Printable Resources[Dayton Trebuchet]

Appendix A: Pre/Post-Test

Appendix B: Pre/Post-Test Answer Key

Appendix C: Trebuchet Simulation

Appendix D: Engineering Design Process

Appendix E: Dayton Trebuchet Packet

Appendix F: Dayton Trebuchet Rubric

Appendix G: Teacher Tips

Appendix H: Background Information

Appendix A: Pre/Post-Test

Name _____________________________

Directions: Read each question carefully and circle the best answer.

1. A bowling ball was dropped from a helicopter. The ball falls 250 meters. Which statement accurately describes the falling bowling ball? (1 point)

a. Its potential energy decreases as its kinetic energy increases.b. Its potential energy increases as its kinetic energy decreases.c. Its potential energy is unchanged as its kinetic energy increases.d. Its potential energy is unchanged as its kinetic energy increases.

2. Which is a form of kinetic energy? (1 point)a. energy of moving molecules in a heated liquidb. energy stored in the chemical bonds of a substancec. energy holding together the particles in an atomic nucleusd. energy stored in an object’s position above Earth’s surface

3. Examine the diagram below. Imagine the ball is at rest at the top of a hill and it is pushed down the hill.

a. Where is the baseball’s potential energy is greatest? ______

b. Where the baseball’s potential energy is the lowest? ______

c. Where is the baseball’s kinetic energy is the greatest? ______

d. Where is the baseball’s kinetic energy is lowest? ______

(4 points)

4. A student throws a ball onto the ground. At first, the ball rolls rapidly. After a few moments the ball stops moving. Why did the ball stop moving? (1 point)

a. The ball was subject to balanced forces.b. Motion always requires an unbalanced force to continue. c. An unbalanced force, friction, stopped the motion of the ball.d. The student did not throw the ball hard enough to keep it rolling.

5. Which of the following is the best example of increasing an object’s potential energy? (1 point)

a. rolling a bowling ballb. turning on a light bulbc. stretching a rubber bandd. dropping a pencil

6. An object that has kinetic energy must be… (1 point)a. lifted above the earth’s surface.b. in motion.c. at rest.d. none of the above.

7. As height increases, so does… (1 point)a. thermal energy.b. mechanical energy.c. kinetic energy.d. potential energy.

8. Label the missing steps of the Engineering Design Process in the diagram provided below. (3 points)

Draft: 5/5/2023 Page 3

A

Think

B

C

Solution

Problem

9. Determine what type of energy (kinetic or potential) is shown in each box below. Put a “K” in the box it is kinetic energy, put a “P” it is shows potential energy. (5 points)

Picture 1 Picture 2

Picture 3

Picture 4

Picture 5 Picture 6

Picture 7

Picture 8

Picture 9

Picture 10

Draft: 5/5/2023 Page 4

Appendix B: Pre/Post-Test Answer Key

1. A2. A3. a. A

b. Cc. Bd. C

4. C5. C6. B7. D8.

9. Potential: 2, 3, 5, 8, 9Kinetic: 1, 4, 6, 7, 10

Question

Think

Design

Test

Solution

Problem

Appendix C: Trebuchet Simulation

Name _____________________________

“Trebuchet” comes from the French word “Trabucher” which means “to throw over.” The trebuchet was invented in China around 300 BC. The trebuchet was the only siege weapon to be invented during the Middle Ages and was a counterweighted, stone-throwing device. Trebuchets were expensive and time-consuming to build, and were only used as a last resort. They typically were built at the site of the battle to break down walls of castles. And, these machines had to be run by experts that were brought in at great expense. Large stones and counterweights had to be found or quarried and brought in as well. Placement of the trebuchet near the target was critical since they have a limited range. Too far away and they missed the target. Too close and the soldiers were attacked by cross bows and killed. While trebuchets typically threw rocks, they also threw a variety of materials including fire, dung, dead bodies, diseased bodies, body parts, dead animals and anything rotting.

