Important Physics Principles for Punkin Chunkin In order for the pumpkin to go flying through the air, work must be done on the pumpkin. Work is a force applied over some distance. When work is done, it requires a transfer of energy. In punkin chunkin, where does this energy come from??
Potential energy– energy due to the position of an object. There are two types of PE that we need to focus on: Gravitational PE and Elastic PE. Gravitational potential energy– the potential energy associated with an object due to the position of the object relative to the Earth or some other gravitational source. Imagine an egg falling off a table. As it falls, it gains kinetic energy. Where does the egg’s kinetic energy come from?
It comes from the gravitational potential energy that is associated with the egg’s initial position on the table relative to the floor. The amount of gravitational PE associated with an object depends on the object’s mass and height above the Earth. PE g = mgh, where m is mass, g is acceleration due to gravity, and h is height.
Elastic potential energy– the potential energy in a stretched or compressed elastic object. It is stored in any compressed or stretched object, such as a spring or the stretched strings of a tennis racket or guitar. The length of a spring when no external forces are acting on it is called the relaxed length of the spring. When an external force compresses or stretches the spring, elastic potential energy is stored in the spring.
The amount of energy depends on the distance the spring is compressed or stretched from its relaxed length. Elastic potential energy can be determined using the following equation: PE elastic = ½kx 2 The symbol k is called the spring constant, or force constant. For a flexible spring, k is small, whereas for a stiff spring k is large. k has units of N/m. x is the distance compressed or stretched.
Projectiles Projectile– objects that are thrown or launched into the air and are subject only to the force of gravity. The path of a projectile is called its trajectory. Projectiles follow a curved path. The horizontal displacement of a projectile is called its range. To achieve maximum range, a projectile should be launched at 45⁰.
Simple Machines Machine-- any device that transmits or modifies force, usually by changing the force applied to an object. All machines are combinations or modifications of six fundamental types of machines called simple machines. The six simple machines are the lever, pulley, inclined plane, wheel and axle, wedge and screw.
Levers Of the 6 simple machines, the lever is going to be the most relevant in the design of a catapult or a trebuchet. A lever is a simple machine that makes work easier. It involves moving a load around a pivot (fulcrum) using force. Many of our basic tools use levers: scissors, pliers, hammer claws, tweezers, nut crackers, and tongs.
In a Type 1 Lever, the pivot (fulcrum) is between the effort and the load. In an off-center type one lever (like a pliers), the load is larger than the effort, but is moved through a smaller distance.
Examples of common tools (and other items) that use a type 1 lever include:
In a Type 2 Lever, the load is between the pivot (fulcrum) and the effort.
Examples of common tools that use a type 2 lever include:
In a Type 3 Lever, the effort is between the pivot (fulcrum) and the load.
Examples of common tools that use a type 3 lever include:
C A T A P U L T S C A T A P U L T S Physics, Background and History
Definition A machine that converts POTENTIAL ENERGY into mechanical motion or KINETIC ENERGY ” Comes from the Greek word “ Katapultos, ” meaning “ shield crusher ” AKA: Siege Engine or Siege Machine
The Invention The catapult, as we would recognize it today, was invented by the Greeks about 399 BC but various forms were found in central Asia much earlier than that
How was it used in Medieval times? First we need to understand the society of the Middle Ages Fear was rampant (AKA: Dark Ages) There was huge disparity between the rich and poor (Feudalism) Castles were constructed to protect nobles (& peasants but only during crisis)
Catapult AKA Siege Machine or Siege Engine What is a siege? Siege--One army surrounds an enemy, keeping help, goods and water from leaving or entering the castle.
A typical catapult has each of the following: Arm Base Elastic Force Fulcrum Catapult Structure & Design
Most catapults were made of wood The elastic force provided by twisted rope, springs, saplings The fulcrum is the point of support for a lever- which in the case of a catapult is the arm
Factors Affecting Distance Mass of object being hurled Strength & flexibility of arm Mass of arm Length of the arm How far the arm is pulled back Angle of base or release (best angle?) Small transfer of energy into distortion
Mangonel French “Engine of War” Typical catapult
Mangonel catapults work just like third class levers. The base of the catapult acts as the fulcrum which the catapult arm pivots on. The force is provided by tension in rubber bands which are attached to the crossbar of the catapult.
When the arm is pulled back, the rubber bands tighten, so when the arm is released, the arm propels forward until it his the crossbar. The load acts as the projectile in the bucket. When the arm hits the crossbar, the projectile leaves the bucket and launches forward. This is due to Newtons 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 stop, the projectile continues to move forward at the same velocity it was before. Gravity brings the projectile back to the ground which gives it its trajectory.
Trebuchet French meaning “to stumble” Used a sling with the arm Extremely accurate Most advanced of all catapults
The trebuchet is a Type-1 lever. In the Type-1 lever, the force is applied to one end, the load is on the other end and the fulcrum sits between the two. The playground see-saw is a Type-1 lever. For the trebuchet, the force is very large and the load is very small. It would be like putting an elephant on one side of the see-saw and a small child on the other. You can imagine the result. The other thing that happens is if you move the fulcrum towards the force end (the elephant), the other end will move further. The elephant drops one foot and the small child end moves six feet.
The sling is the oldest projectile weapon. There is a pouch to hold the projectile and two long strings. Both ends of the string are held in one hand and the sling is swung around and around. Then, at the proper moment, one end of the sling is let go with the other end is still held by the hand. The pouch can no longer hold the projectile and the projectile continues on its way. For the trebuchet, this release is done with a nearly straight hook so that the sling swings out and eventually slips off the hook, releasing the projectile.
The trebuchet starts with a long arm. The axle (fulcrum) is more towards one end than the other. The short end has a heavy counterweight and the other end has a sling. When it's "cocked and locked", the counterweight is high and ready to drop. The projectile sits in the pouch of the sling beneath the trebuchet, ready to be pulled along and flung.
When the trigger is released, the counterweight begins to drop. This moves the other end of the arm very quickly and the projectile in the sling is dragged along underneath the machine. As the weight continues to drop, the arm continues to swing. Newton’s 1 st Law holds the sling taunt as the sling swings out but the one end of the sling is still looped over the hook. Forces try to straighten out the sling and eventually the loop on one end slips off the hook. The projectile is no longer held in the pouch and so continues on its way down range.