Post on 06-Mar-2018
Physics 160 Biomechanics
Basic Concepts in Kinetics
Kinematics & Kinetics
• Kinematics is the description of motion.
• Kinetics deals with the causes of motion.
• The concept of force is the basis for understanding linear kinetics.
Basic Concepts in Kinetics
• Inertia • Mass • Force • Free body diagram • Weight
• Pressure • Volume • Density • Center of Mass
Inertia
Tendency for a body to resist a change in its state of motion
Mass
• Quantity of matter contained in an object • The measure of inertia for linear motion • The property giving rise to gravitational
attraction • Units: SI – kilogram (kg)
English – slug (slug) 1 slug=14.59 kg
Force • Force is a vector. • Force is a push, pull, rub (friction), or blow
(impact). • Forces cause or tend to cause motion
(acceleration) or a change in shape of an object (deformation).
Force vectors are usually drawn as arrows indicating direction and magnitude.
Characteristics of a Force • Vector (magnitude and direction)
– Angle • Point of application • Line of application
Free body diagram
A sketch that shows a defined system in isolation with all of the force vectors acting on the system
Contact Forces
Ground Reaction Force (GRF)
Friction Fluid Resistance Elastic Force Muscle Force Joint Reaction Force
GRF
Actions of Forces
• Forces cause acceleration
• Often assumed that forces cause minimal deformation
2
2
2
[ ]( )[ ]
[ / ]: /
/
net
net
F maF net force in N newtonsm mass in kga acceleration in m sUnits N kg m s
pound force slug ft s
==
=
=
= ∗
= ∗
Example
A soccer player kicks a 0.45 kg ball with a force of 200N. What is the acceleration of the ball?
Example A 100 kg football player is
contacted by two tacklers simultaneously. Tackler A exerts a force of 350N, and tackler B exerts a force of 300N. If the forces are coplanar and directed perpendicular to each other, what is the magnitude and direction of the acceleration of the player?
Center of Mass (Center of Gravity)
• Point representing the “average” location of the mass of a body
• Motion of the com represents the “average” motion
Center of Mass
The center of mass of the body may move as the body’s configuration changes
Fig. 3.7Fig. 3.7
Weight • The force due to gravity (i.e.
the pull of the Earth) • Weight always acts at the
center of mass and points towards the center of the Earth
Fw 2
[ ]
9.8 /[ ]
W
W
F mgF weight in N
g m sm mass in kg
==
==
Example
William Perry, defensive tackle and part-time running back better known as “The Refrigerator”, weighed in at 1352 N. What was Perry’s mass?
Pressure Force per unit of area over which the force
acts
2
2
2
2
[ / ][ ]
[ ]: /
/1 6897
FPA
P pressure in N mF force in NA area in mUnits Pa N m
psi lb inpsi Pa
=
==
=
=
==
Heel-toe runner
Midfoot runner
Pressure
F F
P1 P2
A1 A2
Equal forces acting over different areas produce different pressures
Pressure Plots
Backrest pressure distribution
- A good backrest should provide firm support across a wide area of the back (no pressure points)
Pressure Plots
Seat pressure distribution
2-D 3-D
Pressure Plots
Pressure distribution pattern of a normal foot during walking
Example A boxer hits another boxer with a force of 450N.
The contact area of the boxing glove is 0.025 m2. a) What is the pressure over the area of contact? b) Without the glove the contact area of the boxer’s
fist is 0.005 m2, what is the pressure of the punch in this case?
Volume • Space occupied by an object • Has three dimensions (width, height and
depth) • 1 m3=1,000,000 cm3
1 = 1,000,000 X ( )
Density
Mass per unit volume
3
3
3 3
[ / ][ ]
[ ]1 / 1000 /
mVdensity in kg m
m mass in kgV volume in mg cm kg m
ρ
ρ
=
==
=
=
Example
A bone sample has a mass of 55.0 g and a volume of 29.5 cm3. Calculate the average density of this bone.
Common Units for Kinetic Quantities
Quantity Symbol Metric Unit English Unit Mass m kg slug Force F N lb Pressure P Pa psi Volume (solids) V m3 ft3 (liquids) liter gallon Density ρ kg/m3 Specific weight γ N/m3 lb/ft3
Tension, Compression, Shear
a) Tension - stretching
b) Compression - squeezing
c) Shear - tearing
Stress and Pressure
Stress: The force distributed over a given area Pressure: Stress due to a compressive force
2
2
[ / ][ ]
[ ]
FAstress in N m
F force in NA area in m
σ
σ
=
==
=
Shear
During a squat the shear force acting on the knee is a maximum when flexion at the knee is maximal. The shear at the joint is produced by the axial force in the femur.
Spinal Stress
The surfaces of the vertebral bodies increase in surface area as more weight is supported
Example
How much compressive stress is present on the L1, L2 vertebral disk of a 625 N woman, given that approximately 45% of body weight is supported by the disk. Assume that the disc is oriented horizontally and that its surface area is 20 cm2.
Bending
Asymmetric loading that produces tension on one side of a body’s longitudinal axis and compression on the other side
Compression Tension
Torsion
Neutral axis
Load producing twisting of a body around its longitudinal axis
Stresses on Femur
Deformation The relationship between the amount of force
applied to a structure and the structure’s response is illustrated by a load deformation curve
Elastic region
Plastic region
Failure
Repetitive vs. Acute Loading The stress required to cause a material to fail (i.e. fracture or rupture) decreases as number of loading cycles increases
Injury occurs if load is high and applied a few times or when load is low and applied many times