Study Midterm 1 Flashcards
Parts of a lever system
A fulcrum (pivot point or axis of rotation)
A load moment arm (with a length of dL)
An effort moment arm (with a length of dE)
1st class lever
dL >, < or= dE
load and effort arm on each side of fulcrum
ex: crowbar or scissors
2nd class lever
dL < dE
ex: wheelbarow o bottle opener
3rd class lever
dL > dE
with fulcrum on one end
DA >1
MA <1
ex: most levers in the musculoskeletal system
Mechanical advantage
M.A.
(force advantage)
- the amplification (or reduction) in force due to the relative lengths of the effort and load arm
M.A. = FL/FE = dE/dL
Distance advantage
D.A.
(Speed advantage)
- the amplification (or reduction) in distance moved (and the speed) due to the relative lengths of the effort and load arm
D.A = FE/FL = dL/dE
Torque
tau, moment of force
- the force that causes an object to rotate about the axis
- distance between the axis of rotation and the applied force is called the moment arm
T= F * d , SI units: N m (newton meters)
counter clockwise (CCW) = +ve, CW= -ve
What do you need to know to calculate how much torque is acting on an elbow with the arm held horizontally when all forces are acting perpendicular (ie 90 degrees) o the forearm?
need to know the force acting on the forearm (m * g)
need to know the length of the moment arm (dL= distance from fulcrum to center of gravity of the arm)
Scalar
a physical quantity that has a magnitude
ex: mass, length, area, volume, speed, density, pressure, energy, work
Vecor
has both magnitude and direction
ex: acceleration, velocity, direction, momentum, force, displacement, lift, drag, thrust, weight
Newtons 1st law
a body stays at rest or in uniform motion in a straight line unless a force is applied to it
Newtons 2nd law
accelertation is proportional to the applied force and is in the same direction as the force
Newtons 3rd law
when one body exerts a force on another, the second always exerts a force on the first; the two forces are equal in magnitude, opposite in direction and act along the same line. (action/ reaction)
What is Force?
- an influence that causes an object to undergo change in movement, direction of geometrical construction
- has magnitude and direction (a vector)
- measured in newtons (N) represented by the symbol F
- F= m (mass (kg)) *a (acceleration (m/s^2))
What happens when the forces acting on a stationary object are balanced?
there is no movement (i.e. no acceleration)
What happens when forces acting on an object in motion are balanced?
there is constant velocity (i.e. no acceleration)
What happens when forces acting on a rigid object that is stationary are unbalanced?
the object will move (acceleration) in the direction of the net force
What happens when forces acting on a moving object are unbalanced?
there will be either acceleration (positive or negative if the forces are in line) or a change in direction (if the force is perpendicular to the direction of motion)
gravity
is acceleration acted on a mass due to earths graviational field (9.81 m/s^2)
F= m*g
Work
- is done on a body when a force applied ot the body causes a displacement in the direction of the force
- work= force aplied to an object (N) * displacement (d, meters) of the object, in the direction of the force
- Work (J)= force (N) * displacement (m)
Using SOH CAH TOA what happens when the angle between two vectors of interest is: 0 degrees, 180 degrees, 90 degrees or 270 degrees?
0 degrees, then Fx = F
180 degreed then Fx= -F
90 degrees then Fx=0
270 degrees then Fx= 0
Power
-is in units of watts
-is the rate at which work is done
-the rate at which energy is generated or consumed
-Power(W)= work(J)/ time (s)
For an object surrounded by a fluid (gas or liquid) which direction is pressure exerted?
90 degrees (‘normal’) to the surface of the object.
AKA pressure in fluids is omnidirectional- at any given point within a fluid the molecules are pressing equally in all directions
Atmospheric pressure: what is the diff between sea-level and Eversest in atmospheric pressure?
at sea level= 101.3kPa
the difference between sea level and Mt Everest(30kPa) is 3-fold
Hydrostatic pressure: How does it change?
pressure increases by ~1atm with every 10m of depth
101.3kPa at surface to ~110,000 kPa at bottom (>10000 fold)
Relation between pressure and volume in a container
inversely proportional
if P doubles V is halved
P1V1 = P2V2
If dE > dL then what happens to a 1st class lever
force is amplified by lever i.e. MA >1
If dE < dL then what happens to a 1st class lever?
the force is reduced by the lever i.e. MA <1
and there is a distance advantage/ speed advantage DA > 1 inversely proportional to MA
Why is MA the reciprocal of DA and vise versa?
