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# Lesson Plans

## Marbles and Momentum

Author: Rodney Rowell ((Lesson based on ideas of Darrell Woods and John Grabowskil)
Source: Rules for Marbles, Marble Experiment

#### Abstract

Using the game of marbles, students will explore how momentum is transferred from one object to another object in an elastic collision. Students will determine the properties that make a good shooter.

#### Objectives

What should students know as a result of this lesson?

• Students will be able to define and describe the physical quantity of momentum.
• Students will be able to define and describe conservation of momentum.

What should the students be able to do as a result of this lesson?

• Student should be able to compare the amount of momentum a moving object contains if they know the mass and velocity of each.
• Students will be able to collect and organize (tables and graphs) data from an experiment.

#### Materials

Marbles of many different sizes (mibs and shooters)

Other small balls of high mass (large ball bearings)

Other small balls of low mass (wooden balls)

Other small balls made of different polymers

Tennis Ball

Momentum balls

Copy paper

Pencils

Hole punch

Wooden rulers with grove down the center

#### Procedures

Engagement

Divide the students in to groups of four or an appropriate size for your class. Tell them that they are going to play a game that was very popular when their grandparents or great grandparents were growing up. The students will play the game of marbles with some small changes to the original rules.

Each student should receive seven small marbles (mibs) but no shooter.Students should make a mark on the seventh mib to indicate who it belongs to. (This mibe will be used as the shooter for now.)

Each group should tape a 50 to 70 cm circle on the floor and place six of their mibs in the circle.The game begins by one player knuckling down at the edge of the circle and flicking their mib (shooter). The object is to knock out one or more of the mibs, without the player's shooter leaving the circle. If, the player has been successful, then the player can shoot again from the place where the shooter rested. If, after the player has missed and his/her shooter end up outside the circle, then the player must leave the shooter inside the circle.

The next player takes a turn. Each mib that was knocked out counts for one point. A player may also knock out any other player's shooter that remains in the circle. The game continues until all of the original mibs have been knocked out. The player with the most points wins. In some versions the marbles knocked out of the circle are kept by the shooter. This is sometimes called "keepsies".

Terms: Knuckling down: A player must have at least one knuckle touching the ground while flicking. Fudging: A players hand was lifted off of the ground while shooting. A player will lose their turn for doing so. Flicking: While knuckling down the shooter is flicked by the thumb out of the players hand. Shooter: The marble that the player flicks toward the target mibs. The shooter must be more than 1/2" in diameter, but not over 3/4" in diameter. Mib: One of seven 5/8" marbles placed in the center of the circle.

Allow the students to play and then have them write a paragraph describing what they saw. Check for use of vocabulary and other observation concerning the collisions between the marbles.

Tell the students that they will use science to find a way to “cheat” in marbles. The goal is for the students to find that the heavier the shooter, the more momentum it has and the more marbles it can knock out of the circle, i.e. the conservation of momentum.

Instructions for playing marbles came from the referenced website.

Exploration

Part 1

1. Using a piece of copier paper, form a tube lengthwise that is just slightly larger than a mib. Make a tube for each size of ball being used.
2. Punch a hole completely through each tube about five cm from the end. The hole should be large enough for a pencil to go through.
3. Tape the other end of the paper tube to the end of a wooden ruler that has a grove in the middle. Make sure to tape the bottom of the tube to the top of the ruler.
4. Elevate the end of the tube with the hole about 3 cm.
5. Place one mib in the grove at the center of the rule and line three more mibs on the side toward the tube. All marbles should be touching.
6. Stick a pencil through the holes of the tube and place a mib in the top of the tube. The pencil will hold the mib in place.
7. Create a data table that will compare the number of mibs in the tube, number of mibs on the ruler, and the number of mibs that move off the ruler.Example:
 Trial Number of mibs in tube Number of mibs on ruler Number of mibs sent off the ruler 1 2 3 etc

1. Pull the pencil and let the marble roll down the tube onto the ruler and collide with the other marbles. Watch what happens and record the number of marbles sent off the ruler.
2. Place three marbles on the ruler and two in the tube. Observe and record your data.
3. Perform the same experiment with different number of marbles in the tube and on the ruler. Record your data.

