Pre-midterm Prep Flashcards
What are Newton’s Three laws?
- A body stays at rest or in uniform motion in a straight line unless a force is applied.
- Acceleration is proportional to the applied force and is in the same direction as the force.
- 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.
What is Biomechanics?
The application of physics and engineering principles to biological problems.
Define design. Biological terms.
process by which a functional structure is created.
Biology = evolution. Random changes can lead to competitive advantages.
Biologist starts with a design (or structure) and then figures out the function of it, where the trade offs are etc.
What are the basic forces on structures in water?
buoyancy Thrust Drag Mg Lift -generated by hydrofoils Added Mass - acceleration of fluid around structure increases body mass.
What are the basic forces on structures in air?
Lift
Mg
Thrust
Drag
What are the basic forces on structures on the ground?
Ma
deal with forces much larger than body weight cause acceleration and deceleration are greater than that of gravity.
What are the basic forces of terrestrial locomation?
- Animal pushes off land and moves through the air.
- Earth offers lots of resistance, air not so much
- focus on ground reaction force (force needed to drive self forward) not air resistance.
What happens to the mechanical work generated by muscles? (terrestrial)
It generates the ground reaction force. the load elastic components or tendons help pay for the launch phase.
What are the forces involved in moving through a fluid?
-body pushes off and moved through same stuff. One part of body pushes on fluid, generating thrust, another part pushes fluid out of the way, generating drag
What happens when you increase the density and viscosity of a fluid?
you increase it’s resistance to movement
How do you push against the fluid to produce thrust but not push against the fluid to create drag?
Streamlining
What happens to the mechanical work generated by muscles? (fluid)
Creates vlorticies, pushes against air to generate thrust.
Efficiency = ?
Total work / metabolic cost
How do you visualize flow of fluid? to measure total work in swimming/flying?
- Introduce tracer in fluid (bubbles, dye,ec)
- Digital particle imaging velocimetry (DPIV)
- Computational fluid dynamics (not in course)
Cost = ?
Total metabolism + Waste + Gain
How can you reduce the maintenance cost (total metabolism and waste)?
Reduce activity cost of an animal.
Metabolic Rate =
Fuel + Oxygen = Bond energy available in fluid + reaction products (waste)
What is scaling?
The study of physical parameters as a function of body mass.
- power as a function of body mass
Equation for Energy
force x distance
Equation for Power
Energy / unit time
Minimum power = ?
resting metabolism
Resting metabolism = ?
Power expenditure at rest, in neutrally temperate conditions, in the post-absorptive state (not digesting)
Maximum power output = ?
some multiple of resting metabolism
Available power to do mechanical work = ?
Metabolic scope (maximum output - minimum output)
For a >100kg animal falling from what height will cause the animal injury?
the height of the animal itself
For a 100g - 100kg animal falling from what height will cause injury/
greater than the anima;s own height
100mg - 100g animal falling from what height will cause injury?
no height is too high
<100mg animal falling from what height will cause injury?
none, just as likely to go up as down.
What is Isometric (geometric) Scaling?
scaling of an object by multiplying every dimension by the same amount.
if you increase the size of an object to maintain isometric dimensions do we also maintain the function?
no, it will not be functionally equivalent.
What is Allometric Scaling?
Scaling an object to maintain the function by changing how it looks.
What are the uses of scaling?
- to understand how structure works
2. to differentiate between differences due to size and differences due to adaptation.
Draw backs of scaling
- regression lines are empirical and just because you get a relationship doesnt mean it represents a requirement to maintain functional significance (the relationship may incorporate both size based requirements and adaptations.
- absolute size may not be relevant
What happens to the surface area to volume ratio as size increases?
it decreases. larger animals have smaller surface area relative to their volume.
what is muscle force a product of and why?
it is a product of cross sectional area because it represents the amount of material that is supporting the load.
muscle force is proportional to _____
cross sectional area
Muscle work is proportional to _____
volume
Volume is proportional to _________
Surface area x Length
Work is proportional to _______
M to the 1
Work to jump to height h = ?
Force x Distance = Work / mass x gravity
organisms of different masses should be able to jump to the same height.
What is load supported by?
cross sectional area
If you double the length what does the isometric argument say about the increase in weight and force bones can withstand?
weight increases x8 while force bones can withstand increases x4. therefore mass will always increase at greater rate than the cross sectional area of the bones that support the load. Force per unit area increases for larger animals.
bone mass is proportional to ______
body mass to the 1.08
what does skeletal mass scale more closely too?
length cubed
what should aquatic animals not be concerned with?
gravity, thus their bone mass is smaller –> less skeleton.
What does maintaining functional equivalence by controlling proportions assume?
that absolute size is irrelevant.
in terms of mass specific metabolism, are larger or smaller animals more efficient? why?
large animals –> more fuel efficient. larger animals have lower metabolism. also lose less heat.
