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