# Lab 2: -- The Pendulum Problem: What is the relationship between the length of a pendulum and its period?

NOTE: DO NOT BEGIN THE EXPERIMENT UNTIL EACH PERSON IN YOUR GROUP HAS READ THE BACKGROUND AND ANSWERED THE BACKGROUND QUESTIONS.

Background and Inquiry: A simple pendulum consists of a weight, called a bob attached to the end of a string fixed at the other end. The pendulum has been used since the 16th century to measure time. The famous scientist Galileo was the first to observe its properties. Today you will repeat some of Galileo first experiments.

Begin by observing the swing of the bob. Without doing actual measurements observe the general properties of the pendulum by observing the motion of the bob (e.g., change the length of the string and change the direction the bob swings). If you have additional masses, change the mass and observe what happens. Discuss with your group what are the general properties that you have observed.

Today you will change the length of the string and observe the time it takes for the bob to swing back and forth. What kind of change do you expect to observe? For example: Would you expect if you double the length it will take twice as long to swing? If you double the mass would the bob swing twice as fast? What type of mathematical relationship do you expect to observe? Justify your statement!

Background Questions:
1) What is a pendulum?
2) What scientist first observed the properties of a pendulum? What are some properties he may have observed?
3) Would you expect if you double the length it will take twice as long to swing?

Materials: string, meter stick, two 20 g. masses, digital stopwatch, ring stand

Procedure:

1) Copy table I and table II into your lab notebook.
2) Add a 20 gm. mass to the end of the string. Set the length of the string to 20 cm.

Diagram:

NOTE: The period (T) of a pendulum is the time it takes for a mass (called a bob) to swing back and forth once. Since the time for this event may be too quick to measure, it will be necessary to calculate an average value. Example--Let the weight swing back and forth two times or 2 periods. Divide the time in seconds you measured by 2. This will give you a more accurate value for the period of the pendulum (T).
2) Record the period of a pendulum for six different lengths (20, 40, 60, 80, 100 and 120cm.) of string using the 10 gm. weight. Remember to repeat each measure several times, taking an average. Record your results in Table I shown below.
3) Repeat using 40 gm. of mass.

Record your results in Table II.

Results:
Complete the following table.

TABLE I: Mass of bob = 20 GMs. Length, L (cm.) Two Periods (2T) (sec) One Period (T)

>NOTE: ONE PERIOD IS ONE SWING BACK AND FORTH! MEASURE TWO PERIODS IN THIS LAB, THEN DIVIDE BY TWO TO GET THE ONE PERIOD DATA. DO NOT MEASURE ONE PERIOD WITH THE STOPWATCH.

 Length Two Periods (Student I) Two Periods (Student II) Average One Period (T) sec. (half of average) 20 cm. 40 cm. 60 cm. 80 cm. 100 cm. 120 cm.

TABLE II; Mass of bob = 40 GMs.

 Length Two Periods Student I Two Periods Student II Average One Period (T) sec. (half of average) 20 cm. 40 cm. 60 cm. 80 cm. 100 cm. 120 cm.

Graphing Activities:
1) Using graph paper, label the x-axis length (L) and the y-axis period (T). Using Table I plot your points. Do not Join the points instead make a smooth curve using a french curve as shown in class.

Discussion:
1) Discuss the shapes of your plots.
2) Why does it not matter what the weight of the pendulum is or where the pendulum starts it swing? Can you relate this to why to objects that have the same mass always fall at the same rates?
3) What are the independent and dependent variables in this experiment?
4) What happens to the dependent variable when the independent variable increases? decreases?
5) What factors are held constant in each experiment?
6) What type of relationship is demonstrated in this experiment?
7) How does the relationship shown in this experiment compare with other relationships you have so far seen?

Applications:

How could a pendulum be used to tell time? How would you design a clock using a pendulum?

#### What are Mathematical Relationships

What is a mathematical relationship and WHAT ARE THE DIFFERENT TYPES OF MATHEMATICAL RELATIONSHIPS that apply to the laboratory exercises in the following activities.

#### Labs

Lab 1:    The Spring Constant  -- Problem:  What is the relationship between how much a spring stretches and the force pulling on the spring?

Lab 2:    The Pendulum  --Problem: What is the relationship between the period of a pendulum and the length of the string of  the pendulum?

Lab 3:   Mass, Volume and Density--   Problem: What is the relationship between the mass of a ball and its volume assuming a constant density?

Lab 4:   Light Intensity--  Problem: What is the relationship between the intensity of a beam of light and the distance from a light source?

Lab 5:   Acceleration--  Problem: What is a the relationship between how the distance travels and the time in travel for an accelerating object?

Lab 6:   Polarization --  Problem:  What is the relationship between how much light passes through a Polaroid filter and the angle the filter is rotated?

Lab  7:   Ohms Law--  Problem:  What is the relationship between current, voltage when there is a constant resistance in an electric circuit.

Lab 8:   Radioactive Decay-- Problem: What is the relationship between the decay of radioactive material and the time allowed for the decay?

Lab 9: Water Pressure-- Problem: What is the relationship between water pressure and depth of water?

Lab 10: Attractive and Repulsive Forces--   Problem: What is the relationship between the distance between two magnets  and the force between them?

Lab 11: Damping Motion--  Problem: What is the relationship between the height a ball bounces and the number of times it has bounced?

Lab 12: Buoyancy - Problem: What is the relationship between the volume of a boat and the weight it can hold?