### Summary

Students examine collisions between two skateboards with different masses to learn about conservation of momentum in collisions.### Engineering Connection

Engineers thoroughly understand momentum and collisions so they can design human body replacement parts, safer vehicles, or plan for spacecraft to safely dock at space stations or land on the moon. For the safety of the occupants, engineers design cars with crumple zones — areas of the car that absorb the momentum of the forces hitting the car. Airbags are another engineering safety innovation that protects passengers by accounting for the conservation of momentum.

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### Next Generation Science Standards: Science

- Apply Newton's Third Law to design a solution to a problem involving the motion of two colliding objects. (Grades 6 - 8) Details... View more aligned curriculum... Give feedback on this alignment...

###### Common Core State Standards: Math

- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Give feedback on this alignment...
- Solve linear equations in one variable. (Grade 8) Details... View more aligned curriculum... Give feedback on this alignment...
- Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Grades 9 - 12) Details... View more aligned curriculum... Give feedback on this alignment...

###### International Technology and Engineering Educators Association: Technology

- Knowledge gained from other fields of study has a direct effect on the development of technological products and systems. (Grades 6 - 8) Details... View more aligned curriculum... Give feedback on this alignment...

###### Colorado: Science

- Gather, analyze, and interpret data to describe the different forms of energy and energy transfer (Grade 8) Details... View more aligned curriculum... Give feedback on this alignment...
- Use research-based models to describe energy transfer mechanisms, and predict amounts of energy transferred (Grade 8) Details... View more aligned curriculum... Give feedback on this alignment...

### Learning Objectives

After this activity, students should be able to:

- Predict what can happen in a linear collision using the principle of conservation of momentum.
- Explain that with every action, there is an equal and opposite reaction (Newton's Third Law).
- Experimentally determine the momentum of two objects in a collision.
- Explain why engineers must thoroughly understand momentum and collisions to design many products.

### Materials List

Each group needs:

- 2 skateboards
- weights (textbooks work well)
- meter or yard sticks to create a "runway" for the boards
- scale (optional, but beneficial)

### Introduction/Motivation

Have you ever seen a video of a space ship docking with a space station? Have you ever seen a car crash? Have you ever bumped into someone in the hall? All of these experiences are collisions. In a collision, momentum is transferred between objects. It is important for engineers to understand about momentum so they can design safer cars, plan space missions, learn about joints and muscles, and all sorts of other things!

What happens when you drop a ball of clay on the ground? Is it an inelastic collision? Drop a ball of clay on the ground. Does it go splat and stick? (Answer: If it was perfectly inelastic, yes, but most things in life are not perfect, so clay will not always go splat.)

By observing what happens when skateboards bump into each other, we can learn more about collisions and momentum. When one skateboard collides with another, several things can happen. Imagine a skateboard sitting still and another skateboard rolls into it. What happens if the first skateboard is heavier? What if the second one is heavier? What happens if they are the same weight? Each case is determined by *momentum*. Momentum is what engineers and scientists call the mass of an object multiplied by the velocity at which it is moving. Mathematically,

**
p
** = m x

*v*where:

**
p
**=momentum of the object (kg-m/s or N-s)

*m* = mass of the object in kilograms (kg)

**
v
** = velocity of the object in meters per second (m/s)

In collisions, momentum is always conserved. The mass times the velocity of the objects before bumping into each other is the same as the mass times the velocity of all the objects after bumping into each other.

This relates directly to Newton's Third Law of Physics, which states that for every reaction, there is an equal and opposite reaction. That is, in collisions, energy is conserved. If you push against a wall, the wall is pushing against you with the same force. Figure 1 helps in visualizing this in terms of skateboarding.

### Procedure

Before the Activity

- Gather needed materials. This may include asking the students bring in their own skateboards (two per group).
- Designate an open floor area with enough space for two skateboards to roll at and collide with each other.

