Elastic Potential Energy

Elastic Potential Energy and the Spring Constant

AP Physics I -- Pickert

Multiple Select

An object initially at rest falls from a height H until it reaches the ground. Two of the following energy bar charts represent the kinetic energy K and gravitational potential energy Ug of the object-Earth system at two positions. The first position is when the object is initially released, and the second position is when the object is halfway between its release point and the ground. Which two charts could represent the mechanical energy of the object-Earth system? Select two answers.

• h

Multiple Choice

An amusement park ride has two identical carriages that revolve around the center of the ride’s axle, as shown in the figure. Both carts travel at a constant tangential speed at all points along the circular path. At what position is the total mechanical energy of the cart-cart-Earth system at its maximum value?

• The total energy of the Earth-Ferris wheel ride system is constant.

Objectives: I can...

-Emphasis on designing a controlled experiment where data is collected on a single dependent and independent variable

​🌟Design an experiment to determine the spring constant of a spring

-Emphasis on using energy conservation to predict quantities of motion.

🌟Determine the potential energy stored in a spring

Elastic Potential Energy

Energy that is stored as a result of the stretch or compression of a material.

Essentially, a measure of the "stiffness" of a spring.

Higher spring constant (k) means that more force is needed to stretch or compress the spring.

​

​What is the spring constant?

Hooke's Law

We can illustrate the spring constant through Hooke's Law, which relates the force exerted by a spring to the amount it is stretched/compressed.

Open Ended

Using basic algebra, rearrange the Hooke's Law equation to solve for the spring constant, k

Spring constants are measured in "Newtons-per-Meter" (N/m)

​

​This agrees with our earlier definition:

​This means that a higher spring constant means that a larger force (newtons) is required to stretch or compress the spring a certain distance (meter)

This means that springs do NOT exert a constant force: it varies with how much the spring's length changes.

​

​Slight problem:

​This isn't a major problem, it just means that if we want to find quantities of motion, it is often easier to use energy conservation.

​For Example...

​Now for the Experiment:

Open Ended

Describe the energy transformation that took place in this process. What form of energy did it start with? What did it end with? What forms did it take along the way?

​Goal:

​Design an experiment to determine the spring constant of the spring in the jumper toy.

• What data do we need to collect?

• How will we collect the data?

• How will we analyze the data?

I'm trying to find the spring constant...

What do I need to measure? How would I do that?

​(Δ )

Multiple Choice

In order for the spring toy to work, it must be compressed a specific distance for the suction cup to attach. This would make the change in spring length...

• the independent variable

• the dependent variable

• a constant in the experiment

• irrelevant

Next step:

Now I need another measurement. The spring will always be compressed the same distance each time. Δx does not change.

We can't directly measure spring potential energy, but I can relate the energy stored by the spring to another form of energy...

Using energy conservation, I can set these two potential energies equal to each other

​Constant

​What is my independent variable? (changeable)

What is my dependent variable? (measurable)

Match

Using what we've described so far, identify the parts of the experiment:

• gravitational field strength, "g"

• change in spring length

• maximum height reached by spring toy

• mass of spring toy system

Constant

Constant

Dependent Variable

Independent Variable

• Constant

• Constant

• Dependent Variable

• Independent Variable

How will we collect data?

What makes a good procedure?

• Setup

• Measurements

• Equipment

• Repeatability

Setup:

-This is accomplished by pushing the toy down until the suction cup holds.

​Set up a jumper toy with its spring compressed on a table while keeping compression distance constant.

Match

Measurements. Match the instruments with the quantities being measured in this experiment.

• scale

• centimeter ruler

• meter stick

mass of spring toy

distance spring is compressed

maximum height of toy jump

• mass of spring toy

• distance spring is compressed

• maximum height of toy jump

​Sample data:

​What graph can we make with this data? Can we use the data as is or might we need to transform it?

How do we interpret it? Let's try making a graph of this data (on excel or in google sheets) and find out!