Question 1

A 10 cm long straw is used to draw water straight up from a cup. What gauge pressure must you generate in your mouth to make this happen? Assume water has a density of 1000 kg/m³ and $$g = 9.8\ 	ext{m/s}^2.$$

Accepted Answer

$$-980\ 	ext{N/m}^2$$

Question 2

A spherical helium balloon has a radius of 1 m at standard temperature (0°C) and pressure (1 atm = $$1.013 	imes 10^5$\ 	ext{N/m}^2). $$How many moles of helium are in the balloon and what is the buoyant force? Assume air density is $$1.29\ 	ext{kg/m}^3$$ and $$R = 8.3\ 	ext{J/(mol\cdot K)}.$$

Accepted Answer

190 mol, 53 N

Question 3

For one mole of monoatomic ideal gas undergoing isobaric, isothermal, and adiabatic expansion (each from $$(P_1$, V_1$) to$$ $$(P_2$, 3V_1)$$), how does the heat transferred compare? Assume $$C_V = \frac{3R}{2}$$ and $$C_P = \frac{5R}{2}.$$

Accepted Answer

$$Q_{IT} \u003e Q_{IB} \u003e Q_A$$

Question 4

For the same gas expansion processes, rank the work done by the gas: isobaric ($$W_{IB}$$), isothermal ($$W_{IT}$$), and adiabatic ($$W_A).$$

Accepted Answer

$$W_{IT} \u003e W_{IB} \u003e W_A$$

Question 5

For a Maxwell distribution of speeds in 2D, $$f(v) = \frac{Nmv}{kT} e$$^{-\frac{mv^2}$${2kT}}$$, what is the most probable speed?

Accepted Answer

$$\sqrt{2kT/m}$$

Question 6

Two loudspeakers are placed at $$(0,0)$$ and $$(0,d)$$, emitting sound waves of wavelength $$\lambda in $$phase. At what positions along the x-axis will there be constructive interference?

Accepted Answer

Question 7

For the same gas expansion processes, rank the change in entropy: isobaric ($$\Delta S_{IB}$$), isothermal ($$\Delta S_{IT}$$), and adiabatic ($$\Delta S_A).$$

Accepted Answer

$$\Delta S_{IT} \u003e \Delta S_{IB} \u003e \Delta S_A$$

Question 8

Why are the minima in the single slit diffraction pattern evenly spaced while the maxima are not?

Accepted Answer

Minima are determined by the zeros of the sine function, which are evenly spaced, while maxima are found by solving for the derivative, which is not evenly spaced.

Question 9

If you are playing underwater laser tag, what is the maximum angle you can point your laser (with respect to the bottom of the pool) so that no light escapes? Water's index is 1.33, air's is 1.0.

Accepted Answer

41°

Question 10

A contact lens designer must create a lens with power $$-5.00$$ diopter. The lens material has index $$n = 1.50$$ and the eyeball's radius of curvature is $$1.30 cm. If $$the side touching the eye must have radius $$1.30 cm$$, what must the radius of curvature of the air side be?

Accepted Answer

-1.49 cm

Question 11

An image of Venus appears inverted and magnified 87x by a telescope with a spherical reflecting mirror and an eyepiece of focal length 3 cm. What are the focal length and radius of curvature of the main mirror?

Accepted Answer

26.1 m, 52.2 m

Question 12

Spaceship A is coming toward Earth at $$0.4c$$ and Spaceship B at $$0.6c ($$both relative to Earth). What is the velocity of A as measured by B?

Accepted Answer

$$-0.83c$$

Question 13

What is the diameter of the Earth as measured by observers on Spaceship A, given Earth's diameter is $$1.3 	imes 10^7$ m in its rest frame and A moves at 0.4c$?

Accepted Answer

$$1.19 	imes 10^7$ m

Question 14

What is the energy and momentum of a 100 kg astronaut on Spaceship A as measured by an astronaut on Spaceship B? (Use $$v_{AB}$$ from previous question and $$c.)$$

Accepted Answer

$$E = \gamma m c^2$, p$$ = \gamma m v_{AB}$$

Question 15

Evaluate $$E^2$$ - $$p^2$$ $$c^2$$ for the 100 kg astronaut aboard Spaceship A in each spaceship frame and show that this quantity is invariant.

Accepted Answer

$$E^2$$ - $$p^2$$ $$c^2$$ = $$m^2$$ $$c^4$$

Question 16

If an astronaut on Spaceship A shines a red laser pointer ($$\lambda = 600 nm) $$toward Spaceship B, what wavelength will the astronaut on B measure? What will be the speed of the laser light as measured by B?

Accepted Answer

The wavelength will be shorter due to the relativistic Doppler effect; the speed will be $$c.$$

PHY222 Final Exam Study Guidance

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