An object is elastic if

• it is deformed when a force is applied, and
• it returns to its origin shape when the force is removed

Our example of an elastic object will be a spring. You can apply a force that stretches or compresses it. The force that opposes the applied force is called the restoring force. If the restoring force is proportional to the amount of deformation, the object is said to obey Hooke's law.

Static Case

• Using a tall ringstand, clamps, etc. set a spring hanging vertically as shown below. Recall the motion sensor must be at least 0.50 m from the object being measured.
  

• When setting up the motion sensor, select a trigger rate of 60 Hz.
• We will apply known weights to the hanger and note the displacement.
• It is not convenient to measure displacement x. What we will measure instead is L, the distance from the bottom of the hanger to a motion sensor on the lab table.
• It is crucial that you understand that this length L is not the displacement x that appears in Hooke's law
  F = - k x,

  However, L and x are related. What is the relationship? (Note that even with the just the hanger, there is a bit of displacement from the weight of the hanger.)

• Add masses to the hanger: 50 g, 100 g, 150 g, 200 g and 250 g and note the distance L.
• Calculate the "applied forces" (the weights, hanger included) and make a plot of Applied Force versus L.
• Fit it to a straight line. What is the interpretation of the slope? What is the interpretation of the x intercept? What is the interpretation of the y intercept?
• Find the x's that correspond to your L's.
• The proportionality constant k is called the spring constant. What is the spring constant for this spring? What are the units (dimensions) of the spring constant?
• What is the meaning of the minus sign in Hooke's law?

Kinetic Case

• Pull the mass down a few centimeters and release.
• Record the motion.
• Build an Excel spreadsheet similar to last week's lab.  There should be a number of rows with each row containing: position, position time, velocity, velocity time,  the adjustments so that velocity and position are measured at the same time, calculate all kinetic energy terms, all potential energy terms, total mechanical energy.
• Gravitational potential energy can be measured relative to "any" reference point -- use the motion detector's postion.
• BUT, the spring's potential energy must be measured relative to its equilibrium position.
• Make a plot of position versus time and velocity versus time (2 items on one graph).
• Make a plot of total energy versus time and gravitational potential energy versus time (2 items on one graph)
• Does the spring have kinetic energy? Does the spring have gravitational potential energy?