Catapults-Potential Elastic Energy
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Catapults were invented by Archimedes of Syracuse, Sicily around the year 250 B.C. Archimedes was one of the top three mathematicians of all time along with Sir Isaac Newton and Friedrich Gauss. It was said that Archimedes was so consumed with solving problems, that he often times forgot to eat. His real hunger was to learn as much as he could about mathematics.
Catapults are simple machines. The most common simple machine is the lever. Catapults are third class levers. The base of the catapult acts as the fulcrum on which the catapult arm pivots. Force is provided by tension in rubber bands that are attached to the crossbar of the catapult.
Catapults store energy until you release the arm. This energy is called potential elastic energy. You store energy in elastic like a rubber band when you stretch it. The pulling sensation that you feel is called potential energy. Catapults store potential energy by stretching ropes and rubber bands and by bending and flexing a lever arm of wood or plastic. The more energy you pull back, the farther your projectile will go. When the projectile is released it converts the potential elastic energy into kinetic energy due to its motion.
When the arm of the catapult hits the crossbar or stops, the projectile leaves the bucket and launches forward. This is due to Newton’s first law which states that objects in motion want to stay in motion; likewise, objects at rest want to stay at rest. The projectile is moving at the same speed as the arm and the bucket. When the arm and bucket stops, the projectile keeps moving forward at the same velocity it was before. Gravity brings the projectile back to the ground that gives it its trajectory.
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Fulcrum position: By moving the fulcrum far away from the ball launch pad, the projectile will travel a longer distance. The fulcrum is the spot where a lever moves one way or another as with a seesaw. This catapult is more like a baseball bat (3rd class lever).
Increase potential energy: if you increase the number of sticks in the fulcrum from 7 to 13+, you increase the elasticity in the rubber band that will cause the projectile to go further.
Increase fulcrum length: if you add additional sticks to the lever arm, you will increase the potential energy as well.
Increase the number of spoons: this only makes your catapult more fun; you can launch multiple objects at the same time.
Change the weight of your projectile: Since force = mass times acceleration (F=MA), the children will see how heavier objects will have less acceleration with the same force.
Improve your design: the children were able to see many examples of catapult designs created by a seventh grade class. During the holiday break, they should work with inexpensive household materials to create a better catapult. Invention is a process of continuous improvement.
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Catapult Construction
In class, the children made a simple catapult with the following materials:
9 tongue-depressors or popsicle sticks
5 rubber bands
something to toss around like an eraser, light ball or balled up aluminum foil
hot glue gun is optional (if you use this, you only need 3 rubber bands)
Step 1: stack 7 sticks together and use two rubber bands on either end to secure.
Step 2: stack 2 sticks together and use one rubber band (on one end only) to secure.
Step 3: spread the open end of those two sticks apart and place the 7 sticks perpendicular inside of the open end; push the 7 sticks as far down toward the rubber band side as possible.
Step 4: take another rubber band and secure the cross together.
Step 5: take the spoon and attach to one of the two sticks and secure with two rubber bands.
Step 6: put the projectile in your spoon bowl and launch.
Pictures of these steps were emailed to each Mathlete.
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