P21

A15

Relationship between period and length of a simple pendulum

Equipment Needed

1

P21

A15

-Science WorkshopTM Interface

-end-stop, track (two)

-50 Newton force sensor

-mass

-photogate

-stand

-photogate mounting bracket

-spring

-base and support rod

-track, 1.2 meter

-dynamics cart with mass

1

P21

A15

Purpose

The purpose of this laboratory activity is to find out the relationship between period and length of a simple pendulum.

Procedure: Measuring The Period of Oscillation

Equipment Setup

You do not need to calibrate the photogate.

1.Disconnect the spring on the left end of the cart from the force sensor’s hook. Remove the force sensor and its support rod and base.

2.Put an end stop on the left end of the track.

3.Connect the unattached end of each spring to the peg on top of an end stop.

When the springs are attached at opposite ends of the track, the cart should be near the middle of the track.

4.Attach the photogate to the photogate mounting bracket. Mount the bracket on the side of the track.

5.Position the bracket so the photogate is aligned with the center of the cart when the cart is at rest near the middle of the track.

6.Adjust the height of the photogate so the beam is blocked by the 2.5 centimeter opaque band at the top edge of the picket fence on the cart.

Data Recording

1.Pull the cart about 25 centimeters from its equilibrium position at the middle of the track.

2.Click the REC button. Data recording will begin when the photogate beam is first blocked.

3.Release the cart so that it can move back-and-forth through the photogate.

4.After the cart completes eight or nine oscillations, click the STOP button to end data recording.

Run #1 will appear in the Data list in the Experiment Setup window.

5.Click on the Table display to make it active. Click the Statistics button on the left side of the display.

The bottom part of the Table will display Min (minimum), Max (maximum), Mean, and Std. Dev (standard deviation).

6.Record the value of the Mean of the Period for Run #1 in the Data Table.

7.Measure the mass of the cart’s extra mass bar. Record the mass in the Data Table.

8.Add the extra mass bar to the cart and repeat the measurement as described above.

Run #2 will appear in the Data list in the Experiment Setup window.

9.Examine the Statistics in the Table display and record the value of the Mean of the Period for Run #2 in the Data Table.

Analyzing The Data

Data Table

Item / Value
Mass of cart / kg
Mass of mass bar / kg
Spring constant, “k1” / N/m
Spring constant, “k2” / N/m
Period (cart alone) / sec
Period (cart + mass) / sec

1.Calculate the theoretical period based on the spring constant and the mass of the cart (mass including the picket fence).

2.Calculate the theoretical period for the cart with the extra mass bar in it.

Theoretical Period
Cart / sec
Cart plus mass bar / sec

Conclusion

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