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