With the Students

- Ask students to record their observations during the activity. Instruct them to record anything that seems important.
- Begin with two skateboards that weigh the same. Have a student roll a skateboard into another skateboard so that they bump nose-to-nose. Observe what happens. Do both skateboards move, or does the first one stop? Are the skateboards moving faster than the first skateboard or slower? (If the first stops, the second should move away at the same speed; since they have the same weight, and since momentum is conserved, the second skateboard must have the same velocity. If they are both moving, they should be moving at a slower speed; since momentum is conserved for the whole system, and since the moving mass is greater (now both skateboards), the total velocity must be lower.)
- Ask students to draw the forces acting within the system. For example, draw the two skateboards at the moment of collision (just touching). If you call one skateboard A, and the other skateboard B, tell students that there will be a force AB (skateboard A acting on skateboard B) and a force BA. The magnitude of these two forces are the same. Figure 2 provides an example diagram.
- Add weight to the stationary skateboard. For precision, and if time allows, have the students weigh the skateboard and double its weight exactly. Repeat the collision experiment and observations. (This time, if the first skateboard stops, the second should move away at half the original speed; since the second object has twice as much mass, it must have half the velocity to have the same momentum. If they are both moving, they should be moving at a much slower speed.)
- Move the weights from the stationary skateboard to the moving skateboard. Perform the collision experiment and observations once again. (This time, if the first skateboard stops, the second should move away at twice the original speed; since the second object has half as much mass, it must have twice the velocity to have the same momentum. If they are both moving, the second skateboard should still be moving more quickly than the first skateboard since it has less mass.)

### Safety Issues

Students need to be careful with the skateboards. If they are riding on them, there is a falling hazard. And, heavy skateboards can squish fingers.

### Troubleshooting Tips

If the skateboards miss each other, make a track with meter sticks, or do the experiment next to a wall so that they are unable to turn past each other.

Observations are easiest if one skateboard is still, and the other rolls into it. If both skateboards are rolling, things get more complicated.

### Assessment

Pre-Activity Assessment

*Discussion Question:* Solicit, integrate and summarize student responses.

- What happens if a child skater loses control and collides into an adult skater? Discuss various skater collision situations in which the people involved are of different weights and moving at different speeds.
- If your skateboard runs into a wall at a very fast speed, how is it that the skateboard can get damaged? If the skateboard is moving, why doesn't all the energy just go into the wall? (This is an example of Newton's Third Law, illustrating the wall provides an equal and opposite force on the skateboard to the skateboard's force applied when it hits the wall.)

Activity Embedded Assessment

*Observations:* Have students record their observations of the activity — an activity performed by scientists, researchers and engineers. Have student share their observations with the class. (e.g., Which skate had more momentum?).

Post-Activity Assessment

*Problem solving:* Ask the students and discuss as a class:

- Which has more momentum, a 2000 kilogram car traveling at 10 meters per second or a 4000 kilogram car traveling at 5 meters per second? (Use the
*p*= m*v*formula; Answer: They have an equal amount of momentum.) - Why is it that when someone runs into a wall, they can get hurt, but the wall is fine? Is it because the person and the wall experience different amounts of force? (Answer: No, the same force is experienced by each, but the wall is much more capable of withstanding forces without being damaged due to its composition.)

### Activity Extensions

Show students a Newton cradle (see an example at http://www.walter-fendt.de/ph14e/ncradle.htm ). Ask them how they think that compares to the skateboards.

If a skateboard carrying weights has a total mass of 5 kg and is traveling at 5 meters per second, what is its momentum? (Answer: Multiply the mass times the velocity to find that the momentum is 25 kg–meters per second.) If that skateboard bumps into a stationary skateboard that weighs 10kg and stops, how fast would the 10 kg skateboard move away from the collision? (Answer: The total momentum is conserved, so the skateboard has 25 kg-meters per second of momentum. Divide this by the mass to find the new velocity of 2.5 meters per second.)

### Activity Scaling

- For lower grades, complete the momentum calculations together, as a class.
- For upper grades, have the students do multiple trials with different weights. Have the students complete the activity extension.

### Contributors

Chris Yakacki; Ben Heavner; Malinda Schaefer Zarske; Denise Carlson### Copyright

© 2004 by Regents of the University of Colorado.### Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder### Acknowledgements

The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education, and National Science Foundation GK-12 grant no 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

## Comments