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Basic Concepts in Kinetics

Objectives:

• Define basic concepts in kinetics, including: inertia, mass, force, weight, torque, impulse, and stress

• Define the different types of loading

• Learn how materials behave under loading

Subdivisions of Mechanics

Kinematics• the description of motion, including:

– considerations of space and time– patterns and speeds of movement sequencing

• the forces causing the motion are not considered

Kinetics• study of the relationship between the forces

acting on a system and the motion of the system

Inertia & Mass

Inertia• concept relating to the difficulty with which an

object’s motion is altered

Mass• the quantity of matter composing an object• the measure of inertia for linear motion• the property giving rise to gravitational attraction• Units:

– English: slug– SI: kilogram (kg)

Center of Mass(Center of Gravity)

• Geometric point about which every particle of a body's mass is equally distributed

• Position of the Center of Mass changes with changes in body configuration.

• Motion of the Center of Mass represents the “average” motion of the body as a whole

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Force• A mechanical interaction between an object and

its surroundings• The “push” or “pull” of one object on another• Force is a vector. It has:

– a magnitude– a direction– a point of application F

θpoint of

application

Actions of Forces• Forces cause acceleration or deformation (a

change in shape)– We will assume that the forces acting on a body

cause minimal deformation

• Relationship between force (F), mass (m) and acceleration (a):

F = m a

• Units:– English: pound (lb.) = (1 slug)(1 ft/s2)– SI: Newton (N) = (1 kg)(1 m/s2)– 1 lb. = 4.45 N

Net Force• Resultant force derived from the composition of

two or more forces• Reflects the net effect of all of the forces acting

together

F4F1

F5

F2

F3

F1

F2

F5

F4

F3

Fnet

Concentrated vs. Distributed ForceConcentrated Force• A force that is applied at a single point

Distributed Force• A force that is applied over a distributed area• Can be approximated by a concentrated force

that has the same net effect

Fground

Fground

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Weight• The force due to gravity ( i.e. the pull of the Earth)• Weight has magnitude:

W = m g

where:m = massg = acceleration due to

gravity (9.81 m/s2; 32.2 ft/s2)

• Weight always acts at thecenter of mass and points towards the center of the Earth

W

Density & Specific Weight• Volume : The amount of space occupied by a body.

Measured in (unit of length)3 (e.g. m3, ft3)

• Density (ρ): mass per unit volume:

ρ = (mass)/(volume)

SI Units: kg/m3

• Specific Weight : weight per unit volume

(specific weight) = (weight)/(volume)

English Units: lb./ft3

SI Units: N/m3

Torque• A measure of the extent to which a force will cause

an object to rotate about a specific axis• A net force applied through the center of mass

produces translation• A net force applied away from the center of mass

(i.e. an eccentric force) produces both translation and rotation

F F

Impulse• The motion of a body depends not only on the force,

but also on the duration that the force is applied

• Impulse : a measure related to the net effect of applying of force (F) for a time (t):

Impulse = F t

• Impulse increases with:– Increased force magnitude– Increased duration of application

• Equal impulses result in equal changes in velocity

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Compression, Tension, & Shear• Compression : pressing or squeezing force

directed normal (perpendicular) to a surface

• Tension : pulling or stretching force directed normal to a surface

• Shear : sliding or tearing force directed parallel to a surface

Compression

Fn

Tension

Fn

Shear

Fs

Stress & Pressure• Stress: The force distributed over a given area:

σ =

where:σ = stressF = total force appliedA = area force is applied over

• Units:– English: pounds per square inch (psi) = 1 lb./in2

– SI: Pascal (Pa) = 1 N/m2

• Pressure: stress due to a compressive force

FA

A

F

Bending• Asymmetric loading that produces tension on

one side of a body, compression on the other

• Compressive and tensile stresses are greatest at the surface

F1

Compression

Tension

F2

F3Cross-section

Torsion• Load producing a twisting of a body• Creates shear stresses• Shear stresses are greatest at the surface

Cross-section

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Deformation

Deformation

Str

ess Elastic

Region

Plastic Region

Ultimate Failure Point

• Materials behave elastically at small loads

• Loads above the yield point create permanent plastic deformation

• Rupture or fracture occurs at the ultimate failure point

Yield Point

Repetitive vs. Acute Loading

# of Loading Cycles

Str

ess

Cau

sing

Fai

lure

• The size of the loading required to cause a material to fail (i.e. fracture or rupture) decreases as the number of loading cycles increases

Injury Likely To Occur