As they fall back they push the trampoline down, the springs extend and the energy is transferred into elastic potential energy, ready to propel them back up as the springs return
This group of teenagers need to co-ordinate their jumping, however, so that they get a bigger spring back
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6. Stretching Materials and Storing Elastic Energy

7. extension
force

8. Elastic limit for springs
If a spring is stretched far enough, it reaches the limit of proportionality and then the elastic limit.
The limit of proportionality is a point beyond which behaviour no longer conforms to Hooke’s law.
The elastic limit is a point beyond which the spring will no longer return to its original shape when the force is removed.
force
Elasticity is the ability to regain shape after deforming forces are removed.
extension

10. Stretching Materials and Storing Elastic Energy
Learning Objectives:
Calculate work done in stretching (or, the amount of elastic potential energy stored in a stretched object).
Describe the difference between a linear and nonlinear relationship for force and extension.

11. E = F x d Calculating Work Done
How do we calculate the work done while moving an object?
Remember: Work Done is equal to Energy Transferred
E = F x d
E = energy transferred / work done (J)
F = force (N)
D = distance (m)
Why can’t we use this equation for calculating the energy used to stretch a spring?
The force from a spring changes as we extend it.

12. Applying the Work Done equation to a spring.
Imagine you apply a constant force of 5N to a box an object and you move it a distance of 3m. On a graph it would look like this…..
Distance
Force 5N 3m
Work done = force x distance
15J = N x m
This is the same as the area under the graph.
So, work done is equal to the area under the line of a force-distance graph.
This is the same for force-extension graph for a spring.

13. Applying the Work Done Equation to a Spring.
The area under the line of a force-extension for a spring is a triangle which is half the area of the previous graph, so:
Work done on a spring = x F x e
Extension
Force 5N 3m
How much energy is stored in the spring in this graph?
E = x 5N x 3m = 7.5J

14. E = 0.5 x F x e E = energy/work done (J),
F = force (N), e = extension (m)
E = x F x e
A spring is extended by 0.8m at which point it pulls back with 6N. How much energy is stored in the spring?
What is the minimum amount of work that must be done to stretch the spring to this point? Explain your answer.
50J of energy is used to pull a spring 4m. What force will the spring pull back with at this point?
Extension
What is the spring constant in Q1?
What is the spring constant in Q2?
0.5 x 6N x 0.8m = 2.4J
2.4J
Work done = energy transferred.
50J (0.5 x 4m) = 25N
6N m = 7.5N/m
25N m = N/m

15. Using the Spring Constant to calculate the Energy in Spring
Work done on a spring = x F x e
But Hooke’s Law tells us that force is equal to spring constant multiplied by extension
F = k x e
So, if we replace (substitute) F with k x e we get…...
Work done on a spring = x k x e x e
Which simplifies to….
Work done on a spring = x k x e2

16. E = 0.5 x k x e2 k = spring constant (N/m) e = extension (m)
E = energy/work done (J),
k = spring constant (N/m) e = extension (m)
E = x k x e2
A spring has a spring constant of 3.5N/m. It is extended by 0.7m. How much energy is stored in the spring?
A 0.1m spring with a spring constant of 8.1 N/m is stretched to 0.6m. How much energy is stored in the spring?
A spring is stretched to 3m, it’s original length is 0.5m and it has a spring constant of 24N/m. How much work must be done to stretch the spring to this point?
Extension
4. How much would you need to extend a spring with spring constant 6.4N/m for it to store 4.6 J
0.5 x x =
0.875 J
0.5 x x = J
0.5 x 24 x =
75 J
√( (0.5 x 6.4)) =
1.2m