ML504: MEDICAL PHYSICS, I Internal Question Bank
Unit I
Work Energy and Power: Problem Set
Problem 1
Geetha is out with her friends. Misfortune occurs and Geetha and her friends find themselves
getting a workout. They apply a cumulative force of 1080 N to push the car 218 m to the
nearest fuel station. Determine the work done on the car.
Problem 2
Shah Gull is pulling on a rope to drag his backpack to school across the ice. He pulls upwards and
rightwards with a force of 22.9 Newtons at an angle of 35 degrees above the horizontal to drag
his backpack a horizontal distance of 129 meters to the right. Determine the work (in Joules)
done upon the backpack.
Problem 3
Lamar Gant, U.S. power lifting star, became the first man to dead-lift five times his own body
weight in 1985. Dead-lifting involves raising a loaded barbell from the floor to a position above
the head with outstretched arms. Determine the work done by Lamar in dead-lifting 300 kg to a
height of 0.90 m above the ground.
Problem 4
Sheila has just arrived at the airport and is dragging her suitcase to the luggage check-in desk.
She pulls on the strap with a force of 190 N at an angle of 35° to the horizontal to displace it
45 m to the desk. Determine the work done by Sheila on the suitcase.
Problem 5
While training for breeding season, a 380 gram male squirrel does 32 pushups in a minute,
displacing its center of mass by a distance of 8.5 cm for each pushup. Determine the total work
done on the squirrel while moving upward (32 times).
Problem 6
During the Powerhouse lab, Jerry runs up the stairs, elevating his 102 kg body a vertical
distance of 2.29 meters in a time of 1.32 seconds at a constant speed.
a. Determine the work done by Jerry in climbing the stair case.
b. Determine the power generated by Jerry.
Problem 7
A new conveyor system at the local packaging plan will utilize a motor-powered mechanical arm
to exert an average force of 890 N to push large crates a distance of 12 meters in 22 seconds.
Determine the power output required of such a motor.
Problem 8
The Taipei 101 in Taiwan is a 1667-foot tall, 101-story skyscraper. The skyscraper is the home
of the world’s fastest elevator. The elevators transport visitors from the ground floor to the
Observation Deck on the 89th floor at speeds up to 16.8 m/s. Determine the power delivered by
the motor to lift the 10 passengers at this speed. The combined mass of the passengers and
cabin is 1250 kg.
Problem 9
Problem 10
Problem 11
A bicycle has a kinetic energy of 124 J. What kinetic energy would the bicycle have if it had …
a. … twice the mass and was moving at the same speed?
b. … the same mass and was moving with twice the speed?
c. … one-half the mass and was moving with twice the speed?
d. … the same mass and was moving with one-half the speed?
e. … three times the mass and was moving with one-half the speed?
Problem 12
A 78-kg skydiver has a speed of 62 m/s at an altitude of 870 m above the ground.
a. Determine the kinetic energy possessed by the skydiver.
b. Determine the potential energy possessed by the skydiver.
c. Determine the total mechanical energy possessed by the skydiver.
Problem 13
Li Ping Phar, the esteemed Chinese ski jumper, has a mass of 59.6 kg. He is moving with a speed
of 23.4 m/s at a height of 44.6 meters above the ground. Determine the total mechanical
energy of Li Ping Phar.
Problem 14
Chaitra leads college softball team in hitting. In a game against New Greer Academy this past
weekend, Chaitra struck the 181-gram softball so hard that it cleared the outfield fence and
landed on Hebbal Lake. At one point in its trajectory, the ball was 28.8 m above the ground and
moving with a speed of 19.7 m/s. Determine the total mechanical energy of the softball.
Problem 16
Suzie Lavtaski (m=56 kg) is skiing at Bluebird Mountain. She is moving at 16 m/s across the
crest of a ski hill located 34 m above ground level at the end of the run.
a. Determine Suzie's kinetic energy.
b. Determine Suzie's potential energy relative to the height of the ground at the end of the
run.
c. Determine Suzie's total mechanical energy at the crest of the hill.
d. If no energy is lost or gained between the top of the hill and her initial arrival at the end of
the run, then what will be Suzie's total mechanical energy at the end of the run?
e. Determine Suzie's speed as she arrives at the end of the run and prior to braking to a stop.
