Download - Chapter 1. Mechanics of the Body
-
7/30/2019 Chapter 1. Mechanics of the Body
1/35
-
7/30/2019 Chapter 1. Mechanics of the Body
2/35
(W= weight!) W = m g
The main force acting on the body is the gravitational force!
Gravitational force W applies at the center of gravity CG of the body!
Stability of the body against thegravitational force is maintained by the
bone structure of the skeleton!
CG depends on body mass distribution! to maintainstability CG must be located between feet, if feet are far apart
forces in horizontal directionF
x have to be considered
-
7/30/2019 Chapter 1. Mechanics of the Body
3/35
To maintain stabilitythe vector sum of all forcesapplying at the CG must bezero!
-
7/30/2019 Chapter 1. Mechanics of the Body
4/35
The torque r causes a rotational movement around a pivot point!
Torque is defined by the
force F applied at the distance r from the pivot point.
In rotational equilibrium (no rotation,constant rotation) to maintain stabilityfor a person standing on one leg thetorque requires to shift CG of bodyso, that:
New CG:
-
7/30/2019 Chapter 1. Mechanics of the Body
5/35
-
7/30/2019 Chapter 1. Mechanics of the Body
6/35
-
7/30/2019 Chapter 1. Mechanics of the Body
7/35
EXAMPLE: FORCES ON THE HIP
(a person standing on one leg only)
-
7/30/2019 Chapter 1. Mechanics of the Body
8/35
-
7/30/2019 Chapter 1. Mechanics of the Body
9/35
-
7/30/2019 Chapter 1. Mechanics of the Body
10/35
EXAMPLE: FORCES ON THE SPINAL COLUMN
-
7/30/2019 Chapter 1. Mechanics of the Body
11/35
-
7/30/2019 Chapter 1. Mechanics of the Body
12/35
-
7/30/2019 Chapter 1. Mechanics of the Body
13/35
Body movements are controlled by muscle forces,initiated by contraction or extension of the muscles. Skeletalmuscles control the movements of the body limbs.
Most of the muscle forces involve levers!
-
7/30/2019 Chapter 1. Mechanics of the Body
14/35
Three examples for lever systems, W is theapplied weight, F is the force supporting the pivotpoint of the lever system, and M is the muscles
force.
-
7/30/2019 Chapter 1. Mechanics of the Body
15/35
EXAMPLE: THE FOREARM AS LEVER SYSTEM
The biceps muscle pulls the arm upwardsby muscle contraction with a force M the opposing force is theweight of the arm H at its center of gravity (CG) !
-
7/30/2019 Chapter 1. Mechanics of the Body
16/35
Biceps can be strengthened by weight W lifting this addsanother force which has to be compensated by the muscle force.
-
7/30/2019 Chapter 1. Mechanics of the Body
17/35
The lower arm can be hold by the biceps muscle at different angles q. What muscle forces are required for the different arm positions?
-
7/30/2019 Chapter 1. Mechanics of the Body
18/35
EXAMPLE: THE ARM AS LEVER SYSTEM
The deltoid muscle pulls the arm upwards by muscle contraction with aforce T at a fixed angle a with respect to the arm the opposing force isthe weight of the arm H at its center of gravity (CG) and the (possible)weight W hold in the hand!
-
7/30/2019 Chapter 1. Mechanics of the Body
19/35
Consider arm at an angle q hold by the deltoid muscle ( a 15 )
-
7/30/2019 Chapter 1. Mechanics of the Body
20/35
-
7/30/2019 Chapter 1. Mechanics of the Body
21/35
If a body of mass m is in constant motion noacceleration or deceleration occurs !
Acceleration a can be caused by leg muscle force F !
Deceleration can be caused by friction, muscle force or external forces (by running into a wall for example).
-
7/30/2019 Chapter 1. Mechanics of the Body
22/35
Friction occurs between a moving surface and a surface at rest:
Friction force: F f 640 Ndeceleration: a 7.8 m/s 2
N is the normal force!
mk is coefficient for kinetic friction:for rubber-concrete: m
k 0.8
joints between bones: mk 0.003
As smaller the coefficient as less resistance by frictional forces!
For a walker of N W 800 N (m=82kg):
Accelerating muscle forces maintain a constant walking speed!
-
7/30/2019 Chapter 1. Mechanics of the Body
23/35
When the body bumps into a solid object (like a wall) rapiddeceleration a occurs:
The decelerating force F d applied by the wall to the body (or towhatever body part which hits first) causes pressure P d which causesdeformation:
A is the surface area of the body or body part exposed to the force.
Force is only applied over the time period D t until complete stop.
Therefore:
-
7/30/2019 Chapter 1. Mechanics of the Body
24/35
To calculate the impact force the time structure of thedeceleration process needs to be known.
Approximation: treatment of force as a square pulse actual timestructure may depend on particular impact
-
7/30/2019 Chapter 1. Mechanics of the Body
25/35
-
7/30/2019 Chapter 1. Mechanics of the Body
26/35
Falls from great height
The above equation has to be generalizedbecause of energy transfer arguments!
The average force acting on the part of the body which hits the ground is
-
7/30/2019 Chapter 1. Mechanics of the Body
27/35
Body decelerates with average deceleration a fromimpact velocity v to zero while the center of mass of body moves over a distance a/ DCM during the collision
-
7/30/2019 Chapter 1. Mechanics of the Body
28/35
EXAMPLE: Stiffed leg jump on hard ground
-
7/30/2019 Chapter 1. Mechanics of the Body
29/35
Tolerance levels for whole body impact
Threshold for survival: 20 mi/h = 36 km/h = 8.9 m/s
Effects of impact can be reduced by increasing D t (D h CM ) or bydistributing force F over large area to reduce compressing stress.
proper landing techniques for parachutes
To survive a fall the impact pressure should be: 40 lbs/in 2 = 27.6 N/cm 2
For an impact pressure of 35 N/cm 2 50 % survival chance!
-
7/30/2019 Chapter 1. Mechanics of the Body
30/35
EXAMPLE: Free fall from large heights
-
7/30/2019 Chapter 1. Mechanics of the Body
31/35
h c h
Vf2
Vt2
V2
free fall
actual fall
Solution of force equation yields final velocity v !
-
7/30/2019 Chapter 1. Mechanics of the Body
32/35
h/h c e -h/h c V/Vt 1 0.37 0.792 0.14 0.975
3 0.050 0.9754 0.018 0.991
Exponential approach of speed of fall towards the terminal velocity!
Terminal velocity represents the state where the forces are in equilibrium!
-
7/30/2019 Chapter 1. Mechanics of the Body
33/35
-
7/30/2019 Chapter 1. Mechanics of the Body
34/35
-
7/30/2019 Chapter 1. Mechanics of the Body
35/35