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### Goals:

- To establish understanding about projectile motion, Newton’s Laws of motion, accuracy and precision
- To introduce students to the engineering principles behind simple machines designed to launch a projectile with accuracy and precision

### Prerequisites:

- Have a concept that energy is conserved
- Understand that the acceleration of an object is directly proportional to the net force causing the acceleration and inversely proportional to the mass being accelerated
- Be able to develop a hypothesis that applies the scientific method and design engineering principles
- Be familiar with basic trigonometric relationships to be able to determine the angle of launch.

- Articulate the concept of elastic potential energy
- Describe how the energy stored as potential energy in the machine is converted into kinetic and gravitational potential energy
- Design a ping pong ball launcher to consistently hit a target
- Predict where the ping pong ball will land based on the physics principles taught in class

### Background:

Each group of students designs and builds a catapult that will launch a projectile at a target sixteen feet away with accuracy and precision. The projectile must also pass over a one-meter tall wall without touching it. The projectile will be a ping-pong ball or hollow golf ball (supplied by the teacher). A catapult is not necessarily a device based on the lever. The purpose, as stated, is to launch a projectile sixteen feet with precision and accuracy. There are many ways to accomplish this task. Students are encouraged not to limit their imagination to preconceived concepts or to pictures they may have seen of ancient weapons.

Class discussions will begin with Newton’s Laws of Motion and should lead to a discussion of energy conservation. The students will need to understand how the initial potential energy stored in their machine is converted first into kinetic energy and then into gravitational potential energy and kinetic energy and then finally into solely kinetic energy again.

The students will need to determine the energy stored in their machine before the launch. For a spring powered catapult this can be determined by using the spring constant for their spring and the distance that the spring is stretched or compressed according to the formula:

f=1/2kx^{2 }

where k=spring constant in Newton-Meters

x is the distance the spring is stretched or compressed in meters

f is force

The students will determine the mass of the projectile with a balance, as well as the angle of launch with a protractor or through basic trigonometric calculations.

Using the relationship:

d = v^{2}/ g

g=acceleration due to gravity

v=initial velocity

d=distance the projectile travels (the range)

the students can predict the initial speed of the projectile.

The students will use the V_{y} component of the initial velocity:

V_{y} = V_{i }* sin of the launch angle

to predict the maximum height of the projectile using:

V_{f}^{2} = V_{i}^{2} * 2gh

g=acceleration of gravity

h=height

V_{f} = 0

The PhysicsClassroom.com has a great tutorial on Non-Horizontally Launched Projectile Problems.

The students will then test their hypothesis by building and firing a projectile launcher and compare the results of their experiment to their predictions. In analyzing the reasons for any difference between the prediction and the result, students will gain a deeper understanding about how forces work in nature including the concept of friction and net force.

### Materials:

- 1 ping pong ball
- 1 “wall”: 1 meter high and 1 to 2 meters wide.
- Small target, for example a coffee cup
- Catapult Assignment Sheet #1
- Catapult Assignment sheet #2
- Calculations Sheet

Students will need to provide material that may include the following:

- A spring or springs (which can also be rubber bands, surgical tubing, bungee cords … )
- Wood or plastic tubing to construct a frame
- Various screws, hinges, nuts, bolts and washers as needed
- Tape or glue

### Procedure:

This lesson will require one block to introduce the project and to explain how the physics just covered applies, then another block to have the students demonstrate their catapults, and a last block to reflect on what was learned. Allow about three weeks from assignment to execution.

