PHGY 209 Lecture : 3. Blood.pdf

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6 Apr 2012

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Blood is the medium though which exchanges between the external environment and the milieu interieur can be made. It is considered a tissue because it contains both cells and an external fluid (the isf) In ancient cultures such as greek and indian, it used to be though that bleeding an individual was a treatment for disease. It compromises both the ecf (plasma) and the icf (within blood cells) It may be studied in vivo (inside an individual) and in vitro (on a petri dish) It accounts for approximately 7% of total body mass, around 5l in a standard physiological male. A person with normal blood volume is called normovolemic. Lower blood volume is called hypovolemia and higher blood volume is called hypervolemia. It can be used in transport: nutritive transport, respiratory transport of oxygen, excretion of waste, hormone transport in order to regulate activities in the body, temperature regulation. Acid-base equilibrium: maintain a normal ph range of 7. 30-7. 45.

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How fast can a racecar travel through a circular tum without skidding and hitting the wall? The answer could depend on several factors:

The weight of the car;
The friction between the tires and the road;
The radius of the circle;
The “steepness” of the turn.

In this project, we investigate this question for NASCAR racecars at the Bristol Motor Speedway in Tennessee. Before considering this track in particular, we use vector functions to develop the mathematics and physics necessary for answering questions such as this.

A car of mass m moves with constant angular speed to around a circular curve of radius R (Figure 3.20). The curve is banked at an angle . If the height of the car off the ground is h, then the position of the car at time t is given by the function

As the car moves around the curve, three forces act on it: gravity, the force exerted by the road (this force is perpendicular to the ground), and the friction force (Figure 3.21). Because describing the frictional force generated by the tires and the road is complex, we use a standard approximation for the frictional force. Assume that for some positive constant . The constant is called the coefficient of friction.

Let denote the maximum speed the car can attain through the curve without skidding. In other words, is the fastest speed at which the car can navigate the turn. When the car is navigate at this speed, the magnitude of the centripetal force is

The next three questions deal with developing a formula that relates the speed to the banking angle .

Now that we have a formula relating the maximum speed of the car and the banking angle, we are in a position to answer the questions like the one posed at the beginning of the project.

The Bristol Motor Speedway is a NASCAR short track in Bristol, Tennessee. The track has the approximate shape shown in Figure 3.22. Each end of the track is approximately semicircular, so when cars make turns they are traveling along an approximately circular curve. If a car takes the inside track and speeds along the bottom of turn 1, the car travels along a semicircle of radius approximately with a banking angle of . If the car decides to take the outside track and speeds along the top of turn 1, then the car travels along a semicircle with a banking angle of . (The track has variable angle banking.)

The coefficient of friction for a normal fire in Elly conditions is approximately . Therefore, we assume the coefficient for a NASCAR tire in dry conditions is approximately .

Before answering the following questions, note that it is easier to do computations in terms of feet and seconds, and then convert the answers to miles per hour as a final step.

11. Suppose the measured speed of a car going along the outside edge of the turn is . Estimate the coefficient of friction for the car’s tires.

goldpug777

Materials fracture when the force per unit area, called STRESS,exceeds a critical value. In general, the critical stress dependson the direction as well as the magnitude of the force. Forexample, bones break differently when subjected to torsional(twisting) stress than when subjected to compressional (orsqueezing) stress. Let us consider compressional stress. Wet humanbone for 20-39 year olds has an ultimate compressive strength of ~16x104Ncm2 [8]. Consider a person who falls from a height to theground. Upon landing, the person's kinetic energy is converted towork. If the person decelerates over a distance h, we can estimatethe average force during the collision by

If a person lands stiff-legged on a hard surface and doesn'tbounce, the deceleration occurs over a very short distance, h ~ 1cm. Since the force is transmitted up the leg, the stress isgreatest where the cross-sectional area is least, i.e., the tibiajust above the ankle [8].
The following lists some different conditions that may occur duringlanding and physical explanations for why they make bone fracturefrom a fall more or less likely [8]:

(a) bounce [more likely. The impulse is twice as large for anelastic collision as for an inelastic collision.]
(b) bent knees [less likely. Bending the knees increases the timeand distance over which deceleration occurs, which reduces theforce.]
(c) landing in loose earth or sand [less likely. This increases hwhich reduces F.]
(d) turning the body to land on the side [less likely. Thisincreases h. It also distributes the force widely over the body(increases A), thereby reducing the stress.]

So, why can a properly executed karate kick break a concrete blockwithout fracturing bones [16]? First, bone is a very strongmaterial. Its ultimate compressive strength is approximately 40times larger than concrete. Second, contact is made with the edgeof the foot. This concentrates the force into a small area of thetarget and reduces the likelihood of bending a bone to the point offracture. Third, the collision with the target is essentiallyinelastic and extends over several milliseconds, so the peak force,though large, does not exceed the strength of the bone. If A(cross-sectional area of the tibia) ~ 3.3 cm2, compute how far a 69kg person can fall and land stiff-legged on both legs withoutbreaking a bone. Assume F is split evenly between two legs. (Hint:F<or =2(theta)A )

