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Unformatted text preview: Projectile Motion (Pre Lab Asssignment Included) Objective: This laboratory investigates the motion of projectiles under the influence of gravity. You will do two experiments: 1. Measure the projectile’s range and time-of-flight as a function of launching angle θ for the case where the final height is equal to the initial height. Determine the initial velocity based on these measurements. θ Range 2. Independently measure initial velocity based on 1-D (horizontal) motion. Apparatus: Landing Pad Time Platform r Photogate Trigger Angle indicator Launcher Containment Box Figure 1 Background: θ v 0 x y v 0y v 0x Figure 2 For a projectile launched with an initial speed v and angle θ above horizontal, the x and y components of the initial velocity are: v x = v cos θ ( 1 ) v y = v sin θ ( 2 ) Due to the constant downward acceleration of gravity ( g ), the equations of motion are Range = x − x = v x t ( 3 ) y − y = v y t − 1 2 gt 2 ( 4 ) where x is the starting horizontal position, y is the starting height, x is the final horizontal position, y is the final eight, t is the total time-of-flight, and g is the acceleration of gravity. h As the final height equals the initial height ( y= y ) and equation (4) can be easily solved for t : t = 2 v y g Using equation (2) to substitute for v 0y yields: t = 2 v g sin θ ( 5 ) Time-of-flight vs. launching angle for one-level projectile motion. S ubstituting equations (5) and (1) into equation (3) yields: Range = x − x = 2 v 2 g sin θ cos θ = v 2 g sin2 θ ( 6 ) The initial velocity will be determined from your data. You will have two values for initial velocity, one from the time-of-flight data and one from the range data. Range vs. launching angle for one-level projectile motion. Experimental Procedure Experiment 1: One-level projectile motion. [3.0 points] In this experiment you will launch a projectile at different angles and measure the time-of-flight and range (distance traveled) for each angle. Referring to Figure 1, the time will be measured by the photogate and the landing pad, which start and stop the timer, respectively. The landing position will be measured by carbon paper (to make a mark) and a ruler. Five trials will be taken at each angle to determine the statistical uncertainty of the measurements. Each group will choose ONE of the following set of two angles θ . The sets are: (10,45), (15, 50), (20,55), (25,60), (30,65), (35,70), (40,75), (20,75), (20,70), (15,60). Make sure each group has different set of angles. Inform your TA of your choice. Data collection: 1. Practice: Load the steel ball into the launcher using the plastic plunger to reach the “medium range” setting (two clicks). Make sure to wear safety glasses and DO NOT LOOK INTO THE LAUNCHER once it is armed ....
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- Spring '09
- Standard Deviation, Mean, Observational error