Problem 17
Nicholas is at The Noah's Ark Amusement Park and preparing to ride on The Point of No Return
racing slide. At the top of the slide, Nicholas (m=72.6 kg) is 28.5 m above the ground.
a. Determine Nicholas' potential energy at the top of the slide.
b. Determine Nicholas's kinetic energy at the top of the slide.
c. Assuming negligible losses of energy between the top of the slide and his approach to the
bottom of the slide (h=0 m), determine Nicholas's total mechanical energy as he arrives at the
bottom of the slide.
d. Determine Nicholas' potential energy as he arrives at the bottom of the slide.
e. Determine Nicholas' kinetic energy as he arrives at the bottom of the slide.
f. Determine Nicholas' speed as he arrives at the bottom of the slide.
Problem 18
Justin Thyme is traveling down Lake Avenue at 32.8 m/s in his 1510-kg 1992 Camaro. He spots a
police car with a radar gun and quickly slows down to a legal speed of 20.1 m/s.
a. Determine the initial kinetic energy of the Camaro.
b. Determine the kinetic energy of the Camaro after slowing down.
c. Determine the amount of work done on the Camaro during the deceleration.
Problem 20
Pete Zaria works on weekends at Barnaby's Pizza Parlor. His primary responsibility is to fill
drink orders for customers. He fills a pitcher full of Cola, places it on the counter top and gives
the 2.6-kg pitcher a 8.8 N forward push over a distance of 48 cm to send it to a customer at
the end of the counter. The coefficient of friction between the pitcher and the counter top is
0.28.
a. Determine the work done by Pete on the pitcher during the 48 cm push.
b. Determine the work done by friction upon the pitcher .
c. Determine the total work done upon the pitcher .
d. Determine the kinetic energy of the pitcher when Pete is done pushing it.
e. Determine the speed of the pitcher when Pete is done pushing it.
Problem 21
The Top Thrill Dragster stratacoaster at Cedar Point Amusement Park in Ohio uses a hydraulic
launching system to accelerate riders from 0 to 53.6 m/s (120 mi/hr) in 3.8 seconds before
climbing a completely vertical 420-foot hill.
a. Jerome (m=102 kg) visits the park with his church youth group. He boards his car, straps
himself in and prepares for the thrill of the day. What is Jerome's kinetic energy before the
acceleration period?
b. The 3.8-second acceleration period begins to accelerate Jerome along the level track. What
is Jerome's kinetic energy at the end of this acceleration period?
c. Once the launch is over, Jerome begins screaming up the 420-foot, completely vertical
section of the track. Determine Jerome's potential energy at the top of the vertical section.
(GIVEN: 1.00 m = 3.28 ft)
d. Determine Jerome's kinetic energy at the top of the vertical section.
e. Determine Jerome's speed at the top of the vertical section.
Problem 22
Paige is the tallest player on South's Varsity volleyball team. She is in spiking position when
Julia gives her the perfect set. The 0.226-kg volleyball is 2.29 m above the ground and has a
speed of 1.06 m/s. Paige spikes the ball, doing 9.89 J of work on it.
a. Determine the potential energy of the ball before Paige spikes it.
b. Determine the kinetic energy of the ball before Paige spikes it.
c. Determine the total mechanical energy of the ball before Paige spikes it.
d. Determine the total mechanical energy of the ball upon hitting the floor on the opponent's
side of the net.
e. Determine the speed of the ball upon hitting the floor on the opponent's side of the net.
Problem 23
According to ABC's Wide World of Sports show, there is the thrill of victory and the agony of
defeat. On March 21 of 1970, Vinko Bogataj was the Yugoslavian entrant into the World
Championships held in former West Germany. By his third and final jump of the day, heavy and
persistent snow produced dangerous conditions along the slope. Midway through the run,
Bogataj recognized the danger and attempted to make adjustments in order to terminate his
jump. Instead, he lost his balanced and tumbled and flipped off the slope into the dense crowd.
