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Hooke's Law & Elastic Potential Energy Investigation

Last updated over 4 years ago
19 questions
Note from the author:
In-class investigation of Hooke's Law, a derivation of Elastic Potential Energy, and graphical interpretation of Force vs. Stretch graph.
** Please copy and re-link data tables for your class to this assignment.
Hooke's Law & Elastic Potential Energy Investigation
Objective: During this investigation, you will demonstrate understanding of Elastic Potential Energy (The potential energy stored in something’s “springiness”) and Hooke’s Law by calculating the spring constant of a spring, and comparing a mass’s initial Potential Energy to its final Elastic Potential Energy.
Set up this simulation as shown in the screenshot above. (Simulation is linked here if you want to open it in a new tab to make it larger.)
Please look carefully at the Spring Constant 1 and Spring Contant 2 sliders.

Part 1
  • If you are in groups 1-3, please collect data using Spring 1. If you are in groups 4-6, please collect data using Spring 2
  • Please carefully align the 0 cm position of the ruler with the Natural Length line on the simulation. This is also commonly called the spring's "no load" position.
  • Create a table (on paper) with columns labeled “mass (g)”, "mass (kg), “displacement (cm)”, "displacement (m)", “weight (N)”. Your first entry row should be 0 mass, 0 displacement, and 0 weight. (remember: displacement is measured from the no-load position)
  • Hang a 50g mass on the spring. Carefully make sure that it comes to rest. Record your mass and displacement values in your table.
  • Repeat the previous step with 2 more masses, increasing in value (ie. 100g, 250g)
  • Multiply the value of each mass (in kilograms) by the acceleration due to gravity to obtain the force (in N) acting on the spring. (Remember "weight" is the force due to gravity, and Fg = mg.) Record the weights in your table.
1

Please use this link to graph Weight (force of gravity)(N) vs. Displacement from equilibrium (m) in Desmos.
Please upload a screenshot of your graph in the space below. Please also include the science equation for the line of best fit near the graph, and which spring your group used.

1

What does the slope of your line represent? (When you get to this point, ask Ms. McVay to present the class graphs).

1

Find the area under the Weight vs displacement graph. (Hint: how do you find the area of a triangle?)

1

What two quantities did you have to multiply together to get your answer?

1

What does the area under the line represent? (Look back to our notes at the very beginning of this unit to see what F and d have to do with energy.)
Check your answer with Ms. McVay

Class Discussion
1

What is the name of the law that we just found?

1

  • We graphed the the force that the mass exerts on the spring.
  • HOWEVER, Hooke's Law is intended to represent the force the SPRING exerts on the MASS.
  • Because springs (or elastic cords) exert a restoring force on an object as the spring or cord stretches (or compresses), the force is negative, opposing the applied force.

The equation for this law is written as:

Part 2
Now, select the "Energy" tab in the simulation, and set it up as shown below. Take special care to make Damping "None". Also, take special care to adjust the spring constant to match the one you investigated in Part 1. The slider will still be labelled "Spring Constant 1" no matter what. ¯\_(ツ)_/¯


  • Select the 100g mass. With the spring in its no-load (no stretching) position attach the mass to it. Drop the mass and find the lowest point to which the mass falls. (Try to pause the mass at its lowest point.) Use the movable red line to help you determine the lowest point (measured from where the mass connects to the spring). Do this several times until you are fairly sure of the point.
1

Measure the displacement (in meters) through which the mass stretched the spring while it was falling.

1

Calculate the change in potential energy (potential energy lost) by the mass as it fell. ∆GPE = mg∆h

1

While the mass was falling, what did the GPE turn in to? (Look at the energy bar charts to the left on the simulation. Compare the types of energy just before release, and the energy types just as the mass reaches the bottom of it's bounce.)

1

At the instant that the mass stops at its lowest point, how do you know it will turn around and spring back up? So, what type of energy must all of the GPE have turned into?

1

On the x-axis of your Weight vs. displacement graph, locate the point on the line of the graph which corresponds to the value of your displacement (answer to question 8). On the y-axis of your graph find the force that corresponds to this point.

1

Using these values for displacement and force, find the area under the line on your Weight vs. displacemnt graph, up to this point:

1

The area under a force vs displacement curve represents the work that was done on the mass. Does the value that you calculated match any other value from this lab?

The energy that an object attached to a stretched/compressed spring or elastic has is called Elastic Potential Energy.

STOP HERE and check in with Ms. McVay
Now, choose 5 more massess to test, and record their displacments in the data table linked here.
PLEASE MAKE YOUR OWN COPY OF THE TABLE BEFORE YOU EDIT IT!
1

Please use this link to graph Elastic Potential Energy vs. Displacement from equilibrium (m) in Desmos.
Please upload a screenshot of your graph in the space below. Please also include the science equation for the line of best fit near the graph, and which spring your group used.

1

How does the constant in your EPE vs. Displacement graph compare to the constant in your Weight vs. Displacement graph?

1

So... what do you think is the meaning of the constant in the EPE vs. Diplacement graph?

1

Then, what must be the general equation relating EPE and displacement?

Please head back into the main meeting to debrief as a whole class.
1

Write a brief summary of the investigation telling how it demonstrates the Law of Conservation of Energy.