Levers conserve work!
Work (J) = Force (N) x displacement (m)
example: lifting a 1kg mass 10 m requires the same amount of energy as lifting 10kg mass 1 m
with an arm held at 90 degrees and holding still what is the moment arm for the muscle
distance between muscle insertion point and elbow
this is where the force exerted by he muscle will act
dE
If the force is applied to the lever arm at any angle other than 90 degrees, how do you calculate the force that is not contributing to the torque around he axis of rotation
- calculate the component of the applied effort FE that is perpendicular to the moment arm L using cos(angle)
L= dE for perpendicular component of FEperp
(T= FEperp x L) - or calculate the length of the moment arm (dE) which is perpendicular to the line of action and , therefore, FE!
Muscles
the biological actuators that drive the stiff levers of the musculoskeletal system
Why do muscles attach so close to the fulcrum?
Muscles are good at generating force, but not very good at getting shorter (also keeps them out of the way!)
For a muscle to contract a short distance but produce a long movement at he end of a limb requires a small dE and a large dL (i.e. a D.A. >1)
what is a myofibril
its the basic unit of the muscle that contracts to shorten the muscle and generate force
Sarcomere
the functional unit of the muscle
between two z-lines
fibers shorten in the direction of the contracting muscle
muscle shortens by only ~20- 25% of relaxed length
contraction force of a muscle (ie force of a muscle is determined by)
the number of sarcomeres in parallel
cross-sectional area of muscle is proportional to number of fibers
therefore cross-sectional area of muscle is proportional to the force it can exert
Work a muscle can do proportional to
its volume
Work= Force x displacement
displacement(contraction distance) is proportional to muscle length
muscle volume = CS area (force) x length (proportional muscle shortening proportional to displacement)
A sarcomere can contract ____ and thus speed is determent by ____
~20% of relaxed length
speed determined by number of sarcomeres in series
What is Youngs modulus of elasticity, what relationship does it describe and what’s its equation
The stiffness of elastic modulus of a material
E (young’s modulus) = tensile stress/strain= change in sigma/change in E
steeper slope= stiffer material
What structural property of a biological material leads to a J shaped stress/strain curve
long elastic fibers may show a J-shaped curve (like collagen)
This is because when no stress is applied the fibers are coiled and crumpled up. Thus small increase in stress causes a large increase in stain (extension) as coil unwinds. Once fiber is stretched tight there it requires much greater increase in stress to further strain (stretch)material
Stress
force/ CS area measured in Pa
Strain
Dimensionless ratio of length change due to stretching
(DL) to initial un-stretched length Lo (i.e., DL/Lo)
Where on a stress/ strain curve is stiffness high? where is it low?
Stiffness (E)= change stress (sigma)/ chance in strain (e), units Pa
high is where slope is steep
low is where slope is low
What is toughness? How is it calculated? what are its units?
Work required to strain a unit value of material to failure
units are J/m^3
calculated by integrating area under the stress/ strain curve.
Shear Stress
= shear force (force applied parallel to surface)/ area force is aplied
Shear Strain
=displacement (change x)/ height
Shear modulus
G= shear stress (T)/ shear strain (y “gamma”)
relationship indicated degree an object will deform for a given amount of shear stress
units Pascals
Dynamic viscosity
u= shear stress/ shear strain rate (y “gamma” dot)
describes fluids ability to resist a continuously applied shearing stress by flowing (straining) at a certain rate
units Pascals
Shear strain rate
“gamma” dot = change velocity/ l (distance)
Brigham plastic
flows once stress exceeds yield stress
straight line on shear stress/ shear strain rate graph with a y intercept
Shear thinning
becomes less viscous
down curving line on shear strain/ shear strain rate graph
slope starts high as wilth more stress strain rate is low but as it becomes less viscous less stress is needed for strain rate to increase
newtonian fluid
1-1 straight line on shear stress/ shear strain rate graph
shear thickening
becomes more viscous
upward curve on shear stress/ shear strain rate graph
slope starts low as it takes less shear stress to increase shear strain but as it thickens it takes more shear stress to have slower shear strain rate (steeper slope)
Length of the moment arm
dE
is the perpendicular distance from the axis of rotation (ie fulcrum) to the line of action of the force
line of action
follows the force vector of the musce
If force applied to lever arm at any angle other than 90, then some component of the force is not contributing to the torque around the axis of rotation how do you use this info?
