Linear Kinetics

Example of calculating center of mass problem

x= 2.5 y=2.49

To adequately describe a force, we need to know 3 things

§Magnitude §Direction §Point of application

Center of mass def

§Point about which the matter of a body is evenly distributed §Object supported by COM (center of mass) will balance and rotate freely

Joint reaction force definition

§equal and opposite forces that exist between adjacent bones at a joint caused by the weight and inertial forces of the two segments §The net force acting across the joint

mu and frction

μ = coefficient of friction Function of the contacting surface materials (0-1) Consider: soles of shoes, rug on tile, crutch tips and floor

Balance and rotate freely definition

•The point about which the sum of torques = zero

Ground reaction force is an indirect measure of

Acceleration

Concurrent forces

Act at the same point

Ground reaction forces shape picture

All for right leg Positive is vertical, positive is medial, positive is anterior

Mass def

Amount of matter constituting the body (kg)

Seat belt and momentum

Body stays, but head keeps going forward

There _______ friction without movement

Can be

Consequence of having a large vertical ground reaction force from muscles

Causes joint to rotate, squeezes/compresses joint and causes torque and force

Effective impulse definition

Difference between body weight and ground reactive force) This determines change in velocity (bigger in running than walking)

Common friction coefficients

Don't memorize, they will be given to you

Gait speed and loading picture

During walking, muscle contribution and external ground load is about 50/50. As you run or cut, muscle contraction gets about 5/1 due to high muscle contraction

How to get rotation/translation motion

Eccentric Force couple

1st Newton Law (Law of Intertia) definition

Every body at rest, or moving at a constant velocity in a straight line will continue in that state unless compelled to change by an unbalanced external force exerted upon it.

Ground reaction forces typically recorded using ____-

Extremely sensitive electronic scales (force plate)

Momentum and impulse

F = m times a F= m times (change in velo) divided by time Force times time = mass (change in velo) or Force times time = momentum final minus momentum initial

Kinetic friction formula

Fk = mu of k times N

Newtons Law of Action/Reaction (3rd law)

For every force that is exerted by one body on another, there is an equal and opposite force exerted by the second body on the first Every action there is an equal and opposite reaction

Impulse formula

Force times time Calculated as the integral (area) under the force-time curve)

Friction is a _______-

Force/vector

External forces definition

Forces originating outside the "system" Examples: gravity, ground reaction force, dumbbells, tubing, manual resistance

Internal system forces

Forces within a system Ex: joint reaction force, muscle force, elastic force System can be a segment, joint, the body, more

With walking (1-2 BW), as gait speed increases, our GRF and joint reactive force does what

Goes up

Gravity and PT

Gravity is inherent in pt. evaluation and exercise prescription Patient positioning to alter resistance Effect of gravity on joint torque will vary throughout the range of motion (size of moment arm) §"Crabbin lab"

High coefficient vs low coefficient with friction picture

High picture, the box will tip and stop (imagine bottom is covered in rubber) Low picture, box tips and slides down (imagine covered with silicone)

Force couple examples

Humeral rotation Scapular rotation Muscles would draw humerus/scapula in odd motions, need all of them

If there is an acceleration in any direction, there is an ________ in that direction

Imbalance of force

Acceleration on an object occurs only when there is _______

Imbalance of force In many cases, internal vs external (applied vs resistive)

Vertical ground reaction force picture

Negative equals him moving down Positive means him going up Running = large net impulse Walking = small net impulse

Momentum is constant in the absence of a ____

Net external force

The center of mass may be in a location with _______ mass

No

If resistive force exceeds motive force, the box will

Not move v

Eccentric force

Not through COM or axis of rotation Causes rotation and translation

Vertical force and walking/running what to look for

Notice body weight stays the same throughout, force above body weight (due to gravity) makes him go up, below body weight force makes him come down (gravity!!)

Friction always ______ between contacting surfaces

Opposes motion between contacting surfaces

Force couple

Opposing, not through COM or axis of rotation Causes straight rotation

Parallel forces

Parallel in the same plane

Friction acts at the ______

Point of contact between contacting surfaces

Other name for law of inertia

Principle of conservation of momentum

Kinetic friction definition

Resistance once sliding occurs Fk < motive force

Static friction definition

Resistance prior to sliding Fs= motive force

Medial vs lateral impulse in gait picture

Right foot= Left positive force from ground pushing left Left foot= Right negative force from ground pushing right COM moves from right to left back and forth

How to change ground reactive force in a good way for PT

Slow down gait (decrease GRF, decrease joint reactive force)

Speeding up and slowing down picture

Speeding up (positive velocity of COM) Same speed (equal) Slowing down (- velocity)

Body weight with stairs, running and jumping

Stairs (1-1.5BW) Running (2-5 BW) Jumping (Varies, depends on how high you jump)

Newton's Law of Acceleration (2nd law)

The acceleration of a body is proportional to the net force causing it and takes place in the direction in which the net force acts F = m times A

Linear motion and center of mass

force going through center of mass

Static friction is

linear

Momentum formula

m times V

Momentum formula 1b

mass times velocity

If motive force exceeds resistive force, the box will

move

Friction force =

mu times N

Friction is present when

one body moves or tries to move across the surface of another body

Forces can be resolved into components (3 of them)

rotary components (shear forces at joint) stabilizing (compressive forces at joint) dislocating (tension forces at joint)

_____ produce force to accelerate COM against gravity gait (vGRF)

Muscles

Static friction formula

Fs = mu of s times N

Medial vs lateral in walking and ground force

Ground force always pushes toward medial (Middle)

N and friction

N = normal force Force holding surfaces together Perpendicular to the supporting surface

Coplanar forces

Balance around COM or axis of rotation

4 types of forces to create linear motion

Centric Coplanar Concurrent Parallel

Common resistive forces

(gravity, tubing/bands, air resistance)

motive force

The force parallel to the surface

Friction magnitude is ___-

Variable

Forces from muscles on bones vs vGRF

Knee is ~12x body weight, ankle is ~10x body weight to make an overall ~4x body verticalGRF (bones get much higher forces than anywhere else due to muscle contraction

Muscle contraction and vertical ground reaction force (vGRF)

Larger contraction, larger ground reaction force vertically. Much larger than ground reaction forces (8-15x body weight)

Center of mass for entire individual, how would you calculate?

Mass of segments times x and y divided by whole mass

Weight def

Mass x gravity F = M times a (Newtons)

Reaction force kinetic analysis

Most common form of kinetic analysis in human movement analysis is to quantify the ground reaction force during an activity. Person pushing down, anterior ║ Ground pushing up, posterior

Change in force walking vs running picture

Much bigger change in running than walking (change in v)

Resistive force

The force perpindicular to the surface times the mu coefficient (statice or kinetic)

Friction definition

The force that resists sliding/slipping

Linear kinetics definition

The forces that cause motion

Kinetic friction is always

The same

Gait speed matters example picture

There is force on prosthetic even during swing phase (due to muscle contraction) Force from muscle contraction went way up with faster gait speed due to the required muscle contraction to walk faster. Slower gait allowed for less force which will be easier on joints (less load)

How to calculate motive force and resistive force picture example

Theta is important, g is gravity, but we are on an incline.

Center of mass for humans from cadavers (Know this!!)

Thigh: 43% from proximal end Shank: 43% from proximal end Foot:50% from proximal end

Centric force

Through COM or axis of rotation

How do we make effective impulses?

Through muscle contraction

Largest magnitude in walking comes from what force

Vertical

With jumping, applied and resistive forces

Vertical applied force greater than vertical resistive force

Scale for ground reaction force records forces in 3 directions

Vertical, A/P, M/L