Materials Included In Kit

Additional Materials Required

Prelab Preparation

Use a pair of scissors to cut the 9" x 12" felt pieces so each group has one 3" x 4" piece of felt.

Safety Precautions

Use caution when launching projectile. Do not aim the trebuchet at anyone. Launching should be performed only in the area specified by the instructor. Wear safety glasses at all times during this activity. Please follow all laboratory safety guidelines.

Lab Hints

• The kit provides the classroom with 5 blue rubber spheres and 5 red rubber spheres. When students are ready for the Design Challenge, a fun target would be a bucket on opposite ends of the classroom for the “red team” and “blue team.” The difficulty can be increased by the use of “walls” or obstacles that the projectile must clear.
• Ensure that students tightly seal the eyebolt on the cap of the counterweight bottle to prevent spills of sand and water.
• The fishing line is used to hold the counterweight because it has greater tensile strength than the regular string. When tested with regular string the heavy counterweight had a tendency to rip the string.
• A fun alternative projectile may be small mellocreme pumpkin candies to have your very own pumpkin-chunkin’ competition! These projectiles were tested in lab and work very well with the apparatus.

Teacher Tips

• This activity may be used with a unit on force and motion, energy transfer or simple machines.
• Some smart phones have a slow motion video feature. Allow students to record their launches in order to better analyze the motion of the trebuchet and projectile.
• Complete analysis of the physics of the trebuchet requires complex analysis of angles, friction and torque. The analysis for this activity has been purposely shifted toward a semi-quantitative approach in order to have the activity be more accessible. Feel free to add further mathematical analysis depending on the prerequisite knowledge of your students.
• This can be a great introduction to projectile motion physics to give students an insight into the multiple components that building a machine like this requires. This is a great activity for students to take inspiration from in order to build their own devices at competitive launching events.

Answers to Prelab Questions

1. Examine Figure 4 in the Background section.
   1. At what angle should a projectile be launched to reach the greatest horizontal distance?

      A projectile launched at a 45-degree angle has the greatest horizontal range.

   2. Which pairs of angles reach the same horizontal distance but have different vertical components?

      Angles of 75 and 15 degrees have the same horizontal range, and angles of 60 and 30 degrees have the same horizontal range.

   3. What pattern do you see regarding the pairs of launch angles that result in the same horizontal distance?

      Two angles that add up to 90 degrees have the same horizontal range, but different vertical components.

   4. Based on your answer to 1c, at what other angle could a projectile be launched that would have the same horizontal range as when it was launched at a 15-degree angle?

      Assume initial speed is the same. A projectile launched at 75 degrees would reach the same horizontal distance as when it was launched at 15 degrees.

2. Describe the safety hazards and precautions associated with this activity.

   Projectiles launched from the trebuchet could hit someone. Do not aim the hot glue trebuchet at anyone. Trebuchet launching should be performed only in the area specified by the instructor. Wear safety glasses at all times during this activity.

Answers to Questions

1. Do you think that changing the height of the fulcrum affects the speed at which the projectile is launched? Why or why not?

   Student answers may vary. No, changing the height of the fulcrum does not affect the speed of the projectile at launch because the counterweight still “falls” the same distance and therefore transfers the same amount of potential energy at any chosen fulcrum height. The range may differ simply due to the different height releasing the payload at a different point. The range will change drastically only due to changes in release method and not necessarily due to fulcrum height.

2. Does the ratio of “distance from fulcrum to counterweight” to “distance from fulcrum to sling attachment point” affect the range of the trebuchet?

   The ratio changes the torque that the counterweight can exert on the other end of the fulcrum. The shorter the distance to the counterweight, the less torque may be exerted. The best ratio is 1:3.75.

3. Based on your trebuchet testing experience, rank the variables tested in order from “most affects trebuchet range” to “least affects trebuchet range.”

   Student answers will vary depending on their experimental results and chosen angles and weights to test. Generally, the angle the release wire makes with the cork will have the greatest impact on range closely followed by the fulcrum distance ratio on the pivot arm and mass of the counterweight. The least important factor is the height of the fulcrum.

4. The length of the sling was a constant throughout your trials. Do you believe that changing the length of the sling would affect the performance of the trebuchet?

   Student answers will vary. Yes, sling length will alter the range of the projectile with too short or too long of a sling reducing range and affecting projectile speed. The best length is a sling length equal to the long side of the pivot arm (measured from fulcrum to sling attachment point).