could either a) calculate component of appled effort Fe that is perpendicular to the moment arm L using cos angle. L=dE for perpendicular component of FE perp. (T=FE perp *L)
or b) calculate length of moment arm (dE) which is perpendicular to line of action and therefore FE.
Vertebrate fiber variation
sarcomere length is invariant (2.4-2.6 nanometer long)
so they have multiple muscle fiber types that vary in myosin heavy chain (myosin head has many isoforms)
variation in myofibrillar ATPase activity
Type 1 and Type 11 fibers
Type 1 fibers
motor unit type= Slow Twithch Oxidative (SO)
contraction force= low
contraction speed= low
time to fatigue= long
ATPase activity= low
example: swimming muscle
Type 2 fibers
motor unit type= Fast Twitch Oxidative (llA)/ Glycolytic (llB)
contraction force: medium
contraction speed: high
time o fatigue: short
ATPase activity: high
example: explosive power muscles
Invertebrate muscle
have a range of ATPase activity, etc.
have range in sarcomere length, can be > or < 2.5 nanom
short sarcomeres for rapid fast
long sarcomeres for enlarged crushing claw
A long Invertebrate sarcomere …
has more myosin/ actin cross-bridges pulling directly on the load
can only pull the load as fast as each myosin head can move
Long sarcomeres = high force, low speed
A short Invertebrate sarcomere
has myosin/ actin cross-bridges pulling on each other, as well as on the load
each sarcomere will pull on adjacent sarcomeres and there speed will add
short sarcomeres = low force, high speed
Muscle force
specific force production= force/ cross-sectional area of muscle
Tension (units Pa)
measured during non-moving (isometric) contratcion
average 200kPa
Does holding a weight in a steady position use work? if not what is happening?
No work as no displacement (W= F x d)
energy is expended though to maintain a tension, myosin heads continually make and break contact with actin filaments consuming ATP
What doesn’t need to use energy to hold position
Bivalves
adductor muscle can maintain tension using a ‘catch’ mechanism
locks contracted muscle in position. Using very little additional energy
Phosphorylation of ‘twitchin’ keeps muscle in tense state, allowing muscle to act like a ratchet
Pennate muscles
do not budge
area= width x length and these don’t change as fibers contract
therefore volume says approximately constant
Parallel muscle fibers
long fibers- can contract further
fewer fibers in a given muscle volume
Produce relatively low forces
Force oriented along muscles line of action (ie both muscle and fibers contract along same direction)
bulge outward
Pennate muscle fibers
short fibers- short contraction dist.
contract slowly
more fibers packed into a given muscle volume produce higher forces
force of contraction oblique to the muscles line of action (pennation angle)
do not bulge so occur where space is an issue, and or ther is a requirement for generating large force
Types of pennate muscle
Unipennate
Bipennate
Multipennate
Force generated by the muscle fiber can be divided into what three components?
- Force in line with fiber
- force in line with the muscle
- force perpendicular to the muscle
What is gearing in muscles
it is trading force for distance (same as how levers conserve work-trad force for distance)
skeleal systems alter how force generated by a muscle translates into high force/short distance
muscle fiber arrangement within a muscle can also aler the velocity of contraction and the force generated by the muscle
Architectural gear ration (AGR)
the ratio of whole muscle contraction velocity to fiber contraction velocity
AGR= Velocity of Muscle contraction/ velocity of fiber contraction
AGR= length of muscle contraction/ length of fiber contraction
In parallel muscles what is AGR and why?
