EXSC 408L Fall '03 Problem Set #2 Linear Motion. Linear Motion

Transcription

1 Problems: 1. Once you have recorded the calibration frame for a data collection, why is it important to make sure the camera does not shut off? hat happens if the camera automatically shuts off after being inactive for too long? 2. In your own words, what is the shutter speed of a camera? It is a clear, sunny day, and you are collecting data outside. To prevent white-out of your video, would you increase or decrease your shutter speed? 3. From the calibration frame recorded in your data collection, you note that your meter stick is 53 pixels long within the video. How tall is your subject in real world units if she is 92.5 pixels from head to toe? 4. If a person takes 20 steps to run 30 m in 4.4 s, what is his average velocity? hat is his average step length in meters? ould you expect his step length to increase or decrease with a higher velocity? 5. Explain the disadvantage of using one step length and time to determine velocity. 6. Using position, step length (SL), and step rate (SR) data from the left graph, draw the velocity vs. position curve on the right graph. hat does the velocity graph tell you about the runner? Explain. SL SL 6.00 SR meters SR velocity meters 7. Draw a free body diagram (FBD) and mass acceleration diagram (MAD) of a runner during heel strike. 8. hich of the following statements must be true for a runner to achieve an increase in horizontal velocity? a. The net horizontal impulse is positive in the direction you are running. b. The net vertical impulse is positive in the direction you are running. c. The horizontal velocity is positive and no net horizontal force is applied. d. a & c e. None of the above Page 1 of 9

2 9. Use the table below to answer parts a and b. Event Frame RHS 0 RTO 16 LHS 25 LTO 44 RHS 50 RTO 63 a. Calculate the time, in seconds, for one complete gait cycle (60 Hz camera). b. hat percentage of the cycle is left single support? 10. Label the following events and phases on the gait analysis graph below. a. Left Toe Off (LTO) b. Right Heel Strike (RHS) c. Double Support (DS) d. Right Leg Support (RLT) e. Left Leg Support (LLT) f. Right Leg Swing (RLS) g. Left Leg Swing. (LLS) h. Define the type (walk, jog, run, sprint) of gait in the graph. LHS Events and Phases Left Leg RTO Right Leg % step cycle 11. Is this gait symmetrical? 12. hy does the total body center of mass (TBCM) describe human movement better than a single point on the body? 13. Jackie Joyner-Kersee is throwing a javelin. Draw the FBD-MAD of her javelin just prior to release and indicate any assumptions you are making. 14. hich of the following is an example of temporal analysis? a. Observing the recovery and pull through phases of swimming b. Determining the duration of support and swing in walking c. Measuring the force applied to the force plate during a long jump take -off d. Measuring the height of a vertical jump e. Ca lculating angle of the hip during skiing Page 2 of 9

3 15. hen velocity is determined over a time interval, the result is a. an instantaneous velocity. b. an average velocity. c. an instantaneous velocity if the time interval is less than one second d. the velocity at the end of the interval e. the velocity at the beginning of the interval 16. hich of the following falls under the branch of biomechanics called kinematics? a. Impulse b. Net joint moment c. Velocity and acceleration of a segment d. Ground reaction force and gravity e. Free body diagram 17. Given that a person has a step rate of 3 steps/s and an average walking velocity of 2.1 m/s, what is his step length? 18. hy do we videotape a meter stick before a data collection? a. To make sure that the image is in the plane of motion b. To make sure that the camera captures the motion in a good plane c. To calculate the aspect ratio d. To convert the units of the image on a monitor to a real life units e. To convert the frame number to real time units 19. hen setting up a camera for a two-dimensional analysis, you should a. get the largest image possible. b. make sure the camera is perpendicular to the plane of motion. c. set the focus to manual mode. d. set the camera s shutter factor to the maximum value. e. All of the above 20. During walking, when the ipsilateral foot makes its initial contact, what is the phase of the contralateral foot? a. Toe off b. Single leg support c. Single leg swing d. Terminal double support e. Non-support phase 21. hich of the following adjustments could a race walker make to increase his walking speed? a. Decrease contralateral swing b. Increase single support time c. Increase double support time d. Increase single swing time e. Decrease step frequency Page 3 of 9

