Hooke's Law and Simple Harmonic Motion        Name:______________________________

Partner(s):________________________    Course:______________    Time:____________

Purpose: To investigate Hooke’s law and determine the spring constants of elastic springs.

Apparatus: 3 springs, meter stick, stand w/clamp, mass set, and mass hanger.

Theory: Think about stretching a spring. The more stretching force you apply, the more stretch you get. Robert Hooke (1635-1703), a British physicist, discovered this empirical relationship between the stretching force and the stretch (x), known as Hooke’s law.                                                                                                 

Hooke's law is given by,    Stretching Force = (Spring constant) X Stretch.

Spring constant can be calculated by,    Spring constant = k = (Stretching Force)/Stretch.

The stretching force is provided by the added mass. You can also plot Stretching Force VERSUS Stretch.

Hooke’s law is verified when there is a linear relationship between Stretching Force & Stretch.

The Spring Constant is given by the slope.

Procedure:

1. Attach the mass hanger to the hard spring and hang it from the clamp.

2. Set up the meter stick such that the stretch is zero when there is no mass in the hanger.

3. Add 250-g of mass, measure the stretch, and record your data.

4. Measure the stretches for other added masses and complete the data table.

5. Repeat 1-4 for the other two springs.

I. "Hard" spring.

Start with added mass of 250-g, and increase it by 250-g each time.

Plot a graph added mass Vs. stretch, and find the slope.

II. "Medium" spring.

Start with added mass of 100-g and increase it by 100-g each time.

Plot the above data also on the earlier graph and find the slope.

III. "Light" spring.

Start with added mass of 10-g and increase it by 10-g each time.

Plot the above data also on the earlier graph and find the slope.

Attach the hard copy of your graph and then attach your conclusion page.

Include the following in your conclusion:

1. State whether Hooke’s law is verified or not.

2. Comment about how the spring constant changes as the stretching force & stretch increases.

3. List the values of spring constants you determined from the slopes.

4. Sources for errors and how to correct them.

B. Hooke's law with a force sensor 

Apparatus: PC, interface, force sensor, medium spring, mass set, mass hanger, stand w/clamp, and meter stick.

Procedure:        

1) Make sure that the power is turned on to the ScienceWorkshop750 interface.

2) Connect the Force sensor to analog port A.

3) Mount the force sensor on a stand so that it hangs with the hook pointed down.  

4) Open DataStudio, select “Open Activity”, select "Library", select "Physics Labs", and open “P14 PreLab SHM”.

5) Attach the mass hanger to the medium spring and hang it from the force sensor. Set the meter stick so that the indicator of the mass hanger is set at 0.

6)   Press the Tare button on the side of the sensor.

7)   Double click on the Force and Stretch Table icon under the Displays list on the left side of the screen.  Click on the Start button.  The Start button should now read “Keep” and have a checkmark on it.   Click on the keep button. The first set of data is stored and displayed in the data table. The default stretch is zero, so no need to enter it.   

8)   Add 100-g mass and click on the Keep button, to store the second force data. 

9)  Measure the stretch of the spring and record it in the second row under the “Stretch” heading in the table.  This is done by clicking on the Edit Data button and then clicking on the cell you want to type in.  

10)  Add another 100-g mass and repeat steps 8&9.

11)     Repeat step 10 until the total added mass is 600-g. Then click on the Stop button (the red square to the immediate right of the Keep button.

12)     Double click on the Force vs. Stretch graph icon in the Displays list.  Click on the Scale to Fit button.  Click on the Fit button and select Linear fit.  Record the absolute value of the slope, which is the spring constant, k below. Close DataStudio window without saving. 

    Spring Constant = k = _______________

C. Simple Harmonic Motion with a motion sensor:

Procedure:

1)  Remove the force sensor and connect the motion sensor to the Interface by plugging the yellow plug into digital channel one and the black plug into digital channel two. Make sure that the wide beam is selected.

2)   Record the total mass used below. (don’t forget the mass of the hanger).

3)   Place the motion sensor directly under the hanging masses, on the floor. Make sure that there is plenty of room between the sensor and the masses, about 50 cm. 

4)   Open DataStudio, select “Open Activity”, select "Library", select "Physics Labs", and open “P14 SHM”.

5)  Double click on the Position and Velocity Graphs icon under the Displays list.

6)  Pull down on the mass hanger until the spring is stretched about 15cm or so.  Release the hanger and wait for the side-to-side swinging to minimize.

7)   Click on the Start button.  After about 10 seconds, click on the Stop button.

8)   The curve on the velocity graph should resemble a sine function.  If it does not, delete the data and realign the motion sensor beneath the mass hanger, and try again.

9)   Click on the Scale to Fit button.

10)  Click on the Smart Tool button and move the Smart Tool to the top of the first peak in the position vs. time graph.  Record the value of time in the data table.

11)     Record the value of time for the top of each consecutive peak in the data table as well using the Smart Tool.

12)     Calculate the difference in time for each successive peak (this is the period).  The average of these periods should be recorded in the data table.

13)     Calculate the theoretical value for the period of oscillation based on the measured value of the spring constant of the spring and the mass on the end of the spring.  T=2pÖ(m/k).

14)  What is the percent difference for T, between the calculated value for oscillation and the measured value?

DATA:

Spring constant from part B, k = ___________

Added mass = __________        Mass of the hanger = _________

Total hanging mass = m = _________

Average measured period = Tm = ____________

Calculated period     = Tc = __________

% Difference         = ______________

Q1. When the position of the mass is farthest from the equilibrium position, what is the velocity of the mass?

Q2. When the absolute value of the velocity is greatest, where is the mass relative to the equilibrium position?