Pendulums and the

Passing of Time

 

Background

Information:  Everyone who has witnessed the back and forth swinging motion of a grandfather clock is familiar with a pendulum.  Time was probably first measured by marking the shadow of the sun made by a stationary object (as in a sundial).  This is an effective way of determining the hour of the day for example.   Pendulums are one of the simplest devices used to measure time.  In this experiment you will determine the effects of mass and length on the period of a pendulum.

 

Cycle – A complete motion that begins and ends in the same position.

 

Amplitude (A) – The degree to which an object is moved from its initial or resting position

 

Period (T) – The time it takes to complete one cycle.

 

 

Materials:         set of standard masses              stopwatch                     Protractor                    

                                                meter stick                                String ( 1 m)                 Pendulum apparatus

 

Procedure:     There are three parts to this experiment, read all instructions before proceeding.

 

Part I          Determine how mass effects the period of a pendulum

 

Note in this part of the experiment the length will be held constant at 0.60 m,

 and the amplitude will be held constant at 50 degrees.

 

1.                                          Assemble a table top stand and attach a pendulum clamp.  Thread one end of the string through clamp and secure with the thumb screw.

 

2.                     Tie a loop in the end of the string, and hang a 20 gram mass on the end.

 

3.                              Loosen the thumbscrew and adjust the string until the pendulum is 0.60 m in length.  Measure from the point of attachment to the center of the pendulum mass.

 

4.                                          Using a timer, measure the time it takes to complete ten full swings (cycles) of the pendulum.  Record this number in your data table.

 

5.                     Divide the total time by 10 to find the time of one cycle.  Watch for significant digits.  This number is the period.  Record this number in the data table.

 

6.                        Repeat the above procedure using masses of 50, 100, 150, and 200 g.

 

Part 2         Determine how Amplitude effects the period of a pendulum

 

Note:In this part of the experiment the length will be held constant at 0.60 m,

and the mass will be held constant at 50 g.

 

1.                     Attach the 50 g mass and position the string so the pendulum has a length of

0.60 m.  Measure from the point of attachment to the center of the pendulum.

 

2.                                          Using a timer, measure the time it takes to complete ten full swings (cycles) of the pendulum when released from an amplitude of 30 degrees.  Record this number in your data table.

 

3.                     Divide the total time by 10 to find the time of one cycle.  Watch for significant digits.  This number is the period.  Record this number in the data table.

 

4.                     Repeat Steps 1-3  for amplitudes of 40, 50, 60, and 70 degrees.

 

 

 

 

 

 

 

 

Part 3         Determine how length effects the period of a pendulum

 

Note: In this part of the experiment the mass will be held constant at 50g,

and the amplitude will be held constant at 50 degrees.

 

1.                     Attach the 50 g mass and position the string so the pendulum has a length of

0.10 m.  Measure from the point of attachment to the center of the pendulum.

 

3.                                          Using a timer, measure the time it takes to complete ten full swings (cycles) of the pendulum.  Record this number in your data table.

 

3.                     Divide the total time by 10 to find the time of one cycle.  Watch for significant digits.  This number is the period.  Record this number in the data table.

 

4.                     Repeat Step 1 for lengths 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, and 0.80 m.

 

 

 

 

Graphs:     

 

Part 1. Construct a graph of Period Vs. Mass of a pendulum.  Make sure to follow proper graphing procedures.

 

Part 2. Construct a graph of Period Vs. Amplitude of a pendulum.  Make sure to follow proper graphing procedures.

 

Part 3. Construct a graph of Period Vs. Length of a pendulum.  Make sure to follow proper graphing procedures.

 

 

Note:               Always draw graphs in pencil so you can erase when you make errors, and always use square lined graph paper!

 

Graphing Procedures

 

1.                     Put the independent (manipulated) variable on the x-axis (horizontal).

2.                     Put the dependent (responding) variable on the y-axis (vertical).

3.                     Label both axes and include units.

4.                                          Label the top of the graph with a title.

5.                                          Clearly place all data points on the graph.

6.                                          If appropriate, draw a best fit line or curve to fit the data.

 


 

Questions (Answer in your formal lab report)

 

  1. How did the mass of the pendulum effect its period?

 

  1. How did the amplitude of the pendulum effect its period?

 

  1. How did the length of the pendulum effect its period?

 

  1. Why was the period squared before making the final (fourth) graph?

 

  1. If you wanted to construct a pendulum whose period was exactly one second long, What mass,  amplitude, and length of string would you use?

 

  1. Try to explain why changing the mass of the pendulum caused it to behave as it did.

 

  1. Try to explain why changing the amplitude of the pendulum caused it to behave as it did.

 

  1. Try to explain why changing the length of the pendulum caused it to behave as it did.

 

  1. Try to design a mechanism to use the pendulum inside of a grandfather clock.  Draw a sketch to illustrate your mechanism, and describe how it works.