- Your challenge is to launch a projectile at a target sixteen feet away with precision and accuracy. The projectile must also pass over a one-meter tall wall without touching it. You may use any materials to build your catapult. However, you must use materials that can normally be found around the house. The idea of the contest is to be creative not to purchase high-tech materials. If you have any questions pertaining to the materials you have selected, you must BRING them to your teacher for approval in writing. In addition, there may not be any chemical or nuclear reactions used in the catapult. There may not be any feature that could be deemed as dangerous to the spectators. No part of the catapult may burn during the contest.
- Your catapult may use any means you can devise for launching the projectile. You may not, however, use any electric or gas operated motors nor may you use any chemical reactions. A catapult may use springs or elastics or steel bars to launch the projectile. The action of firing must be reproducible. The catapult may not self-destruct during the contest. The spring constant (k) cannot exceed 2000 N/m.
- Your catapult must support itself at the start. The catapult must be "loaded" and then fired. In other words, the catapult will be put into a launch position; the ping-pong ball placed on it and then you may fire it. This could be by cutting a string, pulling a pin or any other method you devise. Your catapult must be self-operated. You may touch it to start the launch but you may not give it a push.
- Your catapult must occupy a space described by 12 inches long, 12 inches wide and 12 inches high at the start of the launch. The maximum weight of the catapult is 4 pounds.
- Your grade on this project will be determined by the average of the best three out of four throws. A distinguished panel of judges will determine the grade received on each throw.
- A one-meter tall wall will be placed half way from the start line to the target on the other side of the wall. The ball must pass over the wall without touching the wall. The ball may not hit the ceiling.
- Students will launch a ping-pong ball projectile. Everyone is working under the same constraints. The distance from the catapult to the landing site will be measured.

**This is the beginning of an adventure into modeling, cooperative learning, and applied science. ** Each team should complete Catapult Assignment #1, ** **which includes:

- A listing of team members by name, physics period, and teacher
- Acknowledgment that most of the materials needed have been acquired and a model attempted.
- A labeled drawing of plans for the catapult you will be constructing
- A description of how the catapult will work; in which you mention the physics principles/laws that will be applied.

Calculations should be done later and will show maximum height, initial force and total energy of the system. An Experiment that measures these could be done in place of the calculations.

Your team may decide to revise your original plans along the way. That is okay. It is even expected. The second homework assignment, Catapult Assignment #2, which is associated with this laboratory activity, will consist of a revised labeled diagram of plans for the catapult and a final description of how it is going to accomplish its competitive mission. The second homework assignment must also contain calculations for force applied, maximum height, initial velocity and maximum horizontal distance. Please see Catapult Calculations Sheet.** **Revisions are expected to be necessary after your team conducts some trial shots.

On the final project date, we will set up the target, the wall, and test each and every catapult. No late projects will be accepted. You may, of course, hand in the catapult earlier.

*NOTE*: If you use a spring, the value of k must be calculated and you may be required to prove the experiment. To calculate the value of k, you must suspend the spring from a strong bar and hang weights on the spring. When you hang each weight on the spring, you will measure the distance it drops. Then you will plot the Weight on the Y-axis and the Distance on the X-axis. The k value is the slope of the resulting graph. The k value cannot exceed 2000 N/meter.

- This is a cool website to get ideas for building a catapult:

"Everything you want to know about catapults. Because you are Catapult Crazy!

Catapults were engineering feats of the Middle Ages and maybe you can't build an actual catapult that can take down the walls of a castle but you can build a miniature just for fun and to show your friends. Here are projects and information about catapults.

Here is your ultimate resource to learning everything about catapults. Want to make a catapult? Want to learn the history of a catapult. Want to see a video of a catapult? Everything is here.

I also have a whole bunch of pictures of catapults made by web visitors. Some of these are based on my plans and others are new designs or improvements."

http://www.stormthecastle.com/catapult/index.htm

- I have used this in class for a project where the materials are all the same for all students (an inexpensive): A Popsicle Stick Catapult

- The laboratory activity is an exercise in problem solving and of applying some physics principles.
- You will be part of a team and therefore will need to develop cooperative learning skills. Each team will consist of one or two students. All members are expected to contribute to the team effort. All team members will receive the same grade.
- One of the partners will launch the projectile while the other partner will act as a spotter during the actual grading of the project. The launcher will not be able to see the target! The spotter will give the launcher directions on how to hit the sweet spot on the target.
- It is possible for a lab team to miss the target and receive a grade lower than a 65 on this project.
- Grading:

2 Homework Grades

1^{st} Initial diagram, materials list, physics principles / laws

2^{nd} Finalized diagram, materials list, physics principles / laws

2 Laboratory Grades

1^{st} Accuracy and precision of catapult

2^{nd} Lab Report Write-up

- A great website for physics that I continue to use is The Physics Classroom: http://www.physicsclassroom.com/
- The tutorial section is particuarly useful: http://www.physicsclassroom.com/Class/

Developed by the 2007 Mount Olive NJ High School Physics Department.

John Tracey jtracey@mtoliveboe.org