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Unformatted text preview: Name: Derek Teaney Lab Section: 01 Date: 01/01/01 Projectile Motion 1 Introduction The purpose here is to convince the TA that you understood how the lab worked. Needlessly philosoph- ical or lengthy remarks will cost you points. The purpose of this lab was to measure the properties of projectile motion. A schematic of the apparatus is shown below (you could/should simply draw this by hand. I used X-fig which is free) v o h x A small metal ball was released from a ramp at the edge of the table of height h The initial velocity v o of the ball was measured by measuring the time it took for the ball to cross the photogate detector and knowing effective diameter of the ball. The final distance x that the ball landed was recorded as a function of the initial velocity v o . In the Newtonian theory of projectile motion these quantities are related by (If you are using some program like word where entering formulas is time consuming, simply leave a bit of space and write the formula by hand) x = v o s 2 h g . This formula is compared to the measured data in what follows. 2 Recorded and Derived Data The purpose here is to record all relevant numbers and how they were obtained. The raw data should be in the lab notebook. Often when making plots we need derived quantities, e.g. if you know the length and width you could determine the area A = LW . you should explain how you propagated the errors in L and W to determine the error in A . This is described in the error analysis writeup. The data in this Lab is totally made up. Before data taking started, the height of the table was h = (1 . 01 . 005)m measured using ruler stick. The error was estimated to the nearest half centimeter. 1 Ramp Setting x (m) Time t stop (s) v o ( m/s ) 1 0.042 0.003 0.1373 0.087 0.003 2 0.059 0.003 0.0924 0.130 0.005 3 0.087 0.003 0.0758 0.158 0.007 4 0.089 0.003 0.0660 0.181 0.008 5 0.096 0.003 0.0584 0.205 0.009 Table 1: Summary of data taken. The diameter of the ball D eff = (1 . 20 . 05)cm was determined by using the SALT translation stage and the photogate detector. Specifically, the every turn of the nob of the translation stage advanced the stage by 1/28 of an inch. After the photogate detector registered off, an additional 13.5 turns were registered before the light crossed the photogate detector again. The uncertainty was estimated based on repeating the process. To vary the velocity of the projectile, the ball was released from five different positions along the ramp. For a given ramp position the time the photogate detector was off t stop was recorded by the photogate electronics. This together with the effective diameter of the ball was sufficient to determine the projectile velocity for each ramp position v o = D eff t stop ....
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