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Elastic
potential
energy
Objectives
- Investigate examples of elastic potential energy.
- Provide or identify a conceptual definition of the spring constant.
- Calculate the potential energy, spring constant, or deflection of a spring using the elastic potential energy equation.
Assessment
- What do each of the symbols mean in this equation: Ep = Ā½ kx^2?
- Translate the equation EP = Ā½ kx^2 into a sentence with the same meaning.
- How much elastic potential energy is stored in a 100 N/m spring that is compressed 0.10 meters?
- A spring has an elastic potential energy of 100 J when compressed 0.10 m. What is its spring constant?
- How far is a spring extended if it has 1.0 J of elastic potential energy and its spring constant is 1,000 N/m?
Assessment
- Are these statements about the spring constant true or false? a) ___ The spring constant is a measure of the stiffness of the spring. b) ___ The spring constant tells you how many newtons of force it ā¦ā¦takes to stretch the spring one meter. c) ___ If a spring stretches easily, it has a high spring constant. d) ___ The spring constant of a spring varies with x , the amount of ā¦ā¦.stretch or compression of the spring.
Physics terms
- elastic potential energy
- spring constant
Equations
The elastic potential energy of a spring is one half the product of its spring constant multiplied by the square of its extension or compression. or
Energy may be stored in a system when work is done on the system.
Work and energy Springs
free length
Force and deformation
x
When you apply a force to a spring, it deforms.
Work
x
The applied force does work on the spring. The change in the springās length is called the deformation, x.
Elastic potential energy
x
The work done to stretch or compress the spring is stored in the spring as elastic potential energy.
Equations
The elastic potential energy of a spring is one half the product of its spring constant multiplied by the square of its deformation.
x
If the spring constant is 200 N/m and the spring is deflected by 1.0 cm, how much energy is stored?
Engaging with the concepts
200 Elastic potential energy
If the spring constant is 200 N/m and the spring is deflected by 1.0 cm, how much energy is stored?
Engaging with the concepts
200 Elastic potential energy only 0.01 J! 0.01 0. How strong a spring is needed to get 1.0 joule of energy from a 1.0 cm deflection?
Engaging with the concepts
Spring constant 1.0 0. How strong a spring is needed to get 1.0 joule of energy from a 1.0 cm deflection?
Engaging with the concepts
Spring constant 1.0 0. k = 20,000 N/m 20000 How strong a spring is needed to get 1.0 joule of energy from a 1.0 cm deflection?
Engaging with the concepts
Spring constant 1.0 20000 0. This is a pretty stiff spring! What might it be used for? k = 20,000 N/m
Perfect for a mountain bike!
Inside the fork tube is a spring with a spring constant of roughly 20,000 N/m.
Calculating force
x 1 cm How much force is needed to compress this spring one centimeter? k = 20,000 N/m
Calculating force
x 1 cm How much force is needed to compress this spring one centimeter? k = 20,000 N/m
Hookeās law
x 1 cm
Fspring Fapplied
The spring pushes back in the opposite direction with a force of -200 N. How much work must be done to stretch a spring with k = 1.0 N/m by 25 cm?
Engaging with the concepts
Elastic potential energy
How much work must be done to stretch a spring with k = 1.0 N/m by 25 cm?
Engaging with the concepts
Elastic potential energy
Only 0.03 J! This is a very weak springā looser than a SlinkyĀ®.
How about a k = 100 N/m spring? How much work must be done to stretch a spring with k = 100 N/m by 25 cm?
Engaging with the concepts
100 Elastic potential energy
How does the stored energy change if the displacement is doubled? The energy increases by a factor of four (2^2 ). What happens if the displacement is tripled?
Engaging with the concepts
100 Elastic potential energy 2
Elastic potential energy
Where does this formula come from?
Elastic potential energy
Hypothesis: The elastic potential energy is derived from the work done to deform the spring from its free length...
Work
Work is force times distance. W = Fd W = Fd F = -kx
Hookeās law
W = Fd
Hookeās law
F = -kx where k is the spring constant in N/m...
F = -kx W = Fd
Hookeās law
where k is the spring constant in N/m... and x is the change in length of the spring in meters.
Force vs. distance
BUT the force F from a spring is not constant. On a graph of force vs. distance it is a line of constant slope.
Force vs. distance
BUT the force F from a spring is not constant. It starts at zero and increases as the deformation x increases.
Force vs. distance
The area on this graph...
Force vs. distance
The area on this graph is force times distance... The area on this graph is force times distance which is the work done!
Force vs. distance
Elastic potential energy
This expression is true for more than just springs!
Elastic potential energy
Elastic potential energy is stored in all objects that can deform and spring back to their original shape.
Elastic potential energy
such as a rubber band...
Typical elastic potential energies
Assessment
- What do each of the symbols mean in this equation: Ep = Ā½ kx^2?
Assessment
- What do each of the symbols mean in this equation: Ep = Ā½ kx^2? Ep = the elastic potential energy k = the spring constant in N/m x = the displacement of the end of the spring in meters
- Translate the equation EP = Ā½ kx^2 into a sentence with the same meaning.
Assessment
- What do each of the symbols mean in this equation: Ep = Ā½ kx^2? Ep = the elastic potential energy k = the spring constant in N/m x = the displacement of the end of the spring in meters
- Translate the equation EP = Ā½ kx^2 into a sentence with the same meaning. The elastic potential energy of a spring is one half the product of its spring constant multiplied by the square of its extension or compression distance.
- How much elastic potential energy is stored in a 100 N/m spring that is compressed 0.10 meters?
Assessment
- What do each of the symbols mean in this equation: Ep = Ā½ kx^2? Ep = the elastic potential energy k = the spring constant in N/m x = the displacement of the end of the spring in meters
- Translate the equation EP = Ā½ kx^2 into a sentence with the same meaning. The elastic potential energy of a spring is one half the product of its spring constant multiplied by the square of its extension or compression distance.
- How much elastic potential energy is stored in a 100 N/m spring that is compressed 0.10 meters? 0.50 J
Assessment
- A spring has an elastic potential energy of 100 J when compressed 0.10 m. What is its spring constant?
Assessment
- A spring has an elastic potential energy of 100 J when compressed 0.10 m. What is its spring constant?
- How far is a spring extended if it has 1.0 J of elastic potential energy and its spring constant is 1,000 N/m? k = 20,000 N/m
Assessment
- A spring has an elastic potential energy of 100 J when compressed 0.10 m. What is its spring constant?
- How far is a spring extended if it has 1.0 J of elastic potential energy and its spring constant is 1,000 N/m? 0.045 m or 4.5 cm k = 20,000 N/m
Assessment
- Are these statements about the spring constant true or false? a) ___ The spring constant is a measure of the stiffness of the spring. b) ___ The spring constant tells you how many newtons of force it ā¦ā¦takes to stretch the spring one meter. c) ___ If a spring stretches easily, it has a high spring constant. d) ___ The spring constant of a spring varies with x , the amount of ā¦ā¦.stretch or compression of the spring.