For nearly 30 years thereafter, footage of the event was included in the introduction of ABC's
infamous sports show and Vinco has become known as the agony of defeat icon.
a. Determine the speed of 72-kg Vinco after skiing down the hill to a height which is 49 m
below the starting location.
b. After descending the 49 m, Vinko tumbled off the track and descended another 15 m down
the ski hill before finally stopping. Determine the change in potential energy of Vinko from the
top of the hill to the point at which he stops.
c. Determine the amount of cumulative work done upon Vinko's body as he crashes to a halt.
Problem 24
Nolan Ryan reportedly had the fastest pitch in baseball, clocked at 100.9 mi/hr (45.0 m/s) If
such a pitch had been directed vertically upwards at this same speed, then to what height would
it have traveled?
Problem 25
In the Incline Energy lab, partners Anna Litical and Noah Formula give a 1.00-kg cart an initial
speed of 2.35 m/s from a height of 0.125 m above the lab table. Determine the speed of the
cart when it is located 0.340 m above the lab table.
Problem 26
In April of 1976, Chicago Cub slugger Dave Kingman hit a home run which cleared the Wrigley
Field fence and hit a house located 530 feet (162 m) from home plate. Suppose that the 0.145kg baseball left Kingman's bat at 92.7 m/s and that it lost 10% of its original energy on its
flight through the air. Determine the speed of the ball when it cleared the stadium wall at a
height of 25.6 m.
Problem 27
Dizzy is speeding along at 22.8 m/s as she approaches the level section of track near the
loading dock of the Whizzer roller coaster ride. A braking system abruptly brings the 328-kg
car (rider mass included) to a speed of 2.9 m/s over a distance of 5.55 meters. Determine the
braking force applied to Dizzy's car.
Problem 28
A 6.8-kg toboggan is kicked on a frozen pond, such that it acquires a speed of 1.9 m/s. The
coefficient of friction between the pond and the toboggan is 0.13. Determine the distance
which the toboggan slides before coming to rest.
Problem 29
Connor (m=76.0 kg) is competing in the state diving championship. He leaves the springboard
from a height of 3.00 m above the water surface with a speed of 5.94 m/s in the upward
direction.
a. Determine Connor's speed when he strikes the water.
b. Connor's body plunges to a depth of 2.15 m below the water surface before stopping.
Determine the average force of water resistance experienced by his body.
Problem 32
Matthew starts from rest on top of 8.45 m high sledding hill. He slides down the 32-degree
incline and across the plateau at its base. The coefficient of friction between the sled and snow
is 0.128 for both the hill and the plateau. Matthew and the sled have a combined mass of 27.5
kg. Determine the distance which Matthew will slide along the level surface before coming to a
complete stop.
THEORY QUESTIONS
HEAT
AND
COLD
IN MEDICINE
1. Explain the molecular basis of heat and temperature.
2. List the different temperature scales. What is the normal body temperature in each of these
scales?
3. What approach would you use to measure body temperature through non-contact method?
Describe the method in detail.
4. Identify the different features of a clinical thermometer to achieve the following functionality:
a. Improve visibility
b. improve taking readings
5. List the different ways of measuring temperature.
6. From what you have read, which is the fastest way to measure temperature? Describe an
experimental set-up to achieve the same.
7. Among the contact methods of measuring temperature, which is the most sensitive and highly
useful in measuring human body temperature? Describe the working of such a device.
8. Describe in detail the applications of a thermographic device.
9. Summarize all the physical and physiological effects of heat on human body.
10. What form of heat therapy would you recommend for the treatment of following conditions?
Substantiate your answers with reasons:
a. Sprains, strains, contusions, sinusitis
b. Deep muscle spasms, pain from protruded intervertebral discs
c. Degenerative joint disease of the knee, elbow and ankle
d. Fractures, injuries to tendons and arthritis
e. Injuries to bones
11. How are cryogenic methods used in medicine? Explain any one application in detail.
12. How is the problem of absorption of heat by a cryogenic fluid avoided in a Dewar container?
Explain.
