Kinesiology 384

3rd exam

what are impacts

• large force applied over time

• occurs when bodies collide

• could produce a rapid change in velocity in one or both bodies

what happens to KE in an impact that has implications for injury?

lost KE goes into the deformation of colliding bodies

what is the relationship between collisions and momentum?

the net external impulse acting on a “system” of bodies determines change in system’s momentum

• with no net external forces, momentum will not change (it is “conserved”)

what are the 2 types of collisions?

1. perfectly elastic collision

2. perfectly inelastic collision

what is a perfectly elastic collision?

when bodies bounce off one another

• no energy is lost

what is a perfectly inelastic collision?

bodies stick together

• energy is lost

what is the coefficient of restitution?

e, is an indication of how elastic/inelastic the collision is

• e is a property of a collision that depends on materials, temperature

what is the coefficient of restitution for a perfectly elastic collision? what about for a perfectly inelastic collision?

• perfectly elastic collision: e=1.0

• perfectly inelastic collision: e=0

what is e also defined by?

it is defined by the ratio of relative velocity after (rebound velocity) to relative velocity before (approach velocity)

e = (v’b - v’a) / (va - vb)

what is conservation of momentum?

the momentum of a system remains constant before, during, and after a collision

• ONLYYY if the next external force acting on the system is 0

• for 2 bodies a and b

  • mava + mbvb = m’am’v + m’bv’b

• whether a collision is elastic or inelastic doesn’t affect whether momentum of a system is conserved

what is the conservation of energy?

the energy of a system may remain constant during a collision, but 2 conditions must be satisfied:

1. no work is done on the system by external forces

2. the collision must be perfectly elastic (e=1.0)

   • forces associated with elastic collisions are conservative (spring-like)

     • ex: rubber balls, billard balls

   • forces associated with inelastic collisions are non-conservative (“plastically” deforming)

     • ex: clay, bean bags

an image that describes the conservation of energy

image of conservation of energy

what does a fluid do compared to a solid?

a fluid continuously deforms in response to applied shearing (parallel to surface)

• push sideways on a deck of cards and it behaves like a fluid

• glue all cards together and it behaves like a solid

why is air considered a fluid?

both gases and liquids are fluids, except air is compressible and water is not

• called hydrostatic pressure

what is hydrostatic pressure?

• pressure squeezing bodies that are underwater

• increases with depth of water

• squeezing is the same in all directions

what is pressure?

pressure is the force acting evenly over an area

• pressure = force / area

• units: Pascal (Pa) 1 Pa = 1 N/m²

what is density and how does it relate to hydrostatic pressure?

density is the mass per unit volume

• hydrostatic pressure is due to the weight of water above the submerged body

  • depends on depth, density, and gravity

  • p = pgh

    • h = depth of water

    • p = density of fluid kg/m³

what is the density of pure water?

1000 kg/m³

what is buoyancy?

your body floats in water because of the buoyant force

• buoyant force: upward force that acts on a submerged or partially submerged body

  • buoyant force is due to a pressure difference

essentially it works because: weight of the air you displace << weight of the water you displace

how does one know a body will float?

• every submerged body has a buoyant force acting on it; some float and some don’t

• body floats if buoyant force (weight of displaced fluid) is equal to weight of body ….

  • Fnet = FB - W = 0

  • if FB < W, body accelerates downward (sinks)

  • if FB > W, body accelerates upward until just enough body is submerged to make Fnet = 0

• floating depends on densities (equation in image)

what is the center of volume?

the buoyant force acts at the body’s center of volume…RECALL that body weight acts at body’s center of mass

• COV → where COM would be if body had same density everywhere

human body COV is above COM

• buoyant force and weight produces rotation of the body until COM is directly under COV

what is a drag force?

drag force → a force that resists motion through a fluid (equation provided in image)

• drag force acts in backward direction

what is the measurement of CdA in the equation for drag force?

