Defining the Variables
description
Transcript of Defining the Variables
![Page 1: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/1.jpg)
Defining the Variables
Muscle Physiology420:289
![Page 2: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/2.jpg)
Agenda
Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions
![Page 3: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/3.jpg)
Introduction to BiomechanicsBiomechani
csStatics Dynamics
Kinetics and Kinematics
Kinetics and Kinematics
Linear vs. Angular Linear vs. Angular
The study of biological motion
The study of forces on the body in equilibrium
The study of forces on the body subject to unbalance
Kinetics: The study of the effect of forces on the bodyKinematics: The geometry of motion in reference to time and displacement
Linear: A point moving along a lineAngular: A line moving around a point
![Page 4: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/4.jpg)
Agenda
Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions
![Page 5: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/5.jpg)
SI Base Units
Base Unit: Cannot be reduced Length: SI unit meter (m) Time: SI unit second (s) Mass: SI unit kilogram (kg) Distinction: Mass (kg) vs. weight (lbs.)
Mass: Quantity of matterWeight: Effect of gravity on matterMass and weight on earth vs. moon?
![Page 6: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/6.jpg)
Agenda
Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions
![Page 7: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/7.jpg)
Linear SI Derived Units
Displacement: A change in position SI unit m Displacement vs. distance?
Velocity: The rate of displacement SI unit m/s Velocity vs. speed?
Acceleration: The rate of change in velocity SI unit m/s/s or m/s2
![Page 8: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/8.jpg)
Average vs. Instantaneous Velocity Average velocity = displacement/time
Entire displacement start to finish Instantaneous: Velocity at any particular
instant within the entire displacementStill average velocity however time periods
much smaller therefore “essentially” instantaneous
![Page 9: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/9.jpg)
![Page 10: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/10.jpg)
(m) Splits BJ (s) Splits CL (s) Vinst. BJ Vinst. CL
0 10 1.86 1.88 5.38 5.32
10 20 1.01 1.08 9.90 9.26
20 30 0.93 0.92 10.75 10.87
30 40 0.86 0.89 11.63 11.24
40 50 0.89 0.84 11.24 11.90
50 60 0.83 0.84 12.05 11.90
60 70 0.83 0.84 12.05 11.90
70 80 0.90 0.83 11.11 12.05
80 90 0.87 0.87 11.49 11.49
90 100 0.85 0.87 11.76 11.49
![Page 11: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/11.jpg)
Instantaneous Velocity Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100
Meters (m)
Velo
city
(m/s
)
Johnson
Lew is
![Page 12: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/12.jpg)
Acceleration
Acceleration: Rate of change of velocityA = vf – vi
Vector quantity SI unit = m/s/s or m/s2
Uniform accelerationVery rareProjectiles
![Page 13: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/13.jpg)
Average vs. Instantaneous Acceleration Average acceleration = Rate of change in
velocity assumes uniform acceleration Instantaneous: Acceleration between
smaller time periodsProvides more informationJohnson vs. Lewis
![Page 14: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/14.jpg)
Average acceleration for Ben Johnson?A = (vf – vi) / tA = (10.17 m/s – 0 m/s) / 9.83 sA = (10.17 m/s) / 9.83 sA = 1.03 m/s2
v BJ (m/s) v CL (m/s)0 0
5.38 5.326.97 6.767.89 7.738.58 8.399.01 8.919.40 9.309.71 9.609.86 9.85
10.02 10.0110.17 10.14
Average acceleration for Carl Lewis?A = (vf – vi) / tA = (10.14 m/s – 0 m/s) / 9.86 sA = (10.14 m/s) / 9.86 sA = 1.03 m/s2
Enough information?
![Page 15: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/15.jpg)
(m) Splits BJ (s) Splits CL (s) Vinst. BJ Vinst. CL a BJ (m/s2) a CL (m/s2)
0 10 1.86 1.88 5.38 5.32 2.89 2.83
10 20 1.01 1.08 9.90 9.26 4.48 3.65
20 30 0.93 0.92 10.75 10.87 0.92 1.75
30 40 0.86 0.89 11.63 11.24 1.02 0.41
40 50 0.89 0.84 11.24 11.90 -0.44 0.80
50 60 0.83 0.84 12.05 11.90 0.98 0.00
60 70 0.83 0.84 12.05 11.90 0.00 0.00
70 80 0.90 0.83 11.11 12.05 -1.04 0.17
80 90 0.87 0.87 11.49 11.49 0.44 -0.64
90 100 0.85 0.87 11.76 11.49 0.32 0.00
![Page 16: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/16.jpg)
Instantaneous Acceleration Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100
Meters (m)
Velo
city
(m/s
/s)
Johnson
Lew is
![Page 17: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/17.jpg)
Linear SI Derived Units
Force: The product of mass and accelerationSI Unit Newton (N) The force that is able to accelerate 1 kg by 1 m/s2
Rate of force development
![Page 18: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/18.jpg)
Linear SI Derived Units
Work: The product of force and distance SI Unit Joule (J) When 1 N of force moves
through 1 m Energy: The capacity to do work
SI Unit J Power: The rate of doing work (work/time)
SI Unit Watt (W) Note: Also calculated as F*V
Deadlift Example
![Page 19: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/19.jpg)
Agenda
Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions
![Page 20: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/20.jpg)
Angular Displacement The change in angular position Challenge: Difficult to describe angular
displacement with linear units of measurement
A B C
![Page 21: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/21.jpg)
Angular Displacement
Solution: Measure angular motion with angular units of measurement
Three interchangeable units of measurement for rotary motion:Revolution: A complete cycleDegree: 1/360th of a revolutionRadian: 57.3 degrees
1 revolution = 2**57.3
![Page 22: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/22.jpg)
57.3 degrees
How many radians in one revolution?
