Embedded Files
Proof Of Efficacy
Our Design:
We designed our trebuchet to launch a projectile as long as possible. The farthest that we launched our projectile was 40 meters horizontally and 19.6 meters vertically. Our average launch angle was 87.5 degrees. Our trebuchet is able to launch a 27 gram piece of clay at a velocity of up to 22.27 meters per second or 50 miles per hour. The total flight time of our object was 2 seconds. The horizontal velocity of our projectile was 20 meters per second squared. The vertical velocity was 9.8 meters per second squared. This equaled a total velocity of 22.27 meters per second squared. With 8 rubber bands, the spring constant is 666.4 Newtons. When pulled back to a 90 degree angle the potential energy is 97.2 joules. Once released 57% of the potential energy transfers to kinetic energy which makes the kinetic energy 55.4 joules. Our trebuchet is the best because it shot farther than any of our competitors. It is also child friendly and easy to put together. It can also shoot any projectile as long as it has a string attached and it can also shoot farther the more rubber bands that you add. Single Variable analysis:
Our claim is that the farther that the farther that you pull back the arm the farther that it launches the projectile. Our table shows how far the projectile launched relative to how the angle the arm was pulled back. There will be a point where no matter how far back you pull the arm it will either break the rubber bands or the arm will be in the ground. Our reason behind our claim is that the farther that you pull back the arm the potential energy will be larger which will then convert to a larger amount of kinetic energy which will cause the projectile to go farther.
Our 8 modifications:
Change in the angle of the arm: The farther back that you pull the arm the larger the potential energy which then results in a higher kinetic energy which causes the projectile to go farther.
Location of the screw on the base: The location of the screw on the base matters because the farther back that screw is increases how far that the rubber bands have to stretch which increases the potential energy.
Adding weight to the effort side of the arm: Increasing the weight that is on the effort side makes the arm balance better which then helps the arm move faster.
Increasing arm length: The longer that the arm is the higher above the ground the projectile will be which will allow the projectile to fly higher.
Changing the projectile weight: The heavier the projectile is the more inertia it will have allowing it to fly farther.
Load to effort axle ratio: The load to effort ratio allows the rubber bands to pull on the shorter side of the arm. This moves the longer side faster.
Longer projectile string: The longer the string is the longer that the potential centrifugal force is.
Thicker rubber band: The thicker that the rubber band is the more energy it can store.
Physics Terms
Spring Constant - The spring constant, which is shown by the symbol k, is a property of a spring that quantifies its elasticity or how rigid it is. It's defined as the ratio of the force exerted on the spring to the displacement of the spring from its equilibrium position.
Spring Potential Energy - Spring potential energy is the energy stored in a spring when it is either compressed or stretched from its natural length. This energy can be calculated using the formula PE = ½k*x², where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
Kinetic Energy - Kinetic energy is the energy an object possesses due to its motion, and it is calculated using the formula KE = ½m*v², where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
Horizontal Velocity - Horizontal velocity refers to the component of an object's velocity that is directed along the horizontal axis. It is necessary for understanding the motion of projectiles, as it affects how far the projectile will travel before hitting the ground.
5. Vertical Velocity is the rate of an object's movement in the vertical direction, crucial for calculating how fast a projectile will travel to a height which can be calculated using the vertical velocity.
6. Total Velocity combines both vertical and horizontal movements, providing a absolute of the projectile's trajectory. Represented as a vector, it reveals insights into overall performance, including horizontal distance traveled and speed variations due to forces like air resistance.
7. Vertical Height - Measures how high the projectile travels, which is crucial for determining vertical velocity.
Reflection
I believe that our group did well for this project. I think we were fairly well on task across the duration of the project.
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