5. Did your modified trebuchet achieve the desired results? If not, what improvements might be made?

   Student answers will vary.

Introduction

Combining a lever and a sling—two simple machines—can lead to a mechanical advantage capable of launching a 35-kg object a distance of 300 meters! Trebuchets, a compound machine, were popularly used in medieval warfare to breach enemy walls. Optimize your trebuchet to gain an advantage on the battlefield!

Concepts

• Simple machines
• Compound machines
• Potential and kinetic energy
• Projectile motion

Background

When it came to siege warfare, the trebuchet was by far the most popular weapon used before the invention of gunpowder. It easily outperformed the catapult due to the ingenuity of combining the lever and sling that allowed for greater range and accuracy. A lever is a simple machine used for the transfer and modification of force and motion. In a lever system, the lever itself turns or pivots on one point or axis called the fulcrum. The load is whatever is being moved—a rock, a load in a wheelbarrow or the counterweight of the trebuchet. The trebuchet itself was derived from an ancient weapon called the staff sling, a short piece of wood with a sling attached at the end. The first trebuchet, invented by the Chinese around the 4th century BC, was the traction trebuchet and relied on the manpower of several men using ropes to pull the lever arm down and launch the projectile. This proved inefficient and it was not until the 12th century AD that the counterweight trebuchet was built. The force that pulled the lever arm down was now gravity and it drastically reduced the number of men needed to operate it.

A trebuchet works by converting the gravitational potential energy of a falling counterweight to kinetic energy in order to launch a payload while using mechanical advantage to achieve a high launch speed (see Figure 1). Mechanical advantage is defined as the ratio of force output to the force applied.

The trebuchet consists of a beam that can be thought of as two parts divided at the fulcrum: the payload (long) side and the counterweight (short) side. A sling with a pouch is attached to the end of the payload side. One cord on the string is fixed onto the beam while the other end is hooked onto a malleable metal pin (see Figure 2). For best results, the sling should be the same length as the long side of the beam. The heavy counterweight provides the force (its weight) to swing the entire beam at a high speed. As the counterweight falls, the long end swings upright with the speed of rotation causing the ring to slip off the metal pin and allow for the sling to open and launch the projectile. Since the projectile is far from the fulcrum, it is launched with great speed. Several factors affect how far a projectile will travel, including the launch angle (adjusted by moving the metal pin) and the strength of the initial push or pull that sets the object in motion. The component forces acting on the projectile are the initial forces that set the object in motion and the vertical force of gravity pulling down. Once the projectile is launched, no horizontal force acts upon it, only gravity. Without gravity, the projectile would continue to travel upward, following the trajectory of the launch angle. The force of gravity makes the projectile fall beneath its intended path (see Figure 3). As a result, the path a projectile takes is a parabola. Figure 4 illustrates the path of a projectile launched at the same initial speed but at various angles. Neglecting air resistance, this pattern is the same for all projectiles launched with the same initial speed.

Experiment Overview

The purpose of this activity is to construct a model trebuchet with the materials provided. The apparatus allows for testing of different heights, arm lengths, counterweights, and release angles that affect the distance of projectile. The procedure provides a model for guided-inquiry design of experiments to determine what modifications may be made to the trebuchet that provide the best solution to the given challenges.

Materials

Prelab Questions

1. Examine Figure 4 in the Background section.
   1. At what angle should a projectile be launched to reach the greatest horizontal distance?
   2. Which pairs of angles reach the same horizontal distance but have different vertical components?
   3. What pattern do you see regarding the pairs of launch angles that result in the same horizontal distance?
   4. Based on your answer to 1c, at what other angle could a projectile be launched that would have the same horizontal range as when it was launched at a 15-degree angle? Assume initial speed is the same.
2. Describe the safety hazards and precautions associated with this activity.

Safety Precautions

Use caution when launching projectile. Do not aim the trebuchet at anyone. Launching should be performed only in the area specified by the instructor. Wear safety glasses at all times during this activity. Please follow all laboratory safety guidelines.