Pre-Simulation Questions:

1. What is kinetic energy? What are some examples of kinetic energy?

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

2. What is potential energy? What are some examples of potential energy?

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

Video:

1. Watch the short video at the following site about trebuchets.

http://www.teachersdomain.org/resource/hew06.sci.phys.maf.trebuchet/

2. Where does the potential energy in the lever arm come from?

______________________________________________________________________

______________________________________________________________________

3. Where is there potential energy throughout the loading, cocking, and releasing of the trebuchet? ______________________________________________________________________________

______________________________________________________________________________

4. Where is there kinetic energy?

______________________________________________________________________________

______________________________________________________________________________

5. What evidence is there that energy is conserved?

______________________________________________________________________________

______________________________________________________________________________

Simulation:

Go to http://www.virtualtrebuchet.com/Trebuchet.aspx

1. Play the simulation using the pre-set specifications. Using a stop-watch, determine the time it takes for the projectile to land. Record the time, the distance the projectile traveled, height of the pivot, and the mass of the projectile in the table below.

2. Now change the mass of the projectile and replay the simulation. Again, determine the time it takes for the projectile to land. Record the time, the distance the projectile traveled, height of the pivot, and the mass of the projectile in the table below.

3. Reset the simulation. Change the release angle and play the simulation. Again, determine the time it takes for the projectile to land. Record the release angle, the time, the distance the projectile traveled, height of the pivot, and the mass of the projectile in the table below.

4. Reset the simulation. Change the mass of the weight and play the simulation. Again, determine the time it takes for the projectile to land. Record the mass of the weight, the time, the distance the projectile traveled, height of the pivot, and the mass of the projectile in the table below.

5. Reset the simulation. Change the height of the pivot and play the simulation. Again, determine the time it takes for the projectile to land. Record the height of the pivot, the time, the distance the projectile traveled and the mass of the projectile in the table below.

Draft: 5/5/2023 Page 7

Throw #1 Throw #2 Change in Mass

_____kg

Throw #3 Release Angle

_____ °

Throw #4 Mass of Weight

_____kg

Throw #5 Height of the Pivot

_____m

Distance Traveled (m)

_____ m _____ m _____ m _____ m _____ m

Mass of Projectile (kg)

_____ kg _____ kg _____ kg _____ kg _____ kg

Time (s) _____ s _____ s _____ s _____ s _____ s

Velocity (m/s)

_____ m/s _____ m/s _____ m/s _____ m/s _____ m/s

Kinetic Energy

_____ J _____ J _____ J _____ J _____ J

Potential Energy

_____ J _____ J _____ J _____ J _____ J

6. Go back and calculate the velocity of the projectile and record it on the table, using the formula:

Draft: 5/5/2023 Page 8

velocity=distance (m)time(s)

7. Work is done when a force is exerted on an object and the object moves a distance. Energy is the ability to do work. There are two kinds of energy: potential energy (PE) and kinetic energy (KE). Potential energy is the energy of position, or stored energy. Kinetic energy is the energy of motion. Potential energy is transferred to kinetic energy as soon as the object begins to move. Now, go back to each simulation and calculate the potential energy and kinetic energy in each situation and record it in the tables above.

PE=mghKE=12mv2

8. How did changing the mass of the projectile affect the amount of kinetic energy or potential energy available?

9. How did changing the release angle affect the amount of kinetic energy or potential energy available?

10. How did changing the mass of the weight affect the amount of kinetic energy or potential energy available?

11. How did changing the height of the pivot affect the amount of kinetic energy or potential energy available?

Draft: 5/5/2023 Page 9

m= mass of the projectilev=velocity of the projectileg=gravity (9.8m/s2)h=height of the pivot

Appendix D: Engineering Design Process

Appendix E: Dayton Trebuchet Packet

Name _____________________________

STEP 1: Identify the problem. What does your trebuchet need to be able to do? And what might limit how you accomplish this?

Materials Needed

________________________________ ________________________________

________________________________ ________________________________

________________________________ ________________________________

________________________________ ________________________________

STEP 2: Explore PossibilitiesCreate individual designs of the trebuchet on a separate sheet of paper.

