1

Newton’s Laws

Objectives:

• Define linear kinetics, internal & external forces

• Understand and apply Newton’s three laws of motion

• Describe the common types of forces that act on humans

Linear KineticsKinetics• study of the relationship between the forces

acting on a system and the motion of the system

Linear Motion (Translation)• All parts of an object or system move the same

distance in the same direction at the same time

Linear Kinetics• The kinetics of particles, objects, or systems

undergoing linear motion

Internal vs. External Forces

• Internal Force : is applied to a system from within the system

• External Force : is applied to a system from outside the system

Finternal

Fexternal#1

System

Fexternal#2

Fexternal#3

1st Law (Law of Inertia)

• A body will maintain a state of rest or constant velocity unless acted upon by an external force.

• If there is no net external force acting on a body:

– if the body’s center of mass is not moving, it will remain motionless.

– if the body’s center of mass is in motion, it will continue to move at a constant velocity (i.e. at the same speed in the same direction)

2

2nd Law (Law of Acceleration)

where:– F : net external force acting on a body– m : mass of the body– a : linear acceleration of the body center of mass

• If there is a net external force acting on a body, the acceleration of the body’s center of mass is:– directly proportional to the net force– inversely proportional to the body’s mass– in the direction of the net force

F = m a

3rd Law (Law of Reaction)

• For every action, there is an equal and opposite reaction.

• If body 1 applies a force to body 2, then body 1 experiences a reaction force from body 2:– of the same magnitude

– at the same point

– in the opposite direction

Faction

Freaction

Example Problem #1

A cyclist is coasting down a straight hill at 8 m/s.

The mass of the cyclist + bicycle are 80 kg.

The slope of the hill is 15°

The weight of the cyclist + bicycle produces a force of 203 N directed down the hill (and a force of 758 N directed into the hill).

What is the acceleration of the cyclist + bicycle down the hill?

What braking force directed up the hill would be required for the cyclist + bicycle to maintain a speed of 8 m/s down the hill?

Example Problem #2

A 60 kg gymnast is hanging in a stationary “iron cross” position on the rings.

He pushes downward on each ring with a force of 313.2 N at an angle 20° medial of downward.

What are the forces acting on the gymnast?

Will the gymnast be able to remain stationary?

3

Example Problem #3A 50 kg runner is running forward at 4 m/s.

His heel contacts the ground with his lower limb at an angle of 60° from the horizontal in the sagittalplane.

Assume that this contact results in a force of 2 times body weight being directed up his lower limb just after heel contact.

What is the runner’s instantaneous linear acceleration just before and just after heel contact?

What if the lower limb angle had been 45° instead?

Types of Forces

Contact Forces• Forces pushing against or pulling on an object as

the result of physical contact with another object.

• Contact forces in biomechanics include:

– forces applied from outside the body

– forces originating inside the body

Non-Contact Forces• Forces that do not result from direct physical

contact (e.g. weight)

Forces from Outside the Body

• Resistive : normal force resulting from pressure against a rigid body

• Friction : acts over area of contact between two surfaces; opposes sliding between surfaces

• Elastic : produced by spring-like objects; elastic force is proportional to deformation

• Viscous : produced by fluids; viscous force is proportional to velocity

• Viscoelastic : combines behavior of a spring and a fluid; force depends on deformation, rate of deformation, and time

• Active : forces generated from added energy

Viscoelastic Forces• Most body tissues are viscoelastic

• Force produced by stretch increases with rate of stretch

• Under a constant applied force, the tissue will creep (i.e. slowly get longer or shorter)

Stretch

For

ce

slow medium

fast

time

Leng

th

For

ce

4

Ground Reaction Forces• The reaction forces that result from pushing against

the ground or other supporting surface

• Ground reaction force resolved into 3 components:– Vertical (normal)

force– Anteroposterior

shear force– Mediolateral

shear force

Vertical

A/P

M/L

100

For

ce (

% b

ody

wei

ght)

0

Up; Anterior; Medial

Down; Posterior; Lateral

GRF acting on thefoot during gait

Joint Contact Force• Results from the contact of two adjacent articular

surfaces (i.e. bone-on-bone contact)• Joint contact forces are always compressive (directed

into the bone)• Because cartilage causes friction to be very small,

joint contact forces are normal to the articular surface

Femur

Fcontact

Fcontact

Pelvis

Muscle Force• Acts through the muscle’s tendons onto the bone at

the origin and insertion

• Produces tensile forces on bone in the direction given by the tendon’s angle of insertion into the bone

• Forces produced at the origin & insertion are equal

muscle

tendon

tendon

Fmuscle

Fmuscleθ

insertion

origin

0

50

100

150

-5 -3 -1 1 3 5

Muscle Velocity (lengths/s)

For

ce (

%)

-150 -100 -50 0 50 100 150

Stretch (%)

For

cePassive

Active

Total

Muscle Force Properties• Generates passive force when stretched• Generates active force which depends on:

– Neural stimulation level– Muscle length

– Muscle shortening / lengthening velocity– Time (i.e. it takes time for force to increase or decrease)

lengtheningshortening

5

Ligament Force• When stretched, ligaments produce a tensile force that

acts onto the bone at the origin and insertion• Direction of force is given by the ligament’s angle of

insertion into the bone• Forces at the origin & insertion are equal• Ligaments get stiffer as they’re stretched

-2 0 2 4

Stretch (%)

For

ceFacl

Facl

ligament

insertion

origin

Resultant Joint Force• In most cases, contact and muscle forces acting at

a joint cannot be determined individually• Resultant joint force = net force produced by joint

contact and by all the structures that act across a joint (muscle, ligament, etc.)

• It acts at the joint center and is the composition of all forces acting at the joint.

Fcontact

Fcontact

Fhams

Facl

Fquads

Fresultant

Fhams

Facl

Fquads

knee joint center

tibia