4 22. A volleyball player is hitting a ball during a spike. Determine the correct FBD of the ball at contact. a) b) c) d) e) None of the above 23. A basketball player goes for a lay-up with the ball in her hand. Determine the FBD of the player while she is in the air. a) b) c) d) e ) None of the above Rv Rh Rv Rh 24. Determine the MAD for the basketball when the player is landing. a) b) c) d) e ) mah mah mah mah None of the above mav mav mav mav Rv Rh Rv Rh Page 4 of 9

5 25. hat is the ground reaction force trying to do to the ankle joint in the picture below? B A 26. hat happens to the length of a body segment when a subject's movements are not entirely perpendicular to the focal axis of the camera? a. it shortens b. it lengthens c. the angle increases d. the angle decreases e. no change Table 1. The following data was collected from a marathon runner at LA marathon 93. Velocity (m/s) Stride length (m) Stride frequency (Hz) From Table 1, what was the runner's stride length at the velocity of 3.57 m/s? 28. From Table 1 and your knowledge of running, how did this runner increase his speed? 29. During a kinematic analysis, you may need to determine the duration of foot contact. If your force plate sampled at 600 Hz, your camera collected at 60 Hz, initial foot contact occurred at frame 9, and takeoff occurred at frame 14, what was the contact duration time? 30. Suppose an athlete ran a 100 m race in 9.98 s. hat was his average horizontal velocity during the race? hat was his average acceleration during the race? Assume that the velocity of the athlete increased continuously from zero (initial) to some final value. 31. A swimmer completes four laps in a 50.0 m swimming pool, finishing where he started. a) hat was the linear distance he traveled? b) hat was his linear displacement? 32. Suppose an individual moves from point s 1 (3,5) to point s 2 (6,8). hat are the a) horizontal, b) vertical, and c) resultant displacements? 33. It takes a person 20.0 min to drive from point A to point B, a distance of 33.0 mi. hat was his average velocity in m/s? Page 5 of 9

6 34. A runner starts from rest and reaches a maximum velocity of 4.70 m/s in 3.20 s. hat was his average acceleration from rest to maximum velocity? 35. After a cyclist crossed the finish line, it took him 4.0 s to come to a complete stop. If his average acceleration was -3.5 m/s 2, how far did he travel past the finish line, and what was his velocity when he crossed the finish line? 36. In the course of a marathon race, the instantaneous velocity of a runner at the 10 km mark was measured at 8.0 m/s. At the 12 km mark, which she reached 3.2 min later, her instantaneous velocity was measured at 4.0 m/s. Calculate her average acceleration between the 10 km and 12 km mark in m/s Please fill in the blank cells in the table below. (data was collected at 60 frames/s) Frame # x-position (pixels) time constant (s) conversion factor (m/pixels) displacement (m) velocity (m/s) / / / / / hat is the sign of the slope of the velocity curve? Does that mean that the person is speeding up or slowing down? Page 6 of 9

7 Answers: m m/s, 1.5 m, increase 6. 6, 3.75, 4, 10, 8.75, a 9. a) RHS to RHS 0.83 s, RTO to RTO 0.78 s b) 19/50=38% 11. No 14. b 15. b 16. c m 18. d 19. e 20. d 21. d 22. b 23. b 24. e 25. Dorsiflex at the ankle joint 26. a m 28. Increased stride length and increased step frequency s m/s, 1.0 m/s a) 200 m, b) 0 m 32. a) 3 units b) 3 units c) 4.24 units m/s m/s m/s, 56 m m/s Time: 0.017, 0.033, 0.05, 0.067, s; Displacement: 0.075, , 0.025, m; Velocity: 2.27, 1.14, 0.76 m/s 38. Negative, slowing down Page 7 of 9

8 Bonus Problems: 1) If the little old lady from Pasadena crosses the street (100 meters) with a step length of 0.5 meters, what would her step rate need to be in order to cross the street in 40 seconds? a. 0.8 steps/s b steps/s c. 2.5 steps/s d. 4 steps/s e. 5 steps/s Page 8 of 9

9 2) Given the following set of events recorded at 60 frames per second, calculate the swing time for the ipsilateral leg. contralateral Leg Foot Strike Toe-Off ipsilaleral Toe-Off Foot Strike Frame a s b. 0.5 s c s d. 1 s e s Page 9 of 9