AGR= 1 in parallel muscles
b/s individual muscle fibers are oriented in the same direction as whole muscle
therefore muscle contraction velocity is equal to fiber contraction velocity
AGR= Velocity of Muscle contraction/ velocity of fiber contraction
AGR= length of muscle contraction/ length of fiber contraction
AGR of pennate muscle
AGR does not equal 1
b/c rate at which pennate muscle contracts depends on pennation angle of fibers
muscle contracion is faster whe angle is higher
muscle contraction velocity is not equal to fiber contraction velocity
In muscles what is related to force?
type 2 muscle fibers
longer sarcomeres (invertebrates)
increase muscle cross-sectional area (more sarcomeres in parallel)
pennate muscle fibers (force highest at low pennation angle <30)
lever system: MA large as possible
In muscles what is related to speed?
Type 2 muscle fibers
short sarcomeres
long parallel muscle
lever system: DA as long as possible
elastic potential energy
storage of work done by slow, forceful muscle in animals rather than using gravitational potential energy to store the work done:
example grasshopper jumping
1- flexor retracts leg
2- extensor and flexor booth contract slowly bending the semilunar process storing energy in elastic cuticle
3-flexor suddenly relaxes, allowing the elastic cuticle to release its stored energy rapidly catapulting the tibia backwards
Power amplifiers
take slow low power contraction and turn it into rapid high power release (ex catapult)
Isometry
Two variables scale in direct proportion with one another (scale with a factor of 1)
A 1 unit change in x associated with a 1 unit change in y
Allometry
Non-equal scaling (an object scales with a factor <1 or >1 unit change in y
What does scaling allow us to do?
- understand how structure works
- differentiate between differences due to size and diff due to adaption
- examine how changes in shape might be necessary to maintain functional equivalence
Y=aM^b
power law which states that the variable Y changes in proportion with mass to the power b
M= Mass (usually body mass)
a= variable-specific coefficient
b= scaling factor (power)
If the scaling factor b is >1, =1, =0, <0 what does this tell you
b>1 gives an allometric relationship
b=1 gives isometric relationship
b=0 gives independent relationship
b<0 gives allometric relationship
0<b></b>
what is Y=aM^b log trasformed:
axis goes from fixed intervals to orders of magnitude
log(y)=loga +b x log(M)
y axis value = y intercept +slope x Xaxis value
turns curved lines to straight lines
The square-cube law
square Area= LxL therefore area is proportional to L^2
Volme= LxLxL therefore volume is proportional to L^3
Uniform scaling
Objects increase in all linear dimensions by the same factor
(Isotropic)
what does scaling with geometric similarity imply
larger objects have less surface area per unit volume: For every increase in an objects linear (L) dimensions, volume increases with he cube of L (L^3) while area increases wih the square of L (L^2)
Assuming objects have been scaled uniformly and thus geometrically similar (same shape diff size) then what is the length area and volume relationship
Vol. M^1.0
S.A. M^0.67, (M^2/3)
Length. M^0.33, (M^1/3)
non-uniform scaling
(anisotropic)
some linear dimensions increase by diff factors
Kleibers Rule
MR had to be measured under standardized conditions (basal MR)
concluded that BMR= M^0.75 (3/4)
-not based on geometric principles
problems:
unicells have no fractal circulation, but MR still sclas aproxM^0.7
BMR depends mainly on gut metabolism but mas MR depends on muscles
max MR scales to about 0.89
math may be flawed
Is there a single scaling exponent describing relationship b/w basal MR and body mass for all life?
