Lab 6 Projectile Motion Handout FA23-1 (1)

PROJECTILE MOTION EXPERIMENT IRVINE VALLEY COLLEGE PHYSICS LAB REPORT Course Number: Physics 4A Experiment Number: lab 6 Experiment Title: projectile motion Date Performed: 4 october 2023 Due Date: 13 october 2023 RESEARCHER BASE GRADE SCALED GRADE Sejal Chopra ❑ ❑ 50 ANALYST BASE GRADE SCALED GRADE Prof. Boyd ❑ ❑ 50 PRINCIPLE INVESTIGATOR BASE GRADE SCALED GRADE Chaewon Kim ❑ ❑ 50

PROJECTILE MOTION EXPERIMENT THEORY When an object moves within two or three dimensions then it is classified as a projectile. For this type of motion, the projectile’s range is proportional to its launch angle. In the case when projectiles follow a symmetric path, due to the constant acceleration of gravity, then its range is given by the equation R = v 0 2 sin ( 2 θ 0 ) g where v 0 is the projectile’s initial speed, θ 0 is the launch angle of the projectile, and g is the magnitude of the acceleration due to gravity. Using calculus, there exists a launch angle that maximizes the projectile’s range. For a launch angle of 45 ° , the maximum range of a projectile becomes R max = v 0 2 g In the special case when a projectile is launched horizontally and its trajectory is non-symmetric, its range can be calculated from the kinematic equations to produce R = v 0 √ 2 h g where v 0 is the projectile’s initial speed, h is the projectile’s initial height above ground, and g is the magnitude of the acceleration due to gravity. PROCEDURE 1. Mount the projectile launcher to the table. 2. Record the projectile height above ground. 3. Load the metal sphere inside the launcher at the short-range setting. 4. Fire the projectile horizontally and note where it lands. 5. Place a sheet of white paper onto the ground, with its center being directly above the location where the projectile landed on the floor.  Tape this piece of paper securely to the floor by using masking tape. 6. Place a sheet of the carbon paper directly on top of each sheet of blank paper.  The dark blue side of the paper should be facing downwards. 7. Fire the projectile two additional times. 8. Peel back the carbon paper and make sure that you can see each “hit” recorded onto the blank paper as a dark circular mark.

PROJECTILE MOTION EXPERIMENT DATA TABLE 1 & 2 – INITIAL VELOCITY DETERMINATION HORIZONTAL TRIALS HEIGHT h±δh ( cm ) 81.7 ± 0.05 TRIAL RANGE R±δR ( cm ) SHORT-RANGE MEDIUM-RANGE 1 150.4 ± 0.05 187.2 ± 0.05 2 150.7 ± 0.05 187.4 ± 0.05 DATA TABLE 3 – ANGLE TRIALS ANGLE θ 0 ±δ θ 0 ( ° ) RANGE R±δR ( cm ) SHORT-RANGE MEDIUM-RANGE 20 ± 178.9 ± 0.05 247.1 ± 0.05 30 ± 182.8 ± 0.05 259.0 ± 0.05 40 ± 176.1 ± 0.05 261.2 ± 0.05 50 ± 162.4 ± 0.05 234.1 ± 0.05 60 ± 131.9 ± 0.05 193.3 ± 0.05 70 ± 92.6 ± 0.05 135.4 ± 0.05

PROJECTILE MOTION EXPERIMENT DATA TABLE 4 -GRAPH DATA TRENDLINE COEFFICIENTS A ±δA B ±δB C ±δC SHORT RANGE TRIALS − 0.0556 ± 0.00 25 3.29 ± 0.23 135 ± 4.6 MEDIUM RANGE TRIALS ± ± ± Short-Range Horizontal Trials Mean Range R avg = R 1 + R 2 2 R avg = ¿ 150.55 Range Uncertainty ∆ R avg = δ R 1 + δ R 2 2 R avg x 100% ∆ R avg = ¿ 0.03% Mean Initial Speed v 0 , avg = R avg √ g 2 h v 0 , avg = 368.9 Initial Speed Percent Uncertainty ∆ v 0 ,avg = √ ( ∆ R 100% ) 2 +( δh 2 h ) 2 x 100% ∆ v 0 ,avg = ¿ 0.04%

PROJECTILE MOTION EXPERIMENT Maximum Range (Use θ o = θ opt ¿ R 2 max = v 0 ,avg 2 sin ( 2 θ 0 ) g R 2 max = ¿ 120.14 Maximum Range Percent Uncertainty ∆ R max = √ ( 2 ∆v 0 ,avg 100% ) 2 x 100% ∆ R max = ¿ 0.08% Percent Error ( θ o = 45 ° vsθ o = θ opt ¿ PE = | 45 − θ opt 45 | x 100% PE = ¿ 66% Percent Difference PD = | R 1 − R 2 ( R 1 + R 2 )/ 2 | x 100% PD = ¿ 14.3%

PROJECTILE MOTION EXPERIMENT TABLE OF RESULTS HORIZONTAL TRIALS LAUNCHER SETTING SHORT-RANGE MEDIUM-RANGE MEAN RANGE R avg ±∆ R ( % ) ( cm ) 150.55 ± 0.03% 187.3 ± 0.03% MEAN INITIAL SPEED v 0 , avg ±∆v 0 ( % ) ( cm / s ) 368.8 ± 0.04% 458.93 ± 0.04% MAXIMUM RANGE R max ±∆ R max ( % ) ( cm ) 138.71 ± 0.08% 214.70 ± 0.08% ANGLED TRIALS LAUNCHER SETTING SHORT-RANGE MEDIUM-RANGE OPTIMAL LAUNCH ANGLE θ max ±∆θ max (%) ( ° ) 30 ± 37 ± MAXIMUM RANGE R max ±∆ R max (%) ( cm ) 120.14 ± 0.08 206.38 ± OPTIMAL LAUNCH ANGLE PERCENT ERROR PE ( % ) 66% 17.78% MAXIMUM RANGE PERCENT DIFFERENCE PD ( % ) 14.3% 0.11%

PROJECTILE MOTION EXPERIMENT Include a very short (1-3 sentences) conclusion , stating your findings.