![Page 23: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/23.jpg)
Angular Displacement
Angular displacement is denoted as theta ()
= final position – initial position If is not described in degrees (°),
assume it is in radians
![Page 24: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/24.jpg)
Angular Velocity
The rate of angular displacement Angular velocity is denoted as () = / time Unit of measurement
Rads/s or °/s Example
A softball player who moves her arm through 3.2 radians in 0.1 s has an average of 32 rads/s.
Degrees/s? Revolutions/s?
![Page 25: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/25.jpg)
Angular Velocity
Average vs. instantaneous Critical when analyzing sequential
movements high velocities
![Page 26: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/26.jpg)
Figure 11.16, Hamilton
Sampling rate: 150 HzAverage from a b = 37.5 rad/sW at a = ~25 rad/sW at b = ~50 rad/s
b
![Page 27: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/27.jpg)
Angular Acceleration
The rate of change in angular velocity Angular acceleration is denoted as () = final – initial / time
![Page 28: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/28.jpg)
initial = 25 rad/s
final = 50 rad/s
Time/frame = 1/150 = 0.0067 sNumber of frames from a b = 15Time = 15 * 0.0067 = 0.1 s = 50 – 25 / 0.1 = 250 rad/s2
![Page 29: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/29.jpg)
Angular Acceleration
Average vs instantaneous angular acceleration
Much more information
![Page 30: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/30.jpg)
Torque
Torque: The turning effect of a force T = Fd
F = forced = perpendicular distance between line of
force and fulcrum (moment arm)
![Page 31: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/31.jpg)
F
d
F
![Page 32: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/32.jpg)
Torque
How can torque be modified? Modify force Modify moment arm
How is this accomplished in the human body?
![Page 33: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/33.jpg)
When is the moment arm length maximized in this example?
![Page 34: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/34.jpg)
Torque
T = Fd SI Unit: Nm Example: A muscle pulls with a force of 50
N and the moment arm is 0.02 m Torque = (50 N)(0.02 m) = 2 Nm
![Page 35: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/35.jpg)
F = 50 N
d = 0.02 m
T = 50 N * 0.02 mT = 2 Nm
![Page 36: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/36.jpg)
Angular Work and Power
Work = Fd Angular work = T, where
T = torque = change in angular displacement
SI unit = Nm
![Page 37: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/37.jpg)
Angular Work Example
If 40.5 Nm of torque is applied by the biceps and the forearm is moved 0.79 radians, the amount of angular work performed is . . .Angular work = T
Angular work = 40.5 Nm (0.79)Angular work = 32 Nm
32 Nm of work was performed by the 40.5 Nm of torque
0.79 rads
![Page 38: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/38.jpg)
Angular Work
Positive angular work is associated with concentric contractions
Negative angular work is associated with eccentric contractions
![Page 39: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/39.jpg)
Angular Power
Power = Fd/t or Fv Angular power = T/t or T, where
T = torque (Nm) = change in angular displacementT = time = angular velocity
SI Unit = Nm/s or Watts (W)
![Page 40: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/40.jpg)
Angular Power Example
If the 32 Nm of work performed by the biceps was performed in 0.2 seconds, a net power output of . . .Angular power = T/tAngular power = 40.5 Nm (0.79) / 0.2 sAngular power = 32 Nm / 0.2 sAngular power = 160 Nm/s or WThe angular power output of the movement was 160 W
![Page 41: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/41.jpg)
Agenda
Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions
![Page 42: Defining the Variables](https://reader035.fdocuments.net/reader035/viewer/2022062305/56815a82550346895dc7ee27/html5/thumbnails/42.jpg)
Useful Conversions Length:
1 ft = 0.3048 m 1 m = 3.28 ft 1 inch = 2.54 cm
Mass/Weight/Force: 1 N = 0.2248 lb 1 lb = 4.448 N 1 kg = 2.2 lb 1 lb = 0.454 kg 1 kg = 9.807 N
Displacement: See Length
Velocity: See Length
Acceleration: See length
Work: 1 J = 1 Nm = 0.239 cal 1 cal = 4.186 J
Power: 1 W = 1 J/s 1 W = 1 Nm/s
Energy: See work
Angular Conversions: 1 rev = 360 degrees 1 rad = 57.3 degrees
http://www.wscope.com/convert.htm