no
most likely multiple scaling exponents exist for diff organisms
yet BMR with Mass usually b/w 0.67-0.75
Rubner RMR
determined that MR=aM^0.67
b=0.67 (2/3) suggested MR scaled with surface area
argued this was due to heat loss
what is compression
the stress generated when an inward force is applied to a material perpendicular to the surface
what is tension
The stress generated when an outward force is applied to a material perpendicular to the surface
Shear
the stress generated when a force is applied to a material, parallel to the surface/ object cross- section
Gases resist
compression
liquids resist
tension and compresion
solids resist
compression, tension and shear
simple composition
accumulation of only 1 material
composite composition
combination of 2 or more simple materials
Isotropic directional dependence
mechanical properties are not directionally dependent
Anisotropic directional dependence
mechanical properties are directionally dependent
Tensile
capable of stretching
Pliant
capable of bending easily
Rigid
Unable to be forced out of shape
Hookean material
displacement is directly proportional to the applied load
Tensile strength
strength= stress at failure (breaking stress)
units= Pa
Extensibility
Extensibility= strain at failure (breaking failure) Units = ration of change in L/Lo
Resilience
work of contraction/ work of extension
a measure of energy recovered from elastic storage. Dimensionless value expressed as %energy recoverd
Spider silk threads (viscoelastic) has a ___ resilience. Why?
low, because they stretch and don’t want to bounce back(don’t want to catapult prey) (greater energy loss during extension/ contraction cycle
what happens when shear stess is applied to a fluid?
it causes fluid to flow
layers of fluid slide past each other as the fluid attached to the moving plate drags the fluid below it into motion
this is shear strain rate= velocity gradient
Catgut (collagean) has a __ resilience when pre-tensioned. Why?
high, it captures and stores elastic potential energy then releases it (bounces back/ catapults)
small amount of area between contraction curve and extension cure (low energy loss)
Viscoelastic
display both viscous properties and elastic properties (like a solid)
if stress held constant the strain will increase with time
If strain is held constant the stress decreases with time (relaxation)
the effective stiffness of the material depends on the rate of application of the stress
What happens when you increase the strain on a spring (elastic material)
you are stretching it out and its stress will increase in direct proportion to the applied strain
What happens when you increase the strain on a dashpot (viscous material)
the viscosity of the liquid within initially resists the movement of the piston (stress increase)
Over time, fluid flows around the piston, causing an increase in the length of he dashpot and a decrease in stress.
what happens when you increase strain on a viscoelastic material?
stress initially increases with strain with direct proportion like an elastic material but over time will decrease as spring contracts and dashpot extend slowly over time, system will remain at strained length
How is harmonic analysis of materials useful?
sine wave stain input (machine oscillates up and down changing length of sample)
Can analyze the phase difference b/w two sine waves using a lissajous curve
plot the intensity (height) of the two sine waves at each time point as x/y coordinates
depending on the phase shift b/w the two waves, this will produce wither a line or circle or ellips
When both stress and strain are in phase in harmonic analysis…
the material is acting as an elastic (Hookean) solid described by young’s modulus of elasticity: E= stress (sigma)/ strain(e)
(line)
When stress and strain are 90 degrees out of phase….
then the material is acting as a Newtonian fluid, described by the samples dynamic viscosity (u)
(circle)
When stress and strain are somewhere between 0 and 90 degress out of phase….
the material is acting as viscoelastic substance (both elastic and viscous properties)
(ellipse)
Universal rule
in a closed system, mass, momentum and energy must ne the same over time ie conserved
What energy is in a fluid?
Potential energy (pgh)
kinetic energy (1/2pv^2) (dynamic pressure)
pressure energy density: (Px volume/volume) (static pressure)
density= p(rho)= mass/volume
Bernoulli’s theorem and assumptions:
describes how the total energy of a moving fluid is equal to teh sum of the pressure, potential and kinetic energies
total fluid energy= P +pgh+ 1/2pv^2
Assumptions:
- flow is inviscid (moves without drag/friction)
- flow is incompressible (low velocity)
- flow is constant (volume/ time)
- flow is laminar (no turbulance)
Static pressure energy
P is the pressure at some point in a fluid
units= pascals
pressure is exerted equally in all directions within the fluid(scalar force)
acts perpendicular 9normal) to the surface of any object in the fluid
Dynamic energy (kinetic)
energy possessed by a fluid in motion
proportional to density (p) and velocity (v) of the fluid
units= pascals
equivalent to the amount of pressure that would be exerted by the moving fluid if it collided wit an object and stopped
Potential energy of a fluid
is the energy due to the fluids location above some (arbitrary) ground level
as h increases, so dows the potential energy of the fluid
potential energy= pgh
Units= Pascals
