THE FLINDERS UNIVERSITY OF SOUTH AUSTRALIA
November Examinations 1999

PHYS 1202 Introduction to Physics B
PHYS 1203 Physics for the Life Sciences

Time Allowed: 3 hours
Materials allowed in exam room: Calculators (with non-alpha-numeric display)
This examination contributes 60% to the final grade for the topic.
All questions carry equal marks.
Candidates should attempt ALL questions.

Question 1 Diffusion

(a)

Define the term diffusion, and use it in a description of how a `puff' of scent released by a female moth can reach potential mates, even in still air.

(b)

Use Fick's Law to estimate the rate at which water diffuses through the skin, based on the following assumptions:

• There is pure water inside the skin, and zero concentration of water outside.
• 1 m³ of pure water has a mass of 1000 kg.
• The skin area of an average person is about 1.75 m².
• The skin is a uniform layer about 20 $\mu$m thick. (1 $\mu$m = 1×10^-6 m)
• The diffusion coefficient for water in skin is 5.0×10^-14 m²/s

(c)

Express your answer to (b) in litres per day. Does your result seem reasonable?

[10 marks]

Question 2 Fluids

(a)

State, in words and in symbols, the Continuity Equation.

(b)

As blood leaves the heart, it first flows through the aorta, which branches into smaller arteries, which in turn branch into very small capillaries. If the speed of blood in the aorta is 40 cm/s, and its radius is 1.2 cm, find:

(i)

The flow rate Q of blood through the aorta, and

(ii)

The speed of the blood in the capillaries, if their total cross-sectional area is 3500 cm².

(c)

Bernoulli's principle cannot be used to accurately describe blood flow in smaller arteries and capillaries. State the conditions under which Bernoulli's Principle applies, and suggest reasons why it isn't applicable in this case.

[10 marks]

Question 3 Thermal Physics

(a)

A nude person sits still on a chair in a cool room. Briefly discuss the processes of conduction, convection and radiation as they apply to the person. In each case, make clear whether heat energy is transferred to or from the person.

(b)

Explain the term basal metabolic rate, and relate it to the situation described in (a).

(c)

If the person has 1.5 m² of skin at a temperature of 33 ^oC, and the room temperature is 21 ^oC, find the net rate of heat loss due to radiation. Take the emissivity of the skin to be 0.95. Compare your result with a typical basal metabolic rate of about 80 W. Comment.

[10 marks]

Question 4 Sound

(a)

Explain how the intensity of a sound wave generated from a point source changes with distance from the source.

(b)

The world's loudest insect is the African cicada Brevisana brevis (Homoptera: Cicadidae) which produces a calling song with a mean intensity of I = 0.050 W/m² at a distance of 0.50 m. Assume that the sound is emitted equally in all directions.

(i)

What is the sound level intensity $\beta$ (measured in dB) from one cicada at a distance of 0.50 m?

(ii)

Approximately how many cicadas located at a distance of 0.50 m would produce a sound level at the threshold of pain (120 dB)? Explain your reasoning.

(iii)

Assuming no absorption of the sound, at what distance would the sound of one cicada be barely audible?

[10 marks]

Question 5 Optics

(a)

Explain what is meant by a light ``ray''. Under what conditions is the ray model for light valid?

(b)

By drawing both wavefronts and rays, explain why light refracts as it passes across an interface between materials of different refractive index

(c)

Light travelling in air (n = 1.00) encounters an interface with water (n = 1.33). For what range of angles (from the normal) will the light enter into the water? Repeat for light beginning in the water.

(d)

A fish is underwater at the centre of a circular pond. Explain what it sees as it looks upwards towards the water surface at various angles. Could the fish see a small rock located at the water's edge? If so, where would it see it? Illustrate your answer with appropriate ray diagrams.

[10 marks]

Question 6 Radioactivity

(a)

Briefly describe alpha particle ($\alpha$) decay and beta particle ($\beta$) decay. Use as examples the first two decays in the ²³⁸U decay chain: the $\alpha$ decay from uranium (which has 92 protons) to thorium (Th), and the $\beta$ decay from thorium to protactinium (Pa).

