CENTER OF GRAVITY LAB The following description is excerpted from your textbook (Hall, p. 378): A body's mass is the matter of which it is composed. A unique point is associated with every body, around which the body's mass is equally distributed in all directions. This point is known as the center of mass or the mass centroid of the body. In the analysis of bodies subject to gravitational force, the center of mass may also be referred to as the center of gravity (CG), the point about which a body's weight is equally balanced in all directions (or the point about which the sum of torques produced by the weights of the body segments is equal to 0). This denition does not imply that the weights positioned on opposite sides of the CG are equal but that the torques created by the weights on opposite sides of the CG are equal. One method for determining the CG of the body is the reaction board technique. This method calculates the location of the plane that contains the CG. The purpose of this lab is to determine the location of your CG plane that divides your body into equally distributed upper and lower halves. The gure to the right is a schematic of a @ person on a reaction board. One end of the A board sits on the oor and the other end sits on a scale. F1 and F2 are the forces at either end of the reaction board. BW and Wrb represent the weight of the person and the weight of the F2 reaction board respectively. By summing F1 torques (torque = force x moment arm) about an axis through point "A" , one can calculate the distance a person's CG plane is away from distance to CG of point \"A". If point "A" is coincident with the bottom of your feet, you also can determine the height of your CG plane as a percent of d ' d : distance to CG reaction board Procedures To calculate the CG using this method, a person would lie on the reaction board under two separate conditions: one with their arms at their sides (Position 1) and one with their arms overhead (Position 2). The following is then recorded. Choose Subject 1 from the female data in the Excel table provided and write in the appropriate data below: BODY WEIGHT (BW): (lbs): convert to newtons => (N) (1 1b = 4.45 N) BODY HEIGHT (BH): (in): convert to centimeters => (cm) (1 in = 2.54 cm) SCALE READING Position 1 - arms at side (F21): _lbs} = (N) SCALE READING Position 2 - arms overhead (F22): _ lbs) = (N) LENGTH OF REACTION BOARD (L) = 198 cm: DISTANCE TO CG OF RB (LRB) = 99 cm WEIGHT OF REACTION BOARD (WRB) = 218.1 N Calculations & Questions (10 points total) Complete all the following. The points breakdown for each part is listed below, partial credit is possible. If you copy a classmate's work, then you both will receive 0 points on this lab and potentially a 0 for the lab class. Doing this [Lbyourself is an important part of you being successful in the class and will help you grasp these concepts. 1.Calculate the distance in meters the subject's CG plane is from her feet in each position by taking moments atom; point A and equating the sum of moments to zero (use SI units). See lecture KIN 3400-Lec 6.2 and the narrated instructions for this lab for the calculation methods. Show all your working (electronically!) below to calculate d1 (Position 1), and d2 (Position 2) (1 Point) Position 1: Position 2: Position 1 Position 2 Also, calculate the height of the CG plane as a percentage of body height (1 point): d1 Annsat side: d1% = 1m x 100 12 Annsoverhead: d2% = m x 100 2. Calculate the results for both males and females in the Excel sheet on Canvas. You must ll in all _o_f_ the empty values in Excel and import to this report by placing the table below this question. (2 Points) (find J -M on excel d1-d2) 3. From your calculations in Excel, is there a difference between males and females for the height of center of gravity (CG) as a % of body height (relative height) when in the anatomical position? Discuss why or why not? (1 Point) 4. Which gender has the greatest CG relative movement (d2 %- d1%) when the arms are moved overhead and why? Hint: Again, think of body structure. (1 Point) 5. When you jump in the air and become a projectile, can you control where center of gravity is relative to the ground once you are in the air? Why or why not? Hint: See the YouTube video with MJ's dunkl linked on Canvas. (1 Point) 6. When you perform a jump, how would you control where your center of gravity is relative to your body once you are in the air i_n_or_der _t_o_ achieve the greatest vertical reach? That is, would you position your CG as high or as low as possible in the body and how would you arrange your body segments to achieve this? Hint: Review lecture 6.2. (1 Point) 7. After performing the following movements outlined in the narrated instructions, for each movement explain why it was impossible to perform the movement successfully and achieve stability when you were against the wall. Why was it easy when not against the wall? (2 Points): 0 Plantarexion (go up on your tiptoes) against the wall with your nose touching the wall 0 Touch your toes with your bum and heels against the wall I Standing sideways with one foot and shoulder against the wall, lift up the other m \fCenter of Gravity Data - Males versus females Males Subject BW-lbs BW-N BH ins BH cm F21 lbs F21 N F22 Ibs F22 N d1cm d1% d2cm d2% 189 841.05 68.5 173.99 123 547.35 130 578.5 141 627.45 68 172.72 98 436.1 101 449.45 155 689.75 69.5 176.53 106 471.7 112 498.4 161 716.45 68.5 173.99 106 471.7 111 493.95 274 1219.3 69 175.26 166 738.7 173 769.85 135 600.75 71 180.34 94 418.3 99 440.55 7 142 631.9 68 172.72 97 431.65 102 453.9 8 148 659 66 168 97 432 101 449 co 143 636 66 168 95 423 101 449 10 254 1130 70 178 159 708 167 743 Average 174.1944 775.165 68.48622 173.955 114.1236 507.85 119.6764 532.56 #DIV/O! #DIV/O! #DIV/O! #DIV/O! Females Subject BW-lbs BW-N BH ins BH cm F21 lbs F21 N F22 Ibs F22 N d1cm d1% d2cm d2% 119 529.55 63 160.02 79 351.55 82 364.9 139 618.55 66 167.64 93 413.85 96 427.2 W N 214 952.3 68 172.72 131 582.95 137 609.65 156 694.2 63 160.02 98 436.1 102 453.9 122 542.9 64 162.56 82 364.9 85 378.25 CO - OUT A 128 569.6 66 167.64 87 387.15 90 400.5 130 578.5 62 157.48 83.5 371.575 87 387.15 120 534 62 158 77 343 80 356 9 148 659 68 173 99 441 102 454 10 114 507 62 158 75 334 78 347 Average 139.0022 618.56 64.45197 163.708 90.4736 402.6075 93.9 417.855 #DIV/O! #DIV/O! #DIV/O! #DIV/O