### Purpose

To understand the relationship between gravitational forces and the mass of objects, the changes in speed and direction of objects, and the distance between objects.

### Context

This lesson helps students understand concepts related to how gravitational forces act on objects by exploring the motion of pendulums.

Read More### Motivation

Ask students the following questions in order to get a feel for their current knowledge and perceptions of pendulums. Answers to these questions are provided for you, but don't expect or lead students to these answers yet. At this point, simply gather and keep a good record of students' current ideas; students will have a chance to refine these after the website exploration that follows.

Questions to ask:

- How would you define a pendulum?
*(A pendulum is loosely defined as something hanging from a fixed point which, when pulled back and released, is free to swing down by gravity and then out and up because of its inertia, or tendency to stay in motion.)* - How does a pendulum work? What are the parts of a pendulum?

*(A simple pendulum consists of a mass (called the bob) attached to the end of a thin cord, which is attached to a fixed point. When the mass is drawn upwards and let go, the force of gravity accelerates it back to the original position. The momentum built up by the acceleration of gravity causes the mass to then swing in the opposite direction to a height equal to the original position. This force is known as inertia.)* - What is the period of a pendulum?
*(A period is one swing of the pendulum over and back.)* - What is the frequency of a pendulum?
*(The frequency is the number of back and forth swings in a certain length of time.)* - What variables affect the rate of a pendulum's swing?
*(Students may come up with a variety of answers, but the four that they will be testing in this lesson are:* *Length of the pendulum*-Changing the length of a pendulum while keeping other factors constant changes the length of the period of the pendulum. Longer pendulums swing with a lower frequency than shorter pendulums, and thus have a longer period.*Starting angle of the pendulum*-Changing the starting angle of the pendulum (how far you pull it back to get it started) has only a very slight effect on the frequency.*Mass of the bob at the end of the pendulum*-Changing the mass of the pendulum bob does not affect the frequency of the pendulum.*Force of gravity*-This accelerates the pendulum down. The momentum built up by the acceleration of gravity causes the mass to swing in the opposite direction to a height equal to the original position.)

### Development

Begin this part of the lesson by telling students that they will explore websites to learn more about how pendulums help us learn about gravitational forces. In the second part of the lesson, students will work in groups to construct their own pendulums and test what they have observed on the websites.

Have students run the demonstration called The Pendulum, on the Interactive Physics and Math with Java website.

Make sure they understand how to run the experiment by telling them the following:

*This demonstration shows a pendulum suspended on a 'rigid string.' You can click on the bob (the object at the end of the string) and drag the pendulum to its starting position. Also, you can adjust the length of the pendulum by clicking and dragging the bob closer or farther from the center. Once in motion, the pendulum can be 'caught' by clicking and holding the bob. Thus, the pendulum can be brought to its new starting position. *

Point out that the program measures the period, or one swing of the pendulum over and back.

Ask students:

- How does changing the length of the bob affect the period?
*(The shorter the length of the bob, the shorter the period will be.)* - How does changing its starting point or angle affect the period?

*(The smaller the angle, the shorter the period will be.)* - How can you get the shortest period?

*(Decrease the length, and decrease the angle.)* - How can you get the longest period?

*(Increase the length, and increase the angle.)* - Explain why the pendulum continues to move without stopping or slowing down once it is set in motion.

*(According to the law of inertia, a body in motion will continue in motion, unless acted upon by a force.)*

### Assessment

Assess the students' understanding by having them explore the Pendulums on the Moon lesson, found on the DiscoverySchool.com website. Students should click the link for "online Moon Pendulum," found under the "Procedure" section of the lesson. This activity simulates the gravitational force on the moon. Students should experiment for approximately 5-10 minutes, changing the mass, length, and angle to observe the effect it has on the pendulum.

Instruct students to change only one variable at a time. Then, ask students these questions:

- How do you get the quickest swing?
*(Shorten the length of the string and decrease the angle.)* - How do you get the longest swing?
*(Increase the length of the string and increase the angle.)* - In your own words, describe the relationship between mass, length of string, and angle.

*(Mass does not affect the pendulum's swing. The longer the length of string, the farther the pendulum falls; and therefore, the longer the period, or back and forth swing of the pendulum. The greater the amplitude, or angle, the farther the pendulum falls; and therefore, the longer the period.)* - How does the force of gravity on the Moon compare with the force of gravity on Earth? What effect do you think the difference in gravitational forces would have on the pendulum?

*(The force of gravity is less on the moon than on the Earth. Since the force of gravity is less on the Moon, the pendulum would swing slower at the same length and angle and its frequency would be less.)*

### Extensions

**Make Coupled Resonant Pendulums**

This experiment demonstrates that two pendulums suspended from a common support will swing back and forth in intriguing patterns if the support allows the motion of one pendulum to influence the motion of the other. The directions for this experiment are on the Exploratorium website.

**Measuring Falling Time**

When Galileo was studying medicine at the University of Pisa, he noticed something interesting about the periods of a pendulum. In church one day, he watched a chandelier swing back and forth in what seemed like a steady pattern of swings. He timed each swing and discovered that each period was the same length (same amount of time). In the previous activity, students measured the periods of their pendulums using either digital watches or stopwatches. Galileo did not have these tools, so he used his pulse. In this activity, students will time the periods of their pendulums using their pulses and compare their results with those obtained with a watch.

Show students how to find their pulse by pressing two fingers on the artery next to their wrist. Make sure that students have been at rest for several minutes before doing this so that they can obtain a steady pulse rate. Working in teams, have one student set the pendulum in motion while another measures the pulse beats that occur during five complete swings and then ten complete swings. Students should reproduce the distances they used in the earlier experiment, Testing Falling, for the amplitude and length of string. Record the number of pulse beats. Repeat this procedure with different students measuring their pulse rates. Then have students measure and record five complete swings and ten complete swings using a stopwatch or digital watch.

Share each group's results with the entire class. How do the pulse beat measurements compare with those timed with a watch? What are the advantages of using a stopwatch or digital watch over counting pulse beats as a method of timing?