Each group of students designs and builds a catapult that will launch a projectile at a target sixteen feet away with accuracy and precision. The projectile must also pass over a one-meter tall wall without touching it. The projectile will be a ping-pong ball or hollow golf ball (supplied by the teacher). A catapult is not necessarily a device based on the lever. The purpose, as stated, is to launch a projectile sixteen feet with precision and accuracy. There are many ways to accomplish this task. Students are encouraged not to limit their imagination to preconceived concepts or to pictures they may have seen of ancient weapons.
Class discussions will begin with Newton’s Laws of Motion and should lead to a discussion of energy conservation. The students will need to understand how the initial potential energy stored in their machine is converted first into kinetic energy and then into gravitational potential energy and kinetic energy and then finally into solely kinetic energy again.
The students will need to determine the energy stored in their machine before the launch. For a spring powered catapult this can be determined by using the spring constant for their spring and the distance that the spring is stretched or compressed according to the formula:
where k=spring constant in Newton-Meters
x is the distance the spring is stretched or compressed in meters
f is force
The students will determine the mass of the projectile with a balance, as well as the angle of launch with a protractor or through basic trigonometric calculations.
Using the relationship:
d = v2/ g
g=acceleration due to gravity
d=distance the projectile travels (the range)
the students can predict the initial speed of the projectile.
The students will use the Vy component of the initial velocity:
Vy = Vi * sin of the launch angle
to predict the maximum height of the projectile using:
Vf2 = Vi2 * 2gh
g=acceleration of gravity
Vf = 0
The PhysicsClassroom.com has a great tutorial on Non-Horizontally Launched Projectile Problems.
The students will then test their hypothesis by building and firing a projectile launcher and compare the results of their experiment to their predictions. In analyzing the reasons for any difference between the prediction and the result, students will gain a deeper understanding about how forces work in nature including the concept of friction and net force.