How efficient is an animal?
25% <– includes all muscles etc
What is the cheapest form of locomotion? (swimming, flying, walking) which is most expensive?
Cheapest: Swimming because water is used for buoyancy, dont have to deal with gravity. the force of drag is not as cumbersome as the force of gravity so it is cheaper than flying.
Expensive: Running
Swimming COT = ?
Flying COT = ?
Running COT = ?
Swimming COT = 0.6M to the -0.6
Flying COT = 2.3M to the -0.46
Running COT = 7.5M to the -0.59
Solids
- exert force in only one direction (down)
- will remain at rest, until there is a change in momentum.
- at rest, volume and density determine force (pV)g = mg
- exhibit stiffness and elasticity
Momentum = ?
mass x velocity
Force = ? = ?
F = ma = mv/t
how can you characterize solids?
by their structural properties
Stress
- force / unit area
- stiffness x strain
Strain
normalize for the length of an object
change in length / original length
- dimensionless
Toughness
amount of energy required to deform a volume of material
Stiffness
Young’s modulus
types of stress
Tensile stress (pulling) Compressive stress (squishing) Torsion stress (turning) Shear stress (push on unevenly)
Gas
- will fill any container
- double the molecules, double the pressure of molecules
- for a given mass of gas p1V1 / T1 = p2V2 / T2
- will not withstand tension
- exhibit viscosity
Static pressure
pressure exerted on all sides of container that hold it.
pV = nRT
(pressure)(volume) = (# of molecules)(gas constant)(temperature)
Liquids
- identified by internal cohesion.
- fluid will form spherical shape when weightless and windless
- will withstand tension
- exhibit viscosity
Shear stress = ? (solids and fluids)
solids = shear modulus (stiffness) x shear strain Fluids = viscosity x shear strain rate (no stiffness)
True or false?
Greater force doesnt lead to bigger distortion, fluid simply flows
True
Viscosity
resistance of fluid to flow across surfaces and through conduits.
Newtonian fluid
linear viscosity when plot shear stress vs shear rate (slope = viscosity)
Shear thinning
viscosity is decreasing with increasing shear rate
slope is decreasing with increasing shear rate
Shear thickening
viscosity is increasing with increasing shear rate
slope is increasing with increasing shear rate
Bingham plastic
toothpaste
acts like solid until some minimum/critical stress is reached at which it will flow like a fluid.
How are pressure and velocity related in a fluid?
Bernoulli’s principle
surface tension
prevents liquid from leaving container like gas
principle of continuity
the volume of fluid that enters the pipe must leave the pipe.
velocity(1) x Surface area (1) = Velocity (2) x Surface area (2)
Bernoulli’s principle
Static pressure + (kinetic energy / unit volume) = Total pressure
P + 1/2pU to the 2
- sum of static pressure and dynamic pressure must remain constant
- increase pressure –> decrease velocity, increase velocity –> decrease pressure
-increasing height of pipe decreases pressure
-assumes ideal fluid (no viscosity)
Kinetic Energy
1/2 (Mass)(velocity squared)
Increase velocity = ?
decrease pressure
streamline
traces a path along which some particles of fluid travel. can be drawn tangent to every point of local flow.
Pathline
release a particle into the flow and track its position by snapping a series of pictures.
type of streamline
Streakline
type of streamline
instantaneous view of the position of markers (dye/bubbles) steadily released up the stream.
Reynolds Number = ?
Re = inertial forces / Viscous forces
= density x length x velocity / dynamic
Provides an estimate of whether flow is laminar or turbulent viscosity
Inertial forces depend on size and velocity. Viscous forces depend on the ‘stickiness’ or friction
between molecules. At higher Reynolds numbers, inertial forces dominate, and flow tends to be turbulent.
what are two types of drag?
friction drag - due to viscosity
Pressure drag - caused by boundary layer separation
What is drag dependent on?
- function of friction and pressure distribution across object.
- pattern of flow behind object which is a function of reynolds number
What is the drag equation and what does it allow us to do?
1/2 density x S x velocity to the 2 x Cd
- it allows us to convert between the measured drag force and the drag coefficient Cd
What does the drag coefficient scale as a function of?
Reynolds number.
at low reynolds number the Cd is…?
the Cd is quite high cause viscosity dominates. There are few to no vorticies but friction drag is very high
At high reynolds number, Cd is….?
Cd decreases, inertia dominates. Vortices create pressure drag but skin friction is lowered.
Von Karman Street
at moderate reynolds numbers. Get early boundary layer separation and wide, turbulent wake.
Drag crisis
as boundary layer becomes turbulant, separation is delayed. drop in Cd. decrease in drag due to speed. (turbulent boundary layer, turbulent wake
