5-1 Projectile Motion_a PHY 111/211 Pre Laboratory: Projectile Motion Objectives: Become familiar with the apparatus, techniques and equations to measure and analyze projectile motion. Also to test motion equations against experimental results. Activities: The Mini Launcher fires a ball at any angle between -45 and 90. The Time-of-Flight accessory is a digital sensor that will be used in conjunction with photogates in order to determine the initial velocity and time of flight of a ball. Projectile motion is when an object experiences motion in two dimensions. 1. Read the "Mini-Launcher" and "Time-of-Flight Accessory" pages indicated on P. 5-5 and P. 5-6 of this Pre Lab and briefly answer the questions, also on P. 5-3. 2. Review the position, velocity and acceleration during free fall information and Examples below. Work the problem on P. 5-4. During free fall an object experiences motion in one dimension only. Consider a ball that is dropped toward the ground from a height Yo above the ground. Position, velocity and acceleration during free fall Motion Diagram Equations of Motion Start V y = y. +v. At + = a(At)? v=v+aN Yo 0 a=-9.8m/s -V -9.8 Notice in the Motion Diagram that the position for successive time intervals is increasing. Notice in the "v versus t" graph that the velocity vector starts out at zero then becomes a negative value because its direction is opposite the +y axis. When the ball hits the ground at time ty the direction of the velocity vector is still negative but its magnitude is greater. The acceleration vector is constant and also negative because it is opposite to the +y axis.5-2 Examples: The following examples compare free-fall motion to projectile motion. Note that the time-of-flight for both examples is the same because the ball is projected at zero degrees (vey = 0). Example #1: A ball is dropped from an initial height, Yo = Im. Find the time-of-flight for the ball to reach the ground (y = 0). Notes: Since the ball is "dropped" its initial velocity Vo is zero. In the equation, y, not you is equal to zero and a = -9.8 m/s. Y-motion X-mullon Y-motion W. time wtime y= y. +v/+-a y-motion 0=Im +0+-(-9.8m/s')r - Im = -(-9.8m/s')r 1= (2)(Lm) w-motion p 1=0.451 Range Example #2: A ball is projected at an angle of 0" from the same initial height as Example #l, yo = Im, with an initial velocity of 3 m/s. Find the (a) time-of-flight for the ball to reach the ground (y = ") and (b) the range. Y-molon X-motion y motion - Range y-motion (same as above) X-motion y=y. +v. It-ar 2" 0=1m+0+-(-9.8m/s')r x=0+3m/s(0.45Ls)+ -(0]r - Im = -(-9.8m/s' )= x=135m (range) 1= (2)(Lm) 19.8m/s 1=0.4515-3 Name: Soc: PHY111/211 Pre Laboratory Problems: Projectile Motion 1. Read "Mini-Launcher Introduction" (P. 5-5) and answer the questions. a. What are the range settings to choose from when firing the Mini Launcher? b. How do you adjust the angle of the Mini Launcher? c. Sketch the picture that appears on the barrel of the Mini Launcher that is used to find the ball's center of mass and the outer edge of the ball d. What equipment is needed to measure the muzzle (initial) speed of the ball? 2. Read "Time-of-Flight Accessory Introduction" (P. 5-6) and answer the questions. a. How is the Time-of-Flight signal produced or converted to an electrical signal? Is it an analog or digital signal? Explain b. If you were going to measure both time-of-flight and initial muzzle speed list all the digital sensors pannbar5-4 3. A rock is thrown at an angle of Of off a 22-m cliff with an initial velocity of 6 m/s. (a) Find the time-of-flight for the rock to reach (impact) the ground. (b) Find the range of the flight of the rock. (c) Make a sketch (position, velocity and acceleration) with acfinal values showing the y-motion of the rock. (d) Make a sketch (position, velocity and acceleration) with actual values showing the x-motion of the rock. (c) PHY21 1 only. Calculate the magnitude and angle of the velocity-of-impact of the rock. y-motion X-motion XI WI VII 7MINI LAUNCHER Introduction The PASCO Mini Launcher has been designed for . FIXED ELEVATION INDEPENDENT OF projectile experiments and demonstrations. The culy ANGLE: additional equipment required is a C-clamp or ME-93768 Universal Table Clamp for clamping the Launcher to a steel balls ONLY! table. The features of the Mini Launcher