In a circuit containing only resistors, the basic (though notnecessarily explicit) assumption is that the current reaches itssteady-state value instantly. This is not the case for a circuitcontaining inductors. Due to a fundamental property of an inductorto mitigate any "externally imposed" change in current, the currentin such a circuit changes gradually when a switch is closed oropened.
Consider a series circuit containing a resistor of resistance andan inductor of inductance connected to a source of emf andnegligible internal resistance. The wires (including the ones thatmake up the inductor) are also assumed to have negligibleresistance.
Let us start by analyzing the process that takes place after switchis closed (switch remains open). In our further analysis, lowercaseletters will denote the instantaneous values of various quantities,whereas capital letters will denote the maximum values of therespective quantities.
Note that at any time during the process, Kirchhoff's loop ruleholds and is, indeed, helpful:
.
Part A
Immediately after the switch is closed, what is the current in thecircuit?
Hint A.1
How to approach the problem
Hint not displayed
ANSWER:

zero
Answer not displayed
Part B
Immediately after the switch is closed, what is the voltage acrossthe resistor?
Hint B.1
Ohm's law
Hint not displayed
ANSWER:

zero
Answer not displayed
Part C
Immediately after the switch is closed, what is the voltage acrossthe inductor?
Hint C.1
A formula for voltage across an inductor
Hint not displayed
ANSWER:

zero
Answer not displayed
Part D
Shortly after the switch is closed, what is the direction of thecurrent in the circuit?
ANSWER:
clockwise
counterclockwise
There is no current because the inductor does not allow the currentto increase from its initial zero value.
Answer not displayed
Part E
Shortly after the switch is closed, what is the direction of theinduced EMF in the inductor?
ANSWER:
clockwise
counterclockwise
There is no induced EMF because the initial value of the current iszero.
Answer not displayed
Part F
Eventually, the process approaches a steady state. What is thecurrent in the circuit in the steady state?
ANSWER:

Answer not displayed
Part G
What is the voltage across the inductor in the steady state?
Hint G.1
Induced EMF and current
Hint not displayed
ANSWER:
zero

Answer not displayed
Part H
What is the voltage across the resistor in the steady state?
ANSWER:
zero

Answer not displayed
Part I
Now that we have a feel for the state of the circuit in its steadystate, let us obtain the expression for the current in the circuitas a function of time. Note that we can use the loop rule (goingaround counterclockwise):
.
Note as well that and . Using these equations, we can get, aftersome rearranging of the variables and making the subsitution,
.
Integrating both sides of this equation yields
.
Use this last expression to obtain an expression for . Rememberthat and that .
Express your answer in terms of , , and . You may or may not needall these variables. Use the notation exp(x) for .
ANSWER:
=
Answer not displayed
Part J
Just as in the case of R-C circuits, the steady state here is neveractually reached: The exponential functions approach their limitsasymptotically as . However, it usually does not take very long forthe value of to get very close to its presumed limiting value. Thenext several questions illustrate this point.
Note that the quantity has dimensions of time and is called thetime constant (you may recall similar terminology applied to R-Ccircuits). The time constant is often denoted by . Using , one canwrite the expression

as
.
Find the ratio of the current at time to the maximum current.
Express your answer numerically, using three significantfigures.
ANSWER:
=
Answer not displayed
Part K
Find the time it takes the current to reach 99.999% of its maximumvalue.
Express your answer numerically, in units of . Use threesignificant figures.
ANSWER:
=
Answer not displayed

Part L
Find the time it takes the current to reach 99.999% of its maximumvalue. Assume that ohms and millihenrys.
Express your answer in seconds, using three significantfigures.
ANSWER:
=
Answer not displayed
seconds
Part M
Find the time it takes the current to reach 99.999% of its maximumvalue. Assume that ohms and henrys.
Express your answer in seconds, using three significantfigures.
ANSWER:
=
Answer not displayed
seconds
Part N
What fraction of the maximum value will be reached by the currentone minute after the switch is closed? Again, assume that ohms andhenrys.
Use three significant figures in your answer.
ANSWER:
=
Answer not displayed
Now consider a different situation. After switch has been closedfor a long time, it is opened; simultaneously, switch is closed, asshown in the figure. This effectively removes the battery from thecircuit.
The questions below refer to the time immediately after switch isopened and switch is closed.
Part O
What is the direction of the current in the circuit?
ANSWER:
clockwise
counterclockwise
The current is zero because there is no EMF in the circuit.
Answer not displayed
Part P
What is happening to the magnitude of the current?
ANSWER:
The current is increasing.
The current is decreasing.
The current remains constant.
Answer not displayed
Part Q
What is the direction of the EMF in the inductor?
ANSWER:
clockwise
counterclockwise
The EMF is zero because the current is zero.
The EMF is zero because the current is constant.
Answer not displayed
Part R
Which end of the inductor has higher voltage (i.e., to which end ofthe inductor should the positive terminal of a voltmeter beconnected in order to yield a positive reading)?
Hint R.1
How to approach the problem
Hint not displayed
ANSWER:
left
right
The potentials of both ends are the same.
The answer depends on the magnitude of the time constant.
Answer not displayed
Part S
For this circuit, Kirchhoff's loop rule gives
.
Note that , since the current is decreasing. Use this equation toobtain an expression for .
Hint S.1
Initial and final conditions
Hint not displayed
Hint S.2
Let us cheat a bit
Hint not displayed
Express your answer in terms of , , and . Use exp(x) for .
ANSWER:
=
Answer not displayed

PHGY 209 Lecture : 3. Blood.pdf

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