Badminton

Chrystal and Lauren

** TITLE: ** The Ultimate Badminton Package!

**LAB GOAL/ QUESTION:** Goal- To see which badminton racket will deliver the fastest smash with the least amount of energy lost in conjunction with arm power. Question- Which racket will deliver the fastest smash with the least amount of energy lost in conjunction with arm power?

**PROCEDURE:** Part 1- 1) Obtain two badminton rackets, a video camera, a meter stick, and open logger pro. 2) Label one racket with the letter (a) and the other with letter (b). 3) Mass both rackets and record in your lab journal. 4) Turn on video camera and begin to record. 5) Choose one person to smash both rackets. 6) Hold meter stick up to allow logger pro to judge distance. 7) Using good form, smash the air with racket (a). 8) Repeat steps 5-7 seven times. 9) Do steps 4-8 but with racket (b). 10) Connect the video camera to the computer and open up logger pro and utilize video analysis. 11) Place dots beginning at the mid back until the racket is no longer seen on the screen. 12) Find the velocity. 13) Find the time in which it took both rackets to fully "smash 14) From here, calculate the power of both using kinetic energy and power equations.  15) Find the average power for both rackets.

Part 2- 1) Obtain tape and choose a stable table on which the procedure will take place. 2) Tape badminton racket (a) to the table. 3) Obtain a birdie and mass it. Record the value. 4) Take a meter stick and tape it to a solid surface. 5) Turn on the camera and begin recording. 6) Hold birdie at shoulder height and drop onto the racket. 7) Repeat step 6, five times. 8) Repeat steps 2-7 with racket (b) 9) Turn on logger pro and utilize video analysis. 10) Place dots in order to find the initial and final heights. 11) From here, calculate the change in energy by utilizing the potential energy equation. 12) Find the average change in energy for both rackets.

** Part 1- ** Equations: KE=.5mv^2 KE= TME TME/time= Power
 * DATA/CALCULATIONS: **

**Calculations for racket (a):** Mass of racket (a) = 0.095 kg

Video-- 0.196 Time= 0.3 seconds Velocity= 13.83 m/s 0.5(13.83^2)(0.095)= 9.09 Total Mechanical Energy= 9.09 J  9.09/0.3= 30.28 Power= 30.28 Watts

Video-- 0.198 Time= 0.097 seconds Velocity = 14.7768 m/s 0.5(14.7768^2)(0.095)= 10.3717 Total Mechanical Energy= 10.3717 J  10.3717/0.097= 106.097 Power= 106.926 Watts

Video-- 0.199 Time= 0.1 seconds Velocity= 18.60 m/s 0.5(18.60^2)(0.095)= 16.433 Total Mechanical Energy= 16.433 J  16.433/0.1= 164.331 Power = 164.331 Watts

Video-- 0.200 Time= 0.1002 seconds Velocity= 15.281 m/s 0.5(15.281^2)(0.095)= 11.0917 Total Mechanical Energy= 11.0917 J  11.0917/0.1002= 110.695 Power = 110.695 Watts

Video-- 0.201 Time= 0.1334 seconds Velocity= 18.064 m/s 0.5(18.064^2)(0.095)= 15.50 Total Mechanical Energy= 15.50 J  15.50/0.1334= 116.189 Power = 116.189 Watts

Video-- 0.204 Time= 0.10 seconds Velocity= 18.199 m/s 0.5(18.199^2)(0.095)= 17.1457 Total Mechanical Energy= 17.1475 J  17.1475/0.10= 171.457 Power= 171.457 Watts

Video-- 0.205 Time= 0.0666 seconds Velocity= 21.5023 m/s 0.5(21.5023^2)(0.095)= 21.9616 Total Mechanical Energy= 21.9616 J  21.9616/0.0666= 329.754 Power= 329.754 Watts

Average Power: 174.063 Watts


 * Image of logger pro with above data

** Calculations for racket (b): **

Mass of racket (b) = 0.1 kg

Video-- 0.206 Time= 0.0984 seconds Velocity= 14.9513 m/s 0.5(14.9513 ^2)(0.095)= 10.6181 Total Mechanical Energy= 10.6181 J  10.6181/0.0984= 107.908 Power= 107.908 Watts

Video-- 0.207 Time= 0.1334 seconds Velocity= 14.4306 m/s 0.5(14.4306 ^2)(0.095)= 9.89 Total Mechanical Energy= 9.89 J  9.89/0.1334= 74.1492 Power= 74.1492 Watts

Video-- 0.208 Time= 0.599 seconds Velocity= 14.7913 m/s 0.5(14.7913 ^2)(0.095)= 10.3921 Total Mechanical Energy= 10.3921 J  10.3921/0.599= 17.4364 Power= 17.4364 Watts