13. How could you determine the best way to preserve blood? Explain with a representative diagram.
14. Why are protective agents added in preserving blood? What are the disadvantages in preserving
blood this way?
15. What is the difficulty in preserving the entire human body at cryogenic temperature?
Metabolism
1) What are the main mechanisms of heat loss from the body? Explain them briefly
2) Calculate the convective heat loss per hour for a nude standing in a 5m/s wind. Assume Ts =
33°C, Ta = 10°C and Ac = 1.2m2
3) Define BMR. How is it measured?
4) A 75.0 kg weight-watcher wishes to climb a mountain to work off the equivalent of a large
piece of chocolate cake rated at 500 food Calories (kilocalories). How high must the person
climb?
5) A hiker weighing 575 N carries a 175 N pack up Mt. Whitney (elevation 4420 m), increasing
her elevation by 3000 m.
(a) Find the minimum internal work done by the hiker’s muscles.
(b) If she is capable of producing up to 746 W (1.0 hp) for an extended time, what is the
minimum time for her to ascend?
6) As part of your exercise routine you climb a 10.0 m rope. How many food Calories
(kilocalories) do you expend in a single climb up the rope?
7) How much heat is carried away from the body of a sweating person in 1 hour by the
evaporation of 0.500 liter of water from the skin?
8) A student is trying to decide what to wear. The air in his bedroom is at 20° C. If the skin
temperature of the unclothed student is 37° C, how much heat is lost from his body in 10.0
min? Assume that the emissivity of skin is 0.900 and that the surface area of the student is
1.50 m2.
9) Consider the oxidation of the alcohol (ethanol): C2H5OH + 3O2 → 2CO2 + 3H2O + 327 kcal.
(a) Find the energy release/g, calorific equivalent, and respiratory exchange ratio (RER) (or
respiratory quotient (RQ)).
(b) Compare these values to those for carbohydrates, proteins, and fats.
10) A certain fruit has a metabolizable energy of 0.4 kcal/g normally and 2.4 kcal/g after it has
been dried. Assume the fruit consists of only water, sugar, and non-metabolizable matter and
find the fraction of each in the fruit and in the fruit after it is dried.
11) A body consumes 0.3 L-atm. of oxygen every minute.
(a) Determine the rate of heat production if only carbohydrates are being consumed.
(b) Determine the rate of heat production if only fats are being consumed.
12) In a high jump a 70-kg person elevates his center of mass by 51 cm during an extension
phase (with constant acceleration) that takes 0.25 s.
(a) If the muscle efficiency is 20%, how much chemical energy is used to make one jump?
(Express your answer in joules and in kcal (the usual food calories).
(b) What is the average power generated by the person during the jump in watts and
horsepower (1 horsepower (hp) = 746 W)?
(c) How frequently would someone have to jump (during a 12 h awake cycle) to increase
his/her (daily averaged) metabolism rate to twice the basal value (which is 1,500
kcal/day)?
13) A person lifts a 15-kg mass from the floor to over his head (a distance of 2 m). How many
times does he have to do this to lose a pound of fat, assuming a muscle efficiency of 25%?
14) A 50 kg woman does 10 chin-ups in a minute (each raising her center of mass by 0.5 m).
After 5 min how much mechanical work has she done (in J) and how much metabolic energy
has she used (in kcal), assuming 25% muscle efficiency?
15) How much energy (gravitational potential energy) is required to lift a 70 kg person by 1m (in
kcal)? If your muscles can do this with 25% efficiency, how many times would you have to
lift such a person to burn off the caloric content in one standard donut (280 kcal/donut)?
16) If your daily metabolic rate exceeds your caloric intake by 1,000 kcal (which is a very large
difference) for a week, how much weight will you lose? Assume that the change is due only
to the use of body fat to make up this difference, with 9 kcal per gram of body fat, so
there is no other concomitant loss of weight.