STEP 3: Select an ApproachEach member of the team will share their individual design ideas. Then as a team decide on the best team design from the ideas gathered from the individual designs.

STEP 4: Team DrawingCreate a drawing of your team’s design. Be sure it is neat, detailed, labeled, indicates the dimensions of the finished prototype.

STEP 5: Construct the Chosen Design

STEP 6: Test and EvaluateTest your trebuchet for accuracy. Record the data collected in the table below. After each throw, determine and record any problems you encountered. Then, modify one variable to try to overcome that problem and test again. Continue modifying one variable at a time until you are satisfied with the design.

Throw #1 Throw #2 Throw #3 Throw #4 Throw #5

Distance Traveled (m)

_____ m _____ m _____ m _____ m _____ m

Mass of Projectile (kg)

_____ kg _____ kg _____ kg _____ kg _____ kg

Time (s) _____ s _____ s _____ s _____ s _____ s

Velocity (m/s)

_____ m/s _____ m/s _____ m/s _____ m/s _____ m/s

Kinetic Energy

_____ J _____ J _____ J _____ J _____ J

Potential Energy

_____ J _____ J _____ J _____ J _____ J

Draft: 5/5/2023 Page 12

Problems with the Design

Modifications to Design

STEP 7: Summary

On a separate piece of paper, a complete summary about the results of your trebuchet design. Be sure to include all of the steps of the engineering design process (problem, question, think, design, test, solution). Also, be sure to include your results, any problems, modifications, and why any modifications were made.

STEP 8: Questions/Reflections

A. How did the Engineering Design Process help you systematically design your trebuchet? Justify your answer with 2 reasons.

B. Explain the conversion of potential to kinetic energy through the travel path of your projectile.

C. What math did you use to better your design? (Hint: measurements and equations)

Draft: 5/5/2023 Page 13

D. What did you change to improve your design? What evidence or data proves that the modifications worked?

Draft: 5/5/2023 Page 14

Appendix F: Dayton Trebuchet Rubric

Name _____________________________

4 3 2 1Summary documents

design evolutionIncludes all of the following:1. statement of problem2. questioning3. brainstorming 4. designing5. testing6. solutions

Includes at least 5 of the following:1. statement of problem2. questioning3. brainstorming 4. designing5. testing6. solutions

Includes at least 4 of the following:1. statement of problem2. questioning3. brainstorming 4. designing5. testing6. solutions

Includes at least 3 of the following:1. statement of problem2. questioning3. brainstorming 4. designing5. testing6. solutions

Accurate documentation of data from all tests

Data tables include all of the following:1. data collected from all throws2. accurate calculations of KE3. accurate calculations of PE4. Notes on problems and modifications made

Data tables include 3 of the following:1. data collected from all throws2. accurate calculations of KE3. accurate calculations of PE4. Notes on problems and modifications made

Data tables include 2 of the following:1. data collected from all throws2. accurate calculations of KE3. accurate calculations of PE4. Notes on problems and modifications made

Data tables include 1 of the following:1. data collected from all throws2. accurate calculations of KE3. accurate calculations of PE4. Notes on problems and modifications made

Summary documents problems or issues needing

to be addressed in re-design

Summary includes the following:1. results2. any problems with the design3. modifications4. why any

Summary includes 3 of the following:1. results2. any problems with the design3. modifications4. why any

Summary includes 2 of the following:1. results2. any problems with the design3. modifications4. why any

Summary includes 1 of the following:1. results2. any problems with the design3. modifications4. why any

modifications were made

modifications were made

modifications were made

modifications were made

Trebuchet launch repeatability (3 times

accurate hit)

Was able to hit the target 3 times.

Was able to hit target 2 of the 3 times.

Was able to hit the target 1 of 3 times.

Was not able to hit the target.

Step 8: Question A Thoughtfully answered with two supporting justifications.

Answered with two supporting justifications, but lacks detail.