Procedure

Part I. Trebuchet Assembly

1. Obtain the four screws, trebuchet base and both trebuchet legs. Align the pre-drilled holes on the base with one of the legs, with the angled side of the base facing outward (see Figure 5). Note: Make sure the edge of the leg is flush with the edge of the base.
   {14077_Procedure_Figure_5}
2. Place a screw at one of the holes aligned with the leg and using a screwdriver, drive it into the wooden leg.
3. Drive the second screw into the remaining hole. The leg should hold firm and the bottom of the angled side should be flush with the edge of the base.
4. Repeat steps 1–3 for the second trebuchet leg. The angled sides of each leg should be facing away from each other.
5. Obtain the bottle cap, two hex nuts, two washers and an eyebolt. Place a washer and then a hex nut on top of the cap, aligned with the center of the hole.
6. Screw the eyebolt through the hex nut until it cannot go further through the cap.
7. On the bottom of the cap, place a washer and then screw a hex nut onto the eyebolt thread until it is flush with the bottom of the cap. Note: The eyebolt should now be firmly fixed through the center of the cap, if not, tighten the hex nuts.
8. Obtain the 12-cm long metal wire and pivot arm.
9. Take the wire and bend it into an “L” shape with a 3-cm short side.
10. Thread the short side of the wire “L” through the small hole second farthest from the fulcrum holes (see Figure 6).
    {14077_Procedure_Figure_6}
11. Using pliers, bend the 3-cm length of wire so it is as flat as possible against the side of the pivot arm (see Figure 7).
    {14077_Procedure_Figure_7}
12. Make sure the wire is pressed as flat as possible on both sides of the pivot arm. Using a hot glue gun, glue the wire on both sides so it holds firm and does not rotate.
13. Cut a 10-cm long piece of fishing line and thread it through the small hole closest to the fulcrum holes. Tie the line into a loop so it hangs approximately 3 cm from the end of the pivot arm (see Figure 8).
    {14077_Procedure_Figure_8}
14. Obtain a washer, two 40-cm long pieces of string, and a 3" x 4" piece of felt.
15. Use a pair of scissors to cut a hole at each corner of the felt piece leaving a centimeter of fabric between the hole and the edges of the piece.
16. Thread one 40-cm piece of string through the small hole farthest from the fulcrum holes of the pivot arm. Tie each end of the string to a hole on one of the 3" sides of the felt piece (see Figure 9).
17. Fold the remaining piece of string in half and thread the loop through the washer. Thread the free ends of the strings through the loop and pull tight (see Figure 10).
    {14077_Procedure_Figure_9and10}
18. Tie the two free ends of the string to the remaining two holes of the felt piece. This felt piece is now the pouch that holds the projectile.
19. Push the metal wire protruding from the end of the pivot arm through the center of the cork and guide the cork along the wire until it stops at the end of the pivot arm.

Part II. Optimizing Range

Be sure to wear safety glasses when any team is testing a trebuchet. Do not launch the projectile at anyone.

A. Initial Test

1. Fill the counterweight bottle with 150 g of sand. Make sure the bottle is sealed tightly.
2. Place the metal rod (fulcrum) through the middle hole on one stand leg, then through hole “C” of the pivot arm and finally through the middle hole of the second leg (see Figure 6 in Part I).
3. Bend the metal wire so it makes approximately a 40-degree angle with the top of the cork (see Figure 11). Note: Always keep the cork perpendicular to the end of the pivot arm.
   {14077_Procedure_Figure_11}
4. Weigh and record the mass of the projectile (rubber sphere).
5. Set the trebuchet on the floor.
6. Slide the washer onto the metal wire.
7. Make sure no one is in the path of the projectile. Place the rubber sphere in the pouch and pull it down to the center of the base. Release the sling.
8. Note the underwhelming result.

B. Optimize the Variables

9. In order to optimize the range of the trebuchet, change the following variables:
   1. Weight of the counterweight. For example, test the effect of the counterweight on the range of the projectile by adding or removing sand. The weight can also be increased by adding water. .
   2. Ratio of the distance between the fulcrum to the counterweight’s attachment point to the distance between fulcrum and sling’s attachment point (move the fulcrum from hole B and A). .
   3. Height of the fulcrum. .
   4. Angle that the wire makes with the top of the cork.

In your own notes, keep track of how each variable affects the distance covered by the projectile.

Part III. Design Challenge

Modify your trebuchet to hit a target at a set distance provided by your instructor with a minimum 80% accuracy, or at least 4 out of 5 trials.

Student Worksheet PDF

14077_Student1.pdf