17) Consider a person sitting nude on a beach in Florida [300]. On a sunny day, visible radiation
energy from the sun is absorbed by the person at a rate of 30 kcal/h or 34.9 W. The air
temperature is a warm 30◦C and the individual’s skin temperature is 32◦C. The effective
body surface exposed to the sun is 0.9m2. (Assume this same area for sun absorption,
radiative transfer, and convective loss. Is this a good assumption?)
(a) Find the net energy gain or loss from thermal radiation each hour. (Assume an emissivity
of 1.)
(b) If there is a 4 m/s breeze, find the energy lost by convection each hr.
(c) If the individual’s metabolic rate is 80 kcal/h (93.0W) and breathing accounts for a loss
of 10 kcal/h (11.6 W), how much additional heat must be lost by evaporation to keep the
body core temperature constant?
Unit II
Cardiovascular System
1) A cardiac patient has just undergone bypass surgery and is on a blood thinner.
The flow through the new artery is 0.6597 cm^3/s. The radius of the new artery is 1.0
mm. The blood viscosity is 0.03511 poise. The length of the new artery is 8.0 cm. What is
the blood velocity through the new artery?
2) A cardiac patient has just undergone bypass surgery and is on a blood thinner.
The radius of the new artery is 8.0 mm. The blood viscosity is 0.03715 poise. The length
of the new artery is 12.0 cm. The blood velocity through the new artery is 22.0 cm/s.
What is the flow through the new artery?
3) A cardiac patient has just undergone bypass surgery and is on a blood thinner.
The flow through the new artery is 19.63 cm^3/s. The blood viscosity is 0.03674 poise.
The length of the new artery is 6.0 cm. The blood velocity through the new artery is 25.0
cm/s. What is the pressure drop across the new artery?
4) A cardiac patient has just undergone bypass surgery and is on a blood thinner.
The flow through the new artery is 26.01 cm^3/s. The pressure drop across the new
artery is 0.06722 mmHg. The blood viscosity is 0.03506 poise. The blood velocity through
the new artery is 23.0 cm/s. What is the radius of the new artery?
5) A cardiac patient has just undergone bypass surgery and is on a blood thinner.
The flow through the new artery is 35.41 cm^3/s. The pressure drop across the new
artery is 0.067 mmHg. The length of the new artery is 6.0 cm. The blood velocity through
the new artery is 23.0 cm/s. What is the blood viscosity?
6) A cardiac patient has just undergone bypass surgery and is on a blood thinner.
The flow through the new artery is 12.57 cm^3/s. The pressure drop across the new
artery is 0.4814 mmHg. The blood viscosity is 0.0395 poise. The blood velocity through
the new artery is 25.0 cm/s. What is the length of the new artery?
7) What is negative pressure? Calculate the pressure in mmHg equal to a pressure of 20 cm
water.
8) Define absolute pressure and gauge pressure. Assume you are a shallow-water diver
preparing for a 10 m dive into salt water. What absolute pressure and gauge pressure will
you experience?
9) How can blood pressure be measured? Explain one method of measurement with a neat
diagram.
10) Your blood pressure is measured with a sphygmomanometer, however with your arm
pointed upward instead of downward. If your blood pressure is really 120mmHg / 80
mmHg, approximately what pressure would be measured?
11) What are the different guiding principles in studying pressure and flow in fluids? Briefly
explain each one of them.
12) What factors/quantities does Bernoulli’s equation relate? With relevant equations,
explain the three special cases of Bernoulli’s equation.
13) Explain Fick’s I Law and II law of diffusion. Give an expression for diffusion coefficient.
14) Explain the following terms:
a. Viscosity
b. Reynold’s Number
d. Shear Rate e. Newtonian Fluid
g. Irrotational Flow
c. Hydrodynamic drag force
f. Incompressible Fluid
15) Why cannot a human fly?
16) The pressure inside blood vessel walls, P, exceeds that outside, Pext, by ΔP = P −Pext. How
large of a tension should the vessel walls be able to withstand to support this positive
pressure difference in equilibrium?
17) What are the attributes of the flow of fluids? Briefly explain each one of them.
18) Explain the laws associated with conservation of mass and conservation of energy for
flow of fluids.
