27-03-2014, 12:16 PM
Catapult Project
Catapult Project[.doc (Size: 1.13 MB / Downloads: 20)
Introduction
A famous man once said, “Make love, not war.” This man, however, was not protecting his coveted parking and up to date educational facilities. If this had been the case, perhaps he would be instead famous for something like, “An empty space is an envied space.” Our parking area must be saved!
In order to save our cherished downtown campus, drastic measures were taken. These measures came in the form of a catapult. However, to maximize the performance of these catapults the Dynamics class was divided into groups and given the task of developing a prototype. In order to develop a prototype, knowledge gained from class was used, such as projectile motion and the dynamics of particles and rigid bodies.
The intent of this project was to put the theoretical knowledge learned in class to particle use. Each group had the responsibility to design, analyze mathematically, simulate using Working Model, build, and test their catapults to meet the set criteria. The specifications were that the catapult must be capable of clearing a wall 5 feet high but not hit the ceiling 8 feet above the floor. Also the projectile must land 20 feet from the starting position. The catapult must be constructed from wood, steel, or aluminum and use a common linear spring.
Design
The catapult was designed to look like a typical catapult and launch the ½” diameter clay ball when it hit a stop mounted on a shaft (see Figure 1). Its motion was provided by a spring compressed before release. The spring was placed under the arm of the catapult so that it would be compressed and provide force. The design process focused on making the catapult adjustable so that it would work with any spring.
Analysis of catapult
Points on the catapult were named so that they could be referenced. The pivot point was called A, the end of the lever arm was called B and the point represented by the center of mass, cm. The catapult had dimensions, therefore it was a rigid body. Kinematics (of a rigid body) was used to find the angular velocity and the velocity of the center of mass.
Construction
The catapult components were either purchased or machined with an end mill. The catapult was built according to the drawings and bill of materials (see Appendix). The slots and holes were made with end mills, drill bits, and thread tapping was done by hand. The lathe was used to turn the arm shaft to fit the wheel baring inner diameter.
Prediction of performance
Using the calculation above the catapult was tested and modified to acquire the proper projection. The durability and consistency of the catapult were a good indication of what was to be expected. The results from testing provided concrete evidence of the projection and the catapult was equipped for the proper adjustment because of its design.
Conclusion
There were some sources of error that caused minor deviation. These discrepancies were cause by friction at the pivot point, measurement errors due to rounding, and the neglect of air resistance of ball while in flight. Another source of error was due to the inaccurate means in which the spring constant was calculated. Finally, the arc traced by the lever arm produced a changing angle between the arm and the base, which caused some error in the calculation of the desired compression of the spring. In all the catapult was built very well and fully adjustable allowing for fine tuning and will perform well in the competition.