Design Engineering Challenge: The Big Dig Contest Platter Strategies: Ball Liberation

Transcription

1 Poblem Set 4: Unifom Cicula Motion Design Engineeing Challenge: The Big Dig.007 Contest Platte Stategies: Ball Libeation Oeall Notes: You ae not equied to pefom the actual analysis in this poblem set, as they will do some example analysis on the next poblem set. In this poblem set, you should conside each of the aious possibilities and detemine what physic pinciples ae equied to sole the poblem. Fo each question, you should descibe the physics in wods to show a physical undestanding of the poblem, as well as note simple fee body diagams and the impotant equations. Two examples of good dawings and a few sets of supplemental equations ae shown in this solution. The emainde of the answes gien in the solution ae desciptions of the impotant physics, with some eal wold.007 consideations added in. You may hae a solution that is not listed in this solution, which is pefectly acceptable, as long as you can justify it in the futue! PROBLEM 1: Methods to libeate shot put without touching them By centifugal action: Rotate the platte until the centifugal foce on the shot puts is lage enough to dislodge them.? R F cent Figue 1: Sketch of a paticle otating at a speed? Whee, m: mass of paticle : tangential speed of paticle?: angula speed of paticle a adial : adial acceleation F cent : centifugal foce acting on the mass paticle in the adial diection

2 : Radius fom cente of otation to cente of paticle = ω aadial = Fcent = m * aadial = m * To libeate a shot put, F cent must be geate than the foce equied to dislodge it, which you will analyze in the next poblem set. Anothe consideation is the toque equied to acceleate the platte up to the equied otational elocity? (uses the otational esion of F = m*a, Γ= I α ). The inetia I is composed of the platte and the shot puts, while the inetia of the hockey balls can be consideed less than the othe items. Afte the shot puts ae on the gound, the ca can acquie the shot puts using seeal diffeent stategies. Possible stategies fo acquiing the balls include picking them up with a shoel, olling them onto the machine using a amp, o othe mechanisms to load the shot puts onto the machine s body. If the machine will oll the shot puts to the scoing bin, then a shoel o some fom of contolling stuctue is needed. By impacting the platte: Hit the platte with the ehicle so as to impat enegy to the shot-puts. This enegy must be high enough to dislodge them. Physics of impact and collision will hae to be consideed. This stategy is isky as it may damage the table o the machine. By ibating the platte: Shake the platte at a high fequency to incementally impat enegy to the shot-puts until it is high enough to dislodge them. Physics of ibation and collision will need to be consideed. The platte can be ibated by hitting it o spinning it back and foth.

3 PROBLEM : Methods to libeate shot put by touching them By pushing the shot-puts: Fix the otating platte and hit the shot put using an am o some featue of the machine. Physics of this stategy ae simple foce and moment balances, as well as a consideation of enegy aailable. To otate an am with sufficient toque to push a heay shot-put may equie moe poweful motos then the ones used in the.007 competition. By applying a diect impact foce: This can be achieed by means of a plunge, pojectile, o a swinging am. This stategy is a difficult stategy to employ, as it equies a lage foce at high elocity to dislodge the shot put and equies the machine to pecisely aim the stiking mechanism. The physics inoled in this stategy include foce and moment balance, impact and momentum and enegy pinciples. By amming the shot-puts with the machine: While deploying a pojectile o swinging am can be difficult, a supe simple method of impacting a lage foce into the balls on the platte is to am them with a machine. In this case, simila physics to the peious case must be consideed. In addition, the amming momentum must be calculated based on how fast the machine is moing when it hits the shot puts. This momentum is based on acceleation of the ca oe the distance it has taeled combined with the total mass being acceleated. By gabbing the shot-put while on the platte then lifting it: This stategy would equie an analysis based on wok and enegy pinciples, as well as a moment balance to ensue that the ca doesn t tip. Also, concepts such as fiction and slipping will need to be consideed. In a eal wold sense, this stategy can equie complicated mechanism. While the Keep It Supe Simple (KISS) pinciple says this may not be a good stategy, it shouldn t be thown away immediately.

4 PROBLEM 3: Methods to libeate the hockey balls without touching them The same stategies used fo poblem one apply when libeating the hockey balls. Howee, the hockey balls ae much lighte; hence much less enegy is equied to libeate the hockey balls compaed to the shot puts. Since it takes much less enegy to spin the hockey balls loose, it would be easie to spin the platte and send the balls flying. Howee, you still hae to conside the shot puts! Eithe you must emoe them fist o include them in the calculations. When tying to emoe the shot puts by centifugal action, the hockey balls can mostly be disegaded since thei inetia is much smalle than the shot puts. When tying to emoe the hockey balls, the shot puts still epesent moe inetia to acceleate, unless they hae been emoed. In both cases, the toque equied to acceleate the disk must include the inetia of both the hockey balls and the shot puts. The cucial diffeence between the two cases is the time equied to acceleate the platte to the elocity at which the balls o shot puts pop out of thei hole. PROBLEM 4: Methods to libeate hockey balls by touching them The same stategies used fo poblem two apply when libeating the hockey balls. Howee, the hockey balls ae much lighte; hence less enegy is equied to libeate the hockey balls compaed to the shot puts. Fo the hockey balls, the enegy equied to acquie the balls is much less. Stategies such as lifting shoels and plows ae much moe likely to wok successfully.

5 PROBLEM 5: What do you think is the best stategy? Thee ae many stategies that can be defined as best if a logical analysis has been made. Pope justification must be made fo whatee stategy is selected. You solution should include a weighted selection chat of the diffeent stategies. One good stategy is to push the shot puts off the platte then spin the platte to get the hockey balls. Expeiments ae needed to check what foces and speeds ae needed to libeate them by just spinning the wheel. An analysis of powe and enegy aailable in the system (called a Powe Budget) is equied to make sue that you motos can supply sufficient foce at the equied speed. Shot-put Platte Moto output wheel O platte R Figue : sketch of shot-put on the otating platte A simple analysis to get a feel of the powe in the system can be pefomed. (Powe calculations aen t equied in this poblem set!! This is simply to bette you undestanding of a design poblem.) P in : Powe input by the moto P out : Powe to the platte Assume no fiction o any othe losses in the system P = P Ω out platte in R = w Checking the.007 website fom last yea one can get estimate alues fo the angula speeds fo the Tamiya motos used. R platte is a gien and you can design fo to get the O platte equied to geneate enough centifugal foce to push out the pucks. Values fo the centifugal foces will be discussed in the next poblem set. moto