includes . LAUNCH AT ANY ANGLE Between-45" and 90: Balls can be launched at any angle from 0 to 90 de- grees measured above the horizontal The magnetic plastic holds the steel ball in position for launch if any angle from 0 to 45 degrees measured below the UNCHER DO NOT FLEH The Mini Launcher can be mounted so that it piv- PISTON WITH ofs all the muzzle end. The elevation of the bull as it leaves the barrel does not change as the angle is varied. . REPEATABLE RESULTS: WEAR SAFETY There is no spin on the bull since the platon keeps CLASSES the bull from ribbing on the walls is it travel up the WHEN IN LICE barrel. The sturdy have can be secured to a table with a C- clamp or s ME-93760 Universal Table Clamp (not included) so there is very little recoil. The bric- The angle is easily adjusted using the thumb server. ger is pulled with a string to minimize joking The built-in protractor and plumb bob on the sick of the launcher give a convenient and accurate way of . COMPUTER COMPATIBLE: determining the angle of inclination. Photogates may be attached with the accessory . THREE RANGE SETTINGS: bracket (ME-6831) is connect the Mini Launcher to a computer to measure the muzzle speed. Alsoa There are three ranges from which to choose. They photogate at the muzzle and the Time of Flight so ure approximately 0.5 meter, 1.0 meter, and 20 cessary (ME 4810) on be used to time the flight of meters, when the angle is 45 degrees and measured the bull from table top to table top. 0.5m I m 1 m5-6 TIME-OF-FLIGHT ACCESORY Introduction Time-of-Flight and Initial Speed To measure initial speed of the projectile AND the time- of-flight, two photogale beads and a computer phologale aiming system are mooded in addition to the apparatus. Use a photogale mounting bracket to mount the photo- gain beads 10 cm apart in front of the muzzle of the projectile launcher. Place the Time-of-Flight apparatus on the floor where the bull lands. 0900. 10 0 Tim The ME-6810 Time-of-Flight apparatus is an accessory to the ME-6400 Short Range Projectile Launcher or the ME-6801 Long Range Projectile Launcher. It consists of a plexo-electric speaker circuit mounted on a 20 x 20 cm Timed Fight plastic plate. A signal cable with a standard stereo phone Flinanchor Fad plug is attached to the plate. When a ball hits the plate it generates a photogate-type signal (TTL compatible). The cable sends a signal to a computer through the digital Series 6500 Computer Interface or Cl-6585 Game input of a computer interface such as the Series 6500 Port Interface Box Computer Interface or the MacTimer Interface, a Game If you have the Series (6500 Computer Interface or a Fort Interface Box, or an Adapter Cable. The signal can Game Port Interface Box that will accommodate three also be sent to a stand-alone Photogate Timer. photogales, connect photogate head #1, photogate head Measuring time-of-flight and initial speed of the project #2, and the Time-of-Flight apparatus into digital inputs 1, tile requires two photogates and the Time-of-Flight 2 and 3 respectively. Use the PULSE timing mode of the Accessory. The Series 6500 Computer Interface and the Precision Timer program. IAM Game Port Interface Box can secomodate the three Adapter Cable, MacTimer, or Al-6575 Game Fort signals. If your computer interface only has two ports for Interface Box photogates, or if you are using the Photogate Timer, you can measure overall time-of-flight OR initial speed. To If you have a MacTimer Interface, Game Port Interface measure boch simultaneously, you will need to use the Box, or Adapter Cible that accommodairs only two Four-to-One Adapter Box (C1-6430) which allows up to photogates, you will need to use the Four-to-One four photogale-type signals to be received through one Adopter. This adapier allows multiple photogate-type digital input. (Note: The Photogate Timer cannot be used signals from up to four photogates or similar devices to to measure overall time-of flight and Initial speed be sent through one digital isput Connect the signal simultaneously.) ables of the photogale heads and Time of-Flight oppara- tus to the digital inputs of the Four-to-One Adapter. Then conned the signal cable of the Four-to-One Adapter to digital input #1 of the Mac Timer Interface, Game Port Interface Box or Adapter Cable that is connected to the PASCO