19) Explain the Physics involved in swimming.
20)
Calculate the pressure 150 m below the surface of the sea. The density of sea
water is 1.026 g/cm3
21) Calculate the pressure drop per centimeter length of the aorta when the blood flow rate
is 25 liter/min. The radius of the aorta is about 1 cm, and the coefficient of viscosity of
blood is 4×10−2 poise.
22)
Compute the drop in blood pressure along a 30-cm length of artery of radius 0.5
cm. Assume that the artery carries blood at a rate of 8 liter/min.
23)
(a) Calculate the arterial blood pressure in the head of an erect person. Assume
that the head is 50 cm above the heart. (The density of blood is 1.05 g/cm3.) (b) Compute
the average arterial pressure in the legs of an erect person, 130 cm below the heart.
24)
(a) Show that if the pressure drop remains constant, reduction of the radius of
the arteriole from 0.1 to 0.08 mm decreases the blood flow by more than a factor of 2.
(b) Calculate the decrease in the radius required to reduce the blood flow by 90%.
25)
Compute the average velocity of the blood in the aorta of radius 1 cm if the flow
rate is 5 liter/min.
26)
When the rate of blood flow in the aorta is 5 liter/min, the velocity of the blood in
the capillaries is about 0.33 mm/sec. If the average diameter of a capillary is 0.008 mm,
calculate the number of capillaries in the circulatory system.
27)
Compute the decrease in the blood pressure of the blood flowing through an artery
the radius of which is constricted by a factor of 3. Assume that the average flow
velocity in the un-constricted region is 50 cm/sec.
28)
Write short notes on different pressures and flow rates encountered in the body.
29)
Important molecules are formed in the middle of a 2 μm-diameter cell. How long
does it take for them to diffuse throughout the cell? (Assume the cell contents are
liquids and that the diffusion coefficient Ddiff = 10−5 cm2/s.) Is this fast enough to
achieve normal metabolic activity rates?
30)
How much does the blood pressure in your brain increase when you change from a
standing position to standing on your head? Why do you feel uneasy while standing on
head?
31) Why can arteries with small diameter have thinner walls than arteries with large
diameters carrying blood at the same pressure?
32)
If the radius of an arteriole changed from 50 μm to 40 μm, how much would the
flow rate through it change?
33)
How does the venous blood get from the feet to the heart of a standing person?
34)
If the average power consumed by the heart is 10 W, what percentage of a 2500
kilocal daily diet is used to operate the heart?
35)
How can blood flow be modeled when there is a block in the artery? Explain with
relevant principles.
36)
Write a note on blood flow rates and speeds.
37)
What are the different transport processes across the capillaries? Explain each
one of them. What are the factors affecting the transport of nutrients and gas?
38)
Along the systemic circulation, where does the maximum pressure drop occur and
why?
39)
Explain the following terms in brief:
a) Ischemia b) Infarction c) Stroke
d) Aneurysm
Embolus/Embolism
40)
e) Atherosclerosis
f)
What are the different factors leading to the rupture of fusiform aneurysm?
41) Explain the forces acting on the arterial walls of saccular aneurysm in a branched artery.
Derive the equation for pressure acting on such an arterial wall.
42)
An artery with a 2 mm radius is partially blocked with plaque; in the constricted
region the effective radius is 1.5 mm. & the average blood velocity is 50 cm/sec.
a) What is the average velocity of the blood in the unconstricted region?
b) Would there be turbulent flow in either region?
c) For the blood in the constricted region, find the equivalent pressure due to kinetic
energy of the blood.
43)
How can blood be moving more slowly in a capillary than in the aorta? Because for
an incompressible fluid, when the cross-sectional area along a pipe decreases, the velocity
increases, so that the volume flow rate Q is the same. The capillary has a much smaller
cross-sectional area than the aorta. Therefore, the blood should move faster in the
capillary than in the aorta!
44)
Estimate the Reynolds number for the following flows. In each case, determine
whether the Reynolds number is high (>>1) or low (<< 1).