• product of CdA depends on moving body’s size and shape

• normal time-trial position CdA = 0.254m²

• superman position CdA = 0.150m²

what is terminal velocity?

• a falling object keeps falling faster and faster in a vacuum (no air)

  • downward a = 9.81m/s²

• in air, drag force increases with velocity

• upward drag force slows falling until equilibrium is reached: W = Fdrag

• with no net vertical force, vertical velocity is constant

this final velocity is called “terminal velocity”

what is the “loudest injury in sport”?

the rupture of the achilles tendon

what is the relationship between forces and injury?

kinetic analysis (basically F=ma) can tell us how the forces applied to bones, tendons, and ligaments may have differed

• however, forces are not the whole story

what is stress?

stress is the amount of tissue deformation caused by a force; depends on the tissue size

• stress is force divided by the area over which the force is distributed

  • units: N/m², or pascal (Pa)

there is normal stress and shear stress

what is normal stress?

• force applied normal to face

• equation in image

what is shear stress?

• force parallel to face

• equation in image

what is a linear strain?

is change in length divided by the original (unstretched) length: Ɛ = (L - Lo)/Lo

• when Ɛ = 0.02, length has changed by 2%

what is a shear strain?

is the change in shape, given by an angle expressed in radians: γ = theta - thetao

what different ways can forces, moments, and torques be applied to a body?

• bending → compressive normal stress; tensile normal stress; and shear stress

• tension → tensile normal stress

• torsion → shear stress

• compression → compressive normal stress

what is elastic vs. plastic material?

• elastic → describes a material that shapes back to its original shape when unloaded

• plastic → describes a material that has yielded

  • i.e. been loaded past the point when elastic behavior is no longer possible

  • return to a shape that is different from the original shape

what is the stress-strain curve?

• stress plotted on y-axis

• linearly elastic materials have a linear curve

• look at image

what are elastic moduli for biomaterials?

• stiffer biomaterials have higher E

• cortical bone: E = 15GPa

• trabecular bone (spongey):

  • young human spine: E = 60MPa

  • osteoporotic: E = 30MPa

• achilles tendon: E = 600 MPa

• ACL: E = 500MPa

• cartilage: E = 10MPa

how is strength (which is determined by stress at failure) measured?

• determined using material testing

  • stress and strain measured

• yield strength, ultimate strength, failure strength

what is yield strength?

apply this much stress and material will not return to undeformed shape

what is ultimate strength?

the most stress a material can carry

what is failure strength?

stress at which material finally ruptures

physiological tendon loading

look at image

what are the forms of motion analysis?

• 2-dimensional

  • makes 2 markers per segment

  • one camera

• 3-dimensional

  • 3 markers per segment (not in a line)

  • multiple cameras

• either 2D or 3D may be manual or automated

  • manual when human identifies markers

  • automated when computer does this

what is reconstruction?

actual (x,y,z) coordinates of points (look at image)

• we say that the actual coordinates (3D x,y,z) are “reconstructed” from image coordinates obtained from each camera

• involves solving systems of ray equations

  • finding the intersection of several rays, one for each camera

how does 3D motion analysis work?

• each camera sees only one 2D image

• depth cannot be judged by a single camera

• look at image

how does calibration in 3D motion analysis work?

• system initially does not know

  • where cameras are

  • in which directions cameras point

• calibration produces this information

  • results in relationships for operating ray equations from 2D image coordinates

what is a cheap force plate?

• actually reads extension of spring inside scale

• force converted to displacement

  • depends on Hooke’s law: F = kx

• makes one measurement of vertical ground reaction force (GRF)

• doesn’t locate center of pressure

How do force plates work?

• strain gauges located on supports at each corner

• force plate supports deform when foot is on plate

• deformation at corners directly related to force applied

  • Hooke’s Law, F= kx

  • electrical resistance of strain gauge is measured

what is a strain gauge?

they are transducers whose electrical properties change when they are stretched

• how?

