Hooke's Law

In this lab you will investigate Hooke's Law, which states that the force exerted on or by a spring is in direct proportion to the stretch of the spring from equilibrium. With one end of the spring fixed, we define the other end to have position x. For simplicity, we define x = 0 to be the "equilibrium position". It is the position of the end of the spring when no force is applied. With this simplification, Hooke's Law can be expressed as

Fs = -kx    

where Fs is the forced exerted by the spring, k is the spring constant, and x is displacement from the equilibrium position. The minus sign reflects the fact that the force the spring exerts is always in the direction back towards equilibrium. The force exerted on the spring is F = +kx.

Although Hooke's Law was specifically formulated for springs, one of the purposes of this lab is to show that its application is more universal. The displacement response to an applied load will be determined for three objects, all different in material composition and shape. For each case, you will plot the force vs the displacement and determine whether or not the response obeys Hooke's Law.

A. Metal Spring

A metal wire exhibits linear stretching under a load, provided the load does not exceed the metal's elastic limit. However, the amount of stretch is quite small for even a thin wire and a large load. (A one meter long steel wire with a diameter of 1 mm will stetch only about 1 mm under a 30 lb load.) A spring can be constructed from a wire by bending it into a coil. A modest stretch in the wire itself produces a much larger stretch in the spring and can be easily measured. (In most cases, the wire is coiled during the forging process while the wire is very hot and malleable. But you can easily make a spring by wrapping a piece of copper wire around a cylinder.)

Procedure:

  1. Hang the spring and a 50 gm hanger from a support with sufficient space below to allow for full extension of the spring and hanger. Your lab instructor will help you determine an appropriate location.
  2. Place a meter stick vertically near, but not touching, the spring and hanger. Note the position of the bottom of the hanger. This will serve as the equilibrium position.
  3. Add 50 grams to the hanger. In a table. record the new position and total mass. Continue this process for a total of 10 sets of data. (Note: Your instructor may suggest other mass increments.)
  4. In the same table, calculate the force exerted on the spring (w = mg) in units of Newtons.

Report:

  1. Plot the force vs the displacement. The data should lie approximately along a straight line.
  2. Make qualitative comments about the linearity of the data.
  3. Fit a line to the data and determine the spring constant from the slope of the F vs x plot.

 

B. Wood Beam

In this portion of the laboratory you will determine the behavior of a standard 2 by 4 beam (2x4) under flexural stress resulting from a point load at the center of the beam. Each student will use their own weight as a point force applied to the center of a 2x4. The 2x4 is supported at each end.

Procedure:

  1. Mark the center of the 2x4. Measure and record the vertical distance from the floor to the upper surface of the beam at the center. This will be the initial equilibrium position from which central deflection of the beam will be measured. *

  2. Each student in the class will stand at the center of the beam on one foot. (Classmates should help the student to maintain balance while the distance from the floor to the beam is measured.) Record the distance from the floor to the top of the 2x4 and find the mass (in kg) of the student with the bathroom scales provided. Record both these numbers in the table provided at the chalkboard. Remember to copy the completed data set before leaving the lab.

    (*Note: There are many suitable alternative methods of measuring the central beam deflection.)

Report:

  1. Plot the load vs the deflection.
  2. Make qualitative comments about the linearity of the data. Specifically, does the beam deflection follow Hooke's Law?

 

C. Rubber Band

Finally, you will examine the stretch of a rubber band. True rubber is a natural product produced from the sap of the rubber tree. (The rubber band provided may be made from a similar manufactured substance.)

Procedure:

  1. Fix the rubber band to the support and attach the spring scale to the other end.

  2. From the spring scale, determine 10 values of force that you will apply to the rubber band. Determine a consistent location from which to measure the stretch of the rubber band.

  3. Make 10 measurements of the force and resulting stretch of the rubber band provided.

Report:

  1. Plot the force vs the stretch.
  2. Make qualitative comments about the linearity of the data. Specifically, does the response of the rubber band to an applied force follow Hooke's Law?