Answered with one supporting justification.

Answered, but provides no justification.

Step 8: Question B Accurately traces the conversion of potential energy to kinetic energy.

Traces the conversion of potential energy to kinetic energy with one mistake.

Traces the conversion of potential energy to kinetic energy with two mistakes.

Traces the conversion of potential energy to kinetic energy with more than two mistakes.

Step 8: Question C Accurately shows and explains the math used to better their design. Incudes both measurements made and equations used.

Accurately shows the math used to better their design. Incudes both measurements made and the equations used.

Accurately shows the math used to better their design. Incudes measurements made or the equations used.

Does not explain the math used to better the design.

Step 8: Question D Explains the changes made to the design (after each throw) and provides data to prove they worked.

Explains the changes made to the design (for at least 3 of the throws) and provides data to prove they worked.

Explains the changes made to the design (for 1 of the throws) and provides data to prove they worked.

Explains the changes made to the design but does provide data to prove they worked.

Draft: 5/5/2023 Page 16

Appendix G: Teacher Tips

The following pictures show different catapult designs built out of tinker toys. These should not be shown to students, but are to give teachers a starting point for guiding student innovation.

Small frame, small counterweight increasing potential energy.

Balance of arm creates greater potential energy.

Stabilization is key for maximizing potential energy.

Draft: 5/5/2023 Page 18

Appendix H: Background Information

“Trebuchet” comes from the French word “Trabucher” which means “to throw over.” The trebuchet was invented in China around 300 BC (Hennessey & Johnson). Europeans were first exposed to the weapon in the Middle East during the Crusades in 1187. The first trebuchet in England was used in 1213 during a siege to Dover Castle in an attempt to overthrow the English king by France. The trebuchet was the only siege weapon to be invented during the Middle Ages and was a counterweighted, stone-throwing device (Hull, 2004). Trebuchets were expensive and time-consuming to build, and were only used as a last resort. They typically were built at the site of the battle to break down walls of castles. And, these machines had to be run by experts that were brought in at great expense. Large stones and counterweights had to be found or quarried and brought in as well. Placement of the trebuchet near the target was critical since they have a limited range. Too far away and they missed the target. Too close and the soldiers were attacked by cross bows and killed. While trebuchets typically threw rocks, they also threw a variety of materials including fire, dung, dead bodies, diseased bodies, body parts, dead animals and anything rotting (Alchin, 2006). Trebuchets were used for about 100 years in Europe and the Middle East and eventually were replaced in war by the cannon (Hull, 2004).

The trebuchet hurls a projectile, which is put in a sling secured to the end of an arm with a large counterweight on the other end. When triggered, the counterweight fell which sent the projectile like a large rock on a high trajectory typically at a castle wall. These rocks could weigh 100 kg or more and were thrown 150-300 m. Range was adjusted by changing the length of the arm on the pivot (Hennessey & Johnson 2010). Some trebuchets also had a pivoting counterweight, while some were non-pivoting. Trebuchets also were on a cart with wheels while others were stationary. These changes allowed the projectile to be thrown straighter, faster and higher, resulting in better conversion of potential to kinetic energy (Hennessey & Johnson 2010).

Assuming a fixed counterweight, there are three phases needed to throw a projectile – slide, free hurl and unconstrained projectile motion. During the slide phase, the projectile moves on top of a trough until the force exerted by the trough on the projectile is zero. The projectile is released from the sling and moves in a gravity field (Hennessey & Johnson, 2010). The trebuchet illustrates Newton’s second law of motion that states that force equals mass times acceleration (F=MA). In this case, the forces are the weights of the beam, sling and counterweight. Acceleration is represented by the rotational acceleration of the beam and sling (O’Connor). The throwing action by the trebuchet is similar to an overhand baseball pitch where most of the acceleration is transferred to the baseball. The projectile trajectory once it is released is mostly determined by the weight of the projectile and the angle of the arm, while the range is determined by the counterweight, arm length and the length of the sling attachment (Metz, 2009).