The beginning of the launch is illustrated in the figure below. As you can see, the counterweight pivots around a much shorter distance than the payload end. The advantage of this is that the payload end of the beam reaches a much higher linear velocity than the counterweight end of the beam.
This is the principle of mechanical advantage, and is what allows the payload to reach a high launch velocity. However, because the counterweight pivots around a much shorter distance, its weight must be much greater than the weight of the payload, to get a high launch velocity.
However, increasing the mass of the counterweight beyond a certain point will not help, since the limiting speed of the falling counterweight is free-fall speed. At this point the ring which is connected to the sling and loops around the finger for support slips off and the payload is launched. The figure below illustrates the trebuchet at the release point. As the beam rotates clockwise due to the falling counterweight , the payload experiences centripetal acceleration which causes it to move outwards since it is unrestrained.
This results in a large increase in linear velocity of the payload which far exceeds that of the end of the beam to which the sling is attached.
This is the heart of the physics behind a trebuchet and is the reason why a trebuchet has such great launching power. For a more in-depth explanation on how a trebuchet works see Trebuchet Physics. In this page the basic equations describing the physics of a trebuchet will be introduced. To assist you in building a trebuchet you can use this simulator to help you come up with the design that throws the payload the farthest.
This is very useful for helping you come up with the winning design in a trebuchet competition! In the next section we will look at the mangonel. Author: ChrisO The above picture of the mangonel is what people are most familiar with when they think of catapults. The mangonel consists of an arm with a bowl-shaped bucket attached to the end. In this bucket a payload is placed.
Upon release, the arm rotates at a high speed and throws the payload out of the bucket, towards the target. The launch velocity of the payload is equal to the velocity of the arm at the bucket end. The launch angle of the payload is controlled by stopping the arm using a crossbar.
This crossbar is positioned so as to stop the arm at the desired angle which results in the payload being launched out of the bucket at the desired launch angle. This crossbar can be padded to cushion the impact. There are are three primary technologies that fall into the "catapult" category. The catapult : the winched-down bucket that people normally think about when they hear the word "catapult" see this page for a picture.
The ballista is a very large crossbow see this page for a picture. A trebuchet is a weighted beam that swings a sling carrying the projectile see this page for pictures. A trebuchet tends to be easier to build because it consists simply of a pivoting beam and a counterweight that rotates the beam through an arc.
Catapults can launch things a fair distance -- to 1, feet to meters is common. It is surprising how much energy they can store.
The key thing to remember about any projectile-motion problem is that once the projectile has been released, the only force it is subjected to is that of its own weight resulting from gravity. When a projectile is released, it has both horizontal and vertical components of motion.
Luckily for physicists and students, these can be analyzed separately, since gravity does not affect horizontal motion. Thus if you want to launch a projectile as far as possible, point it exactly halfway to a point directly overhead and fire away!
Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs. More about Kevin and links to his professional work can be found at www. How Does a Catapult Work? See the Resources for a handy guide to making your own small-scale catapult. Related Articles Modern Uses of a Catapult. How to Calculate Tangential Force. How to Build an Easy Catapult for Kids.
History of the Pendulum. How to Calculate Catapult Force. How to Make a Pulley for Children.
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