(a) E. coli bacteria (length 2 microns) swim in water at speeds of about 0.01 mm s−1.
(b) An Olympic swimmer (length 2 m) swims in water at speeds of up to 2 m s−1.
(c) A bald eagle (wingspan = 2 m) flies in air (density = 1.2 kg m−3, viscosity = 1.8 × 10−5 Pa s)
at speeds of 20 km hr−1
Unit III
Electrical Properties of Body
1) Describe electrical signals from heart.
2) What are the advantages of myelinated nerves over unmylinated nerves?
3) Describe all the mechanisms that help in developing the resting potential in a neuron.
4) Describe how direction is sensed in the ear and that helps in maintaining the stability of a
person.
5) Estimate the electrical resistance of the blood in a 50-cm long, 3-mm diameter artery.
6) During an accident, 120V AC from a wall socket connects your body to electrical ground,
from hand to hand:
(a) If the resistance across the body is 500 ohms, what is the current flow?
(b) Is this dangerous?
(c) If the region from hand to hand can be modeled as a cylinder of constant diameter
(equal to the diameter of the upper arm) and length (from finger tip to finger tip) of
your own body, and all material is assumed to be uniform, estimate the electrical
resistivity of the body tissue.
(d) How much power is dissipated in this section? (Calculate both the total power and the
power per unit volume.) (Remember that the power dissipated is P = IV and Ohm’s Law
is V = IR. Assume here and below that the power is the same as that for a DC voltage
source.)
7) Suppose that an action potential in a 1 μm diameter unmyelinated fiber has a speed of
1.3ms−1. Estimate how long it takes a signal to propagate from the brain to a finger.
Repeat the calculation for a 10 μm diameter myelinated axon that has a conduction speed
of 85ms−1. Speculate on the significance of these results for playing the piano.
8) The median nerve in your arm has a diameter of about 3mm. If the nerve consists only of
1 μm diameter unmyelinated axons, how many axons are in the nerve? (Ignore the volume
occupied by extracellular space.) Repeat the calculation for 20 μm outer diameter
myelinated axons. Repeat the calculation for 0.5mm diameter unmyelinated axons (about
the size of a squid axon). Speculate on why higher animals have myelinated axons instead
of larger unmyelinated axons.
9) The resistivity of the fluid within an axon is 0.5 Ω m. Calculate the resistance along an
axon 5 mm long with a radius of 5 μm. Repeat for a radius of 500 μm.
Unit IV
Physics of Sound and Senses
Calculate the wavelength in air for the lowest audible frequency (20 Hz for most people) and
the highest audible frequency (20 kHz for most young people).
The area of a typical eardrum is about 5.0 x 10-5 m2. Calculate the sound power (the energy per
second) incident on an eardrum at (a) the threshold of hearing and (b) the threshold of pain.
Threshold of hearing: I = 10-12 W/m2; Threshold of pain: I = 1 W/m2
Sound with intensity 60 dB in air is incident on water. How much of it is transmitted into the
water (in W/m2)?
What is the change in dB if the intensity of a sound wave is:
(a) halved
(b) doubled (c) tripled
(d) quadrupled?
Which sound is more intense 20m from its isotropic source: a 10 Hz sound that is 80 dB SPL a
distance 4m from its source or a 4,000 Hz sound that is 60 dB SPL a distance 3m from its
source?
(a) At what distance from an isotropic 10 μW acoustic source is the sound at the audibility
threshold for a human?
(b) The hearing threshold for dogs is 1 × 10−15 W/m2. At what distance can a dog hear this
source?
Show that when sound goes from a transducer with Ztransducer = 30 × 106 Pa s m−1 to tissue
with Ztissue = 1.5 × 103 Pa s m−1, the transmission coefficient is T = 2× 10−4.
If the intensity of a sound wave falls to half its original value, what is the change in dB?
Show that the intensity of a sound wave, can be written as
, as
or as
A sound wave with intensity of 1 × 10−12 W m−2 is the threshold for hearing. Convert that to a
pressure amplitude P. Convert the pressure amplitude to a displacement amplitude, with f = 1
kHz, κair = 10−5 Pa−1, and cair = 344 m s−1. Compare your result with the size of an atom, which is
on the order of 0.1 nm. Surprised?