Video-- 0.209 Time= 0.133 seconds Velocity= 14.7268 m/s 0.5(14.7268 ^2)(0.095)= 10.3017 Total Mechanical Energy= 10.3017 J  10.3017/0.133= 77.4567 Power= 77.4567 Watts

Video-- 0.210 Time= 0.1002 seconds Velocity= 14.5655 m/s 0.5(14.5655 ^2)(0.095)= 9.93941 Total Mechanical Energy= 9.93941 J  9.93941/0.1002= 99.1957 Power= 99.1957 Watts

Video-- 0.211 Time= 0.1687 seconds Velocity= 12.0508 m/s 0.5(^2)(0.095)= 6.89807 Total Mechanical Energy= 6.89907 J  6.89907/0.1687= 41.6299 Power= 41.6299 Watts

Video -- 0.212 Time= 0.1336 seconds Velocity= 16.3332 m/s 0.5( 16.3332^2)(0.095)= 12.6717 Total Mechanical Energy= 12.6717 J  12.6717/0.1336= 94.8483 Power= 94.8483 Watts

Average Power: 202.817 Watts


 * Image of logger pro with above data

**Part 2-** mass= 0.005 kilograms equation: PE=m*g*h PEf- PEi= Change in Energy

** Racket (a) **

Video: 0.0231 Initial Height= 0.30 meters Final Height= 0.15 meters Initial Potential Energy: 0.0498*0.30 = 0.0147 J Final Potential Energy: 0.0498* 0.15= 0.00736 J  Change in Energy: 0.00736- 0.0147= -0.00734 J

Video: 0.0232 Initial Height= 0.40 meters Final Height= 0.10 meters Initial Potential Energy: 0.0498* 0.40= 0.196 J Final Potential Energy: 0.0498* 0.10= 0.0049 J  Change in Energy: 0.0049- 0.0196= -0.0147 J

Video: 0.0233 Initial Height= 0.42 meters Final Height= 0.15 meters Initial Potential Energy: 0.0498* 0.42= 0.02058 J Final Potential Energy: 0.0498* 0.15= 0.00735 J  Change in Energy: 0.00735- 0.02058= -0.01323 J

Video: 0.0234 Initial Height= 0.52 meters Final Height= 0.10 meters Initial Potential Energy: 0.0498* 0.52= 0.025896 J Final Potential Energy: 0.0498* 0.10= 0.00498 J  Change in Energy: 0.00498- 0.025896= -0.020916 J

Video: 0.0235 Initial Height= 0.50 meters Final Height= 0.12 meters Initial Potential Energy: 0.0498* 0.50= 0.0249 J Final Potential Energy: 0.0498* 0.12= 0.005976 J  Change in Energy: 0.005976- 0.0249 = -0.018924 J

Average change in energy: -0.015022 J


 * Image of logger pro with above data

** Racket (b) **

Video: 0.0239 Initial Height= 0.45 meters Final Height= 0.15 meters Initial Potential Energy: 0.0498*0.45= 0.02352 J Final Potential Energy: 0.0498*0.15= 0.00735 J  Change in Energy: 0.00735- 0.02352= -0.01617 J

Video: 0.240 Initial Height= 0.38 meters Final Height= 0.18 meters Initial Potential Energy: 0.0498*0.38= 0.01862 J Final Potential Energy: 0.0498*0.18= 0.00882 J  Change in Energy: 0.00882- 0.01862= -0.0098 J

Video: 0.241 Initial Height= 0.45meters Final Height= 0.17 meters Initial Potential Energy: 0.0498*0.45= 0.02205 J Final Potential Energy: 0.0498*0.17= 0.00833 J  Change in Energy: 0.00833- 0.02205= 0.01372 J

Video: 0.242 Initial Height= 0.42 meters Final Height= 0.16 meters Initial Potential Energy: 0.0498*0.42= 0.02058 J Final Potential Energy: 0.0498*0.16 = 0.00784 J  Change in Energy: 0.00784- 0.02058= -0.01274 J

Video: 0.243 Initial Height= 0.43 meters Final Height= 0.20 meters Initial Potential Energy: 0.0498*0.43 = 0.02107 J Final Potential Energy: 0.0498*0.20 = 0.0098 J  Change in Energy: 0.0098 - 0.02107= -0.01127 J

Average change in energy: -0.01274


 * Image of logger pro with above data

**REFLECTIONS/CONCLUSION:** Through our experiments, we were able to discover that more power is generated from a smash when using racket (b). We were also able to determine that racket (b) loses less energy when it hits a birdie. Thus, racket (b) would deliver the fastest smash with the least amount of energy lost in conjunction with arm power. We realized that by keeping the “smasher” constant, we would be able to convey a more accurate depiction of arm power with a different racket. We also kept constant the person who dropped the birdie in order to eliminate any potential discrepancy between drops. We understand that air resistance was brought into play while it was dropped onto the badminton racket, but in reality, air resistance is always present.