Lab+7+-+Center+of+Mass+-+Handout copy

.pdf

School

University of Kentucky *

*We aren’t endorsed by this school

Course

415

Subject

Chemistry

Date

Dec 6, 2023

Type

pdf

Pages

Uploaded by jadewatson1212

KHP 415 - Biomechanics and Human Movement 1 Section: Name: KHP 415 - Biomechanics of Human Movement Laboratory Lab 7 – Center of Mass (a.k.a. Center of Gravity) of the Body Reading Hay (1978), pp. 120-139 Introduction The purpose of this lab is to estimate COM location based on reaction board and segmentation methods. COM is the theoretical location that represents the balance point of the body in a gravitational field. The COM of a body depends on the distribution of the mass and could be either located inside the body or outside the body. Two major methods used to estimate the COM location: 1) reaction board method (easy to apply in static position) 2) segmentation method (can be applied in both dynamic and static conditions) Equipment Reaction board, ruler, calculator. Report Consult with your TA regarding report format. Tasks Part I: Reaction Board Method Figure 1. Reaction Board Method The reaction board, a long and rigid wooden board is supported by a scale as the board is level. The measurement of the COM location is based on the principle of static equilibrium in which the sum of all moments or torques acting about an axis of rotation equals zero: ΣM A = 0 With reaction board unloaded (left panel) the equation of static equilibrium is written as: ΣM A = (R 1 ×d) – (m b ×x b ) Where R 1 is the scale reading, d is the moment arm of R 1 , m b is the board weight and x b is the moment arm of the board weight (distance from axis A to the COM of the board). With a subject lying on the reaction board the equation changes to:

KHP 415 - Biomechanics and Human Movement 2 Section: Name: ΣM A = (R 2 ×d) – (m b ×x b ) – (M×x) Where R 2 is the scale reading as board loaded, W is the subject’s body weight and x is the moment arm of COM of the subject (COM location needs to be found out). The location of COM can be solved combining the above two equations: x = (R 2 – R 1 )×d/M Reaction Board Data Collection and Analysis Procedures (20 points) 1. Identify one person in your group who will be tested. Obtain an accurate measure of height (h) and body mass (M) using the same scale which will be used for the reaction board: BM (M) = __87.6__ kg Height (h) = _187.5__ cm 2. Record the initial scale reading when the reaction board is unloaded (R 1 ) and the distance between the edges of the board (d) : R 1 = _7.5___ kg Length (d) = _196__cm 3. Instruct the subject to lie supine on the reaction board, taking care to align the soles of the subject's feet with axis A (see Figure). a. Record the scale reading, R 2A , while the subject lies on the board with both arms at sides: R 2A = __54.5____ kg b. Record the scale reading, R 2B , while the subject lies on the board with one arm raised overhead: R 2B = 56.2____ kg c. Record the scale reading, R 2C , while the subject lies on the board with both arms raised overhead: R 2C = _57.6___ kg 4. Compute the distance from axis A to the subject's COM (x) in absolute terms (cm) and then as a percentage of the subject's body height. Perform these calculations for each of the three arm positions R 2(A,B,C) (A) Arms at sides ............................ x = ____105.16__ cm x = __56____ % body height (B) One arm raised overhead ........... x = ______108.96 cm x = __58.1____ % body height (C) Both arms raised overhead ........ x = ______ 112.1 cm x = __59.8____ % body height Discussion Questions : (8 points each) 1.What might account for gender differences in the location of the COM (Figure 1 right panel)? Because of body shape and anatomy. The female will have larger lower bodies so a lower center of mass makes a difference 2. In which direction does the COM shift when the arms are raised overhead? What was the relative shift in the COM position when comparing conditions B and C (i.e., one arm vs. two arms shifted overhead)? Would the shift in COM position have been larger or smaller if the subject had held a 5 kg weight in each hand? Why? The center of mass shifts more towards the feet when the arms are raised above the head.When arms of the head the COM went higher up on the body. The should’ve would have been larger because it would have been an added mass to the shift. 3. How does your subject's computed COM location expressed as a percentage of body height compare with values reported for the general adult population (Figure 1 right panel)?

KHP 415 - Biomechanics and Human Movement 3 Section: Name: 4. Assuming that the gymnast in Figure 2 is maintaining a static position, where would you expect his line of gravity (i.e., a vertical line passing through the COM) to intersect the ground relative to his hands? Explain. We would expect it to be perpendicular from both hands so that it’s at equilibrium 5. In order to reach as high as possible in a vertical jump, what position should an athlete adopt at the peak of the jump? Refer to Hay (1993), p. 126. The text says that at the peak of the jump, one should have one arm down which should increases distance by 1 inch. Figure 2. Gymnast Part II: Segmentation Method The segmentation method is based on calculating the weighted average of the center of mass locations of the individual body segments: Σ (m i ×x i ) = M B ×X B and Σ (m i ×y i ) = M B ×Y B Where m i represents the weight of individual segment i , x i and y i represent the x and y coordinates of the COM of segment i . BM is the total body mass and X B and Y B represent the x and y coordinates of the total body COM. Segmentation Procedures Compute the whole body COM location for an eight-segment representation of the person in Figure 3. Use only the right side of the figure for your measurements. A sample calculation for the determination of the whole body COM is provided in Hay (1978), pp. 136-138. (Tables 1 and 2 are worth 8 points each, as is your marked version of Figure 3) 1. Print one extra copy of Figure 3 (page 6 on the handout) and save the original in case you make a mistake. 2. Make an educated guess of the location of the whole body COM. You will compare this estimated COM with your calculated location. 3. Carefully mark the position of the segment endpoints (see Figure 3 and Hay, p. 137). Refer to Figures 4 and 5 for extra information on segment endpoints. 4. Construct a stick figure representation of the individual by drawing straight lines between appropriate segment endpoints (see Hay, p. 137). 5. Measure the length of each segment in millimeters ( note that these are millimeters measured on the page, not the actual length) and record the values in Table 1. Using these lengths and the data expressing the locations of body segment COM's as a percentage of segment length from the noted

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version