The threshold for audible sound is 10−12 W m−2. convert this to the amplitude of the pressure
oscillation in air, using Zair = 400 Pa s m−1. Compare this to 105 Pa (atmospheric pressure), and to
5×10−6 Pa (which is on the order of the amplitude of random pressure variations in the air due to
thermal motion). Are the pressure oscillations small? Perform the same analysis for the
threshold for pain, I = 10−4 W m−2.
Assume the attenuation is proportional to frequency, and is given by 100 dB m−1 MHz−1. If you
use a 5MHz ultrasound wave to image a surface 30 mm below the surface of the skin, the
measured echo is what fraction of the original intensity? Ignore impedance differences at the
surface of the skin and assume that 100% of the wave is reflected by the surface, so that the
reduction of the echo intensity is caused entirely by attenuation. Remember that you must
consider the round-trip distance traveled by the wave. Express your answer in decibels.
Assume there is a fat-muscle boundary 50 mm below the tissue surface. Calculate the intensity
of the reflected wave, ignoring attenuation. Now, assume there is a bone that lies in the region
from 20 to 30 mm below the surface, with the fat-muscle boundary still 50 mm below the
surface. Calculate the intensity of the wave reflected from the fat-muscle boundary,
accounting for the front and back bone surfaces, ignoring attenuation. If the minimum
measurable intensity is −25 dB, will the fat-muscle boundary be observable in each case? In
general, surfaces behind a bone do not appear in ultrasound images. The bone casts an acoustic
shadow.
A person is nearsighted, and the relaxed eye focuses at a distance of 50 cm. What is the
strength of the desired corrective lens in diopters?
What is the distance of closest vision for an average person with normal vision at age 20? Age
40? Age 60?
A person of age 40 is fitted with bifocals with a +1 diopter strength bifocal lens. What are the
closest and farthest distances of focus without the bifocal lens and with it? By the time the
person is age 50, what are they with and without the same lens?
Find the prescription in diopters (D) to correct the eyesight for:
(a) A myopic person with a far point of 2m (using contact lenses).
(b) A hyperopic person with a near point of 1m who wants to read material 25 cm away and who
has very good crystalline lens accommodation (using eyeglasses).
(c) A person with perfect vision for far points who, because of poor accommodation
(presbyopia), has a near point of 1 m, and who wants to read material 25 cm away (using
eyeglasses).
(d) How do the people in parts (b) and (c) differ? (Could they both use their eyeglasses while
attending a baseball game and working at a computer terminal?)
(e) What is the accommodation of the person in part (c) (assuming a standard 17mm long eyeball
for the Standard eye model, with air replacing the humors)?
(f) If the near point for the person in part (a) is 15 cm without contact lenses, what is it when
the prescribed contact lenses are worn?
1. The light from a red laser pointer has a wavelength near 650 nm. Where in the eye is
most of this wavelength absorbed?
2. How well is the transmission spectrum of the eye matched to the spectral responses of
rods and cones?
3. How well are the spectral responses of the rods and cones matched to the spectrum of
solar light? How well are they matched to the spectrum of solar light that actually
reaches sea level?
4. How small would the pupil diameter need to be to affect the ultimate diffraction limit of
the eye lensing system? Given the sizes of cones, would this change make a practical
difference?
5. (a) Assume for the moment that the rods and cones are 0.1 μm in diameter, that they are
tightly packed (with no space between them), and that each is individually connected to
the brain by a single neuron. Ignoring optical aberrations, would you see images sharper in
the blue or the red? Why?
(b) Ignore the assumptions in part (a), returning to the normal conditions, and address
the same questions again.
6. A person with myopia has a far point 60 cm from her eye. What corrective eyeglasses and
contact lenses should she wear? (Give your answer in D.)
7. A person with hyperopia has a near point 500 cm from his eye. What corrective
eyeglasses and contact lenses should he wear? (Give your answer in D.)