(b)

Find the activity, in Bq, of uranium in a rock sample that contains 23.8 g of ²³⁸U. (²³⁸U has a half life of 4.5×10⁹ years.)

(c)

The air in a room contains a small amount of radon gas that has been produced from uranium decay in the surrounding rocks. Explain what happens when radon decays, and why radon in air can be a health hazard.

[10 marks]

Useful Equations

Diffusion
Fick's Law	$${\frac{\Delta M}{\Delta t}}$$ = DA $${\frac{C_2 - C_1}{L}}$$
Characteristic Diffusion Length	l = $\sqrt{4 Dt}$
Fluids
Continuity Equation	A1v1 = A2v2
Bernoulli's Equation	P + ${\frac{1}{2}}$$\rho$v2 + $\rho$gy = const.
Surface Tension	$\gamma$ = F/L
Thermal Physics
Linear Expansion	$\Delta$L = $\alpha$L0$\Delta$T
Volume Expansion	$\Delta$V = $\beta$V0$\Delta$T
Ideal Gas	PV = nRT = NkT
Specific Heat	C = $${\frac{Q}{m \Delta T}}$$
Heat Conduction	H = $${\frac{Q}{\Delta t}}$$ = kA $${\frac{T_H - T_C}{L}}$$
Stefan's Law	P = $\sigma$AeT4 , $\sigma$ = 5.67×10-8 W/m2 . K4
Waves and Sound
Pendulum	f = $${\frac{1}{2\pi}}$$ $$\sqrt{\frac{g}{L}}$$
Speed of Wave on String	v = $$\sqrt{\frac{F}{\mu}}$$, F =  tension
Speed of Sound Wave	v = $$\sqrt{\frac{B}{\rho}}$$
where B = Bulk modulus defined as	B = - $${\frac{\Delta p}{\Delta V/V_0}}$$
Sound Intensity Level	$$\beta$$ = 10 log $${\frac{I}{I_0}}$$     dB, I0 = 1×10-12 W/m2

Optics
Refractive Index	n = $${\frac{c}{v}}$$
Snell's Law	n1sin$\theta_{1}^{}$ = n2sin$\theta_{2}^{}$
Critical Angle	$$\theta_{c}^{}$$  = sin-1$$\left(\vphantom{\frac{n_2}{n_1}}\right.$$$${\frac{n_2}{n_1}}$$$$\left.\vphantom{\frac{n_2}{n_1}}\right)$$
Thin Lens Equation	$${\frac{1}{p}}$$ + $${\frac{1}{q}}$$  = $${\frac{1}{f}}$$
Lateral Magnification	M  = $${\frac{h'}{h}}$$  = - $${\frac{q}{p}}$$
Magnification of Microscope	M  $$\simeq$$ - $${\frac{L}{f_o}}$$$$\left(\vphantom{\frac{25 {\rm cm}}{f_e}}\right.$$$${\frac{25 {\rm cm}}{f_e}}$$$$\left.\vphantom{\frac{25 {\rm cm}}{f_e}}\right)$$
Atoms and Radioactivity
Energy of a Photon	E = hf
Exponential Decay	N = N0e- $\lambda$t
Decay Constant	$$\lambda$$ = $${\frac{0.693}{T_{1/2}}}$$
Activity	A = $$\lambda$$N
Physical Constants
Avogadro's Number	NA = 6.022×1023 mol-1
Speed of Light in Vacuum	c = 3.00×108 m/s
Speed of Sound in Air at 1 atm	v = 343 m/s
Universal Gas Constant	R = 8.31 J/mol . K
Boltzmann's Constant	k = 1.38×10-23 J/K
Mass of Electron	me = 9.11×10-31 kg
Mass of Proton	mp = 1.67×10-27 kg
Gravitational Acceleration	g = 9.8 m/s2
Atmospheric Pressure	P0 = 101, 300 Pa