  • current flows less readily through wires that have been stretched

• strain gauge: a small wire glued to something whose deformation we want to monitor

how do you find the “center of pressure”?

COP → point at which GRF would act if GRF acted at a single point

• use of multiple strain gauges gives information about the location of the COP: (look at image)

How do you calculate COP in a 2D example?

look at image!!

what is a wearable sensor?

• smartphones and fitness trackers contain several useful for measuring activity and tracking progress

• apple, xiaomi, fitbit, etc

• information from multiple sensors integrated to measure motion

whats inside a wearable sensor?

1. accelerometer

2. gyroscope sensor

3. magnetometer

4. GPS receiver

what is an accelerometer?

• tiny microelectromechanical systems (MEMS) device

• essentially a mass attached to the case by a spring

• change in spring length is proportional to acceleration: F = ma → k(x - xo) = ma

• useful for step counters, estimating metabolic energy expenditure, identifying activiting (driving, etc)

what is a gyroscope sensor?

• MEMS device that makes use of Coriolis effect to sense angular velocity

• provides improved exercise identification in a Fitbit (e.g. detecting sleep)

what is a magnetometer?

• earth generates a magnetic field with lines of flux that run from magnetic South to magnetic North

• a magnet placed in this field experiences forces that make it align with these lines

• magnetometer determines orientation and heading during navigation or tracking activities (e.g. running, cycling)

what is a GPS receiver?

• satellites carrying very stable clocks continually sending out radio time signals

• GPS receiver recevies multiple signals, uses the speed of the radio signal (the speed of light) to find distances from satellites

• if 4 distances are known, the 3D position of the receiver may be found

  • latitude, longitude, altitude

• useful for logging routes, mileage, and for estimating pace

what does validity mean?

measures are valid if they measure what they are designed to measure

• validity is relative

  • people often want to know if a test or measure has been “validated”

  • no test is perfectly valid

  • better to discuss how valid a test is rather than whether it is valid

what is reliability?

a test is reliable if it gives consistent results

what are the different forms of reliability?

inter-rater reliability and test-retest reliability

what is inter-rater reliability?

measurements made at the same time

what is test-retest reliability?

measurements made at different times

what is the relationship between accuracy and precision?

• accuracy:

  • Refers to how close a measured value is to the true or accepted value.

  • If a measurement is accurate, it means it is close to the correct or standard value.

• precision:

  • Refers to how consistent or repeatable measurements are when repeated under the same conditions.

  • If a set of measurements are precise, they are very close to each other, regardless of whether they are close to the true value.

what is sampling frequency?

sampling frequency (fsamp): rate at which data are sampled

• aka “sampling rate”

• measured in samples per second, or hertz (Hz)

what happens if fsamp is too low?

aliasing will occur

• a signal can appear to be a different signal (have an “alias”) when sampled too slowly

how to choose a sampling frequency?

• sampling faster is better, but sometimes sampling rate is limited

  • by available data storage

  • by sensor/sampling technology

• minimum sampling rate

  • at least 2x the frequency of the signal you care about

  • depends on the question you want to answer

what are the 2 measurement errors?

1. systemic error

2. random error

what is systemic error?

• affects repeated measurements in the same way

• every data point is “off” by the same amount

what is random error?

• varies unpredictably with each measurement

• also called “noise”

  • as opposed to “signal” (data of interest)

what problems can occur due to random errors in position data?

• errors in position may be small, but we often need velocities or accelerations

• velocity and acceleration computed from position are sensitive to position noise

what is the signal and noise relationship?

look at image

what is data smoothing?

“smoothing”: eliminates high-frequency (rapidly changing) noise, leaving lower frequency (slower changing) signal

what is a low-pass filter?

low pass filter:

• saves (lets pass) low-frequency signal

• discards high-frequency noise

• cut-off frequency separates the two

  • typically 5Hz for motion data

  • typically 45Hz for force data