Part 2

1. Remove the small tube from the ruler and replace it with the tube for the shooter. Place six mibs in the grove of the ruler. Release the shooter and record your observation/data? Repeat the procedure to determine the total number of mibs the shooter can send off the ruler in one trial.
 Shooter Trial Number of mibs in tube Number of mibs on ruler Number of mibs sent off the ruler 1 2 3 etc

Part 3

1. Remove the previous tube from the ruler and replace it with the tube for the ball bearings. Place six mibs in the grove of the ruler. Release the shooter and record your observation/data? Repeat the procedure to determine the total number of mibs the ball bearing can send off the ruler in one trial.
 Ball Bearings Trial Number of mibs in tube Number of mibs on ruler Number of mibs sent off the ruler 1 2 3 etc

1. Remove the previous tube from the ruler and replace it with the tube for the wooden ball. Place six mibs in the grove of the ruler. Release the shooter and record your observation/data? Repeat the procedure to determine the total number of mibs the ball bearing can send off the ruler in one trial.
 Wooden Ball Trial Number of mibs in tube Number of mibs on ruler Number of mibs sent off the ruler 1 2 3 etc

Students should repeat this procedure for different types of balls.NOTE: I did not have time to try Part II of this activity. Six mibs on the ruler is just a guess. The teacher may want to try this part to determine the best number of mibs to begin with.The teacher should monitor the students and make sure they are writing down the data.A more extensive procedure can be found at the referenced website.

Explanation

Have the students discuss with each other how rolling small marbles into small marbles, rolling small marbles into large marbles, rolling small marbles into ball bearings, and rolling small marbles into wooden balls were all different or alike with each other.

Students should write their answers in a paragraph. Students should be able to see the heavier the object, the more small marbles it took to move it.

Elaboration

Discuss with students that momentum is mass times velocity. A train has a huge mass, but even at low speeds it takes a long time to stop because it has a large momentum. A bullet has a low mass but a large velocity and therefore a large momentum.

Using momentum balls, demonstrate conservation of momentum. Swing one, then two, then three balls.

Have the student discuss the results of the exploration/explanation in terms of momentum and conservation of momentum.

Have the students determine which of the balls would make the best shooter and why?

Each group should prepare data tables or graphs to share with the class to support their decision on which type of ball makes the best shooter. A written report should also be developed.

Evaluation

Teacher demonstrationHold a tennis ball on top of a basketball and drop them at the same time. When the basketball hits the floor it will collide with the tennis ball and the tennis ball will move a way with a great velocity. Have the students write a paragraph on what is happening in terms of the conservation of momentum.

Collecting data for the basketball/tennis ball demonstration is tricky, but can be done. According to the formula d=(1/2)gt2 , it will take about 0.45 s for a ball at one meter to fall to the floor. According to the formula V=2gt, the velocity of the ball at the time of impact is 4.43 m/s. The momentum of a ball falling from a height of one meter is the (mass)(4.43 m/s). It is very hard to measure this small amount of time accurately with a stop watch.

Tape paper from the top of a wall in your classroom to the floor and mark of increments of 10 cm. Using a video camera, tape the dropping of the balls. In a four head VCR, each frame represents 1/30th of a second (or it takes 30 frames to make one second of time). Play the tape back in slow motion and count the number of slides it takes for the ball to hit the floor and then divide by 30. (The ball should take about 15 slide to fall.) This will give you the approximate fall time. The velocity and momentum can be calculated with the aforementioned equation.

Tape the basket ball drop and determine time of fall, velocity and momentum.Tape the tennis ball drop and determine the time of fall, velocity, and momentum. Tape the basketball/tennis ball drop determine the time of fall, velocity and final momentum of the tennis ball. The final momentum of the tennis ball should be approximately the sum of the individual momentum of the basket ball and the tennis ball.

Demonstration

Demonstrations are presented in the Elaboration portion of the learning cycle.

Direct Instruction

Direct instruction takes place in the Elaboration portion of the learning cycle.

Cooperative Learning

Cooperative learning takes place in the Engagement and Exploration portions of the learning cycle.

#### Prerequisites

Skills - Students should be able to define and describe velocity and mass of an object.Students should be able to collect and organize data from an experiment.

Goals - Students should be able to compare the momentum of two different objects.Students should be able to describe how momentum is conserved in an elastic collision.

#### Best Teaching Practices

• Structured Problem Solving
• Hands-on Teaching
• Using Writing

#### Alignment with Standards

NGSS Standards:

• HS-PS2-1 Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
• HS-PS2-2 Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on them.

Common Core Standards:

• RST.9-10.3 Follow pecisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
• WHST.9-10.2 Write informative/expanatory texts, including narration of historical events, scientific procedures/experiments, or technical processes.

National Standards:

• Science Teaching Standards B
• Assessment in Science Education A and B
• Science Content Standards A and B

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#### Applications

• Discuss why you should obey traffic signals at railroad crossings. The train has a large momentum and will take a long time to stop.
• A bullet from a firearm has a small mass, but a large velocity. The momentum of the bullet is what causes so much damage to the object it hits.

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#### Other Considerations

Pacing/Suggested Time:

• Engagement: One period
• Exploration: One period
• Explanation: One period
• Elaboration: One period
• Evaluation: One period

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