1. Linear Kinetics
Kinetics
Newton’s Laws • study of the relationship between the forces
acting on a system and the motion of the system
Linear Motion (Translation)
Objectives: • All parts of an object or system move the same
• Define linear kinetics, internal & external distance in the same direction at the same time
forces
Linear Kinetics
• Understand and apply Newton’s three
• The kinetics of particles, objects, or systems
laws of motion
undergoing linear motion
• Describe the common types of forces that
act on humans
Internal vs. External Forces 1st Law (Law of Inertia)
• Internal Force : is applied to a system from within
the system • A body will maintain a state of rest or constant
velocity unless acted upon by an external force.
• External Force : is applied to a system from outside
the system • If there is no net external force acting on a body:
Fexternal#3 – if the body’s center of mass is not moving, it
System will remain motionless.
– if the body’s center of mass is in motion, it will
Finternal
continue to move at a constant velocity
(i.e. at the same speed in the same direction)
Fexternal#2
Fexternal#1
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2. 2nd Law (Law of Acceleration) 3rd Law (Law of Reaction)
• For every action, there is an equal and opposite
F=ma reaction.
where: • If body 1 applies a force to body 2, then body 1
– F : net external force acting on a body experiences a reaction force from body 2:
– m : mass of the body – of the same magnitude
– a : linear acceleration of the body center of mass – at the same point
• If there is a net external force acting on a body, the – in the opposite
acceleration of the body’s center of mass is: direction Freaction
– directly proportional to the net force Faction
– inversely proportional to the body’s mass
– in the direction of the net force
Example Problem #1 Example Problem #2
A cyclist is coasting down a straight hill at 8 m/s. A 60 kg gymnast is hanging in a stationary “iron
The mass of the cyclist + bicycle are 80 kg. cross” position on the rings.
The slope of the hill is 15° He pushes downward on each ring with a force of
313.2 N at an angle 20° medial of downward.
The weight of the cyclist + bicycle produces a
force of 203 N directed down the hill What are the forces acting on the gymnast?
(and a force of 758 N directed into the hill). Will the gymnast be able to remain stationary?
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?
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3. Example Problem #3 Types of Forces
A 50 kg runner is running forward at 4 m/s. Contact Forces
His heel contacts the ground with his lower limb at • Forces pushing against or pulling on an object as
an angle of 60° from the horizontal in the sagittal the result of physical contact with another object.
plane. • Contact forces in biomechanics include:
Assume that this contact results in a force of 2 – forces applied from outside the body
times body weight being directed up his lower
– forces originating inside the body
limb just after heel contact.
What is the runner’s instantaneous linear Non-Contact Forces
acceleration just before and just after heel
• Forces that do not result from direct physical
contact?
contact (e.g. weight)
What if the lower limb angle had been 45° instead?
Forces from Outside the Body Viscoelastic Forces
• Most body tissues are viscoelastic
• Resistive : normal force resulting from pressure
against a rigid body • Force produced by stretch increases with rate of
stretch
• Friction : acts over area of contact between two
surfaces; opposes sliding between surfaces • Under a constant applied force, the tissue will
creep (i.e. slowly get longer or shorter)
• Elastic : produced by spring-like objects;
elastic force is proportional to deformation slow
medium
• Viscous : produced by fluids; fast
viscous force is proportional to velocity
Length
Force
Force
• Viscoelastic : combines behavior of a spring and
a fluid; force depends on deformation, rate of
deformation, and time
• Active : forces generated from added energy Stretch time
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4. Ground Reaction Forces Joint Contact Force
• The reaction forces that result from pushing against • Results from the contact of two adjacent articular
the ground or other supporting surface surfaces (i.e. bone-on-bone contact)
• Ground reaction force resolved into 3 components: • Joint contact forces are always compressive (directed
– Vertical (normal) into the bone)
force Up; Anterior; Medial • Because cartilage causes friction to be very small,
– Anteroposterior joint contact forces are normal to the articular surface
Force (% body weight)
100 Vertical
shear force Fcontact
– Mediolateral Pelvis
shear force Fcontact
M/L Femur
GRF acting on the 0
foot during gait A/P
Down; Posterior; Lateral
Muscle Force Muscle Force Properties
• Acts through the muscle’s tendons onto the bone at • Generates passive force when stretched
the origin and insertion • Generates active force which depends on:
• Produces tensile forces on bone in the direction given – Neural stimulation level
by the tendon’s angle of insertion into the bone – Muscle length
• Forces produced at the origin & insertion are equal – Muscle shortening / lengthening velocity
– Time (i.e. it takes time for force to increase or decrease )
origin 150
tendon Passive
Active
Fmuscle muscle Total
100
Force (%)
Force
shortening lengthening
tendon 50
θ Fmuscle
0
insertion -150 -100 -50 0 50 100 150 -5 -3 -1 1 3 5
Stretch (%) Muscle Velocity (lengths/s)
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5. Ligament Force Resultant Joint Force
• When stretched, ligaments produce a tensile force that • In most cases, contact and muscle forces acting at
acts onto the bone at the origin and insertion a joint cannot be determined individually
• Direction of force is given by the ligament’s angle of • Resultant joint force = net force produced by joint
insertion into the bone contact and by all the structures that act across a
• Forces at the origin & insertion are equal joint (muscle, ligament, etc.)
• Ligaments get stiffer as they’re stretched • It acts at the joint center and is the composition of
all forces acting at the joint.
origin Fcontact Fresultant
Facl ligament Force
knee Facl
Facl joint Fquads Fcontact
insertion center Fquads
-2 0 2 4 Fhams tibia Facl
Stretch (%) Fhams
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