**Physics 4C--Exam 1 Sample Problems**

In a hurricane, the air (density = 1.29 kg/m^{3})is blowing over
the roof of a house at a speed of 120 km/hr. If the roof area is 110 m^{2},
what is the lifting force on the roof?

A 6 kg mass is suspended by a string so that it it submerged beneath a liquid of unknown density. The tension in the string is measured to be 45 N. Find the ratio of the liquid density to the density of the submerged mass.

The amplitude of a 400 hz travelling wave on a string is 0.003 m. By what percentage would the power carried by the wave change if the amplitude is increased by 12 percent and the frequency decreased by 8 percent?

A certain sound wave has a measured intensity of 40 dB at a distance of 125 m from the point source where the waves originated. At what distance from the source would the intensity be increased to 70 dB?

A steel rod of length 1.44 m is clamped at a point 1/4 of its length from one end. The ends of the rod are free to vibrate. If the velocity of longitudianl wave in steel is 5000 m/s, find the frequency of the first three allowed harmonics. Make diagrams to show the three standing waves.

Two speakers are mounted on a wall in an auditorium. One is at floor level and the other is 3 m directly above the first. The speakers emit sound waves in phase at a frequency of 686 Hz. A line is drawn on the floor, perpendicular to the wall beginning at the lower speaker and extending out into the room.

a. What is the greatest distance from the lower speaker along this line where there will be a minimum in the sound intesity?

b. How many minimas altogether will there be along this line? Explain.

**Physics 4C--Exam 2 Sample Problems**

One mole of an ideal monatomic gas, initially at a volume of 0.05 m^{3}and
a pressure of 1.0 x 10^{5} Pa, is taken through a reversible cycle
that consist of three processes:

a-->b: An isobaric compression that decreases the volume from 0.05 m^{3} to 0.01 m^{3}

b-->c: An isochoric process where the pressure goes from 1.0 x 10^{5} Pa to 5.0 x 10^{5} Pa

c-->a: An isothermal expansion that returns the system to its original state

a. Show the cycle on a PV diagram, labeling all three processes. Be sure to label the axes with appropriate scales, units, etc.

b. Find the net work done by the gas per cycle.

c. Find the heat added to the gas per cycle.

d. Find the heat expelled by the gas per cycle.

e. Find the efficiency of the cycle.

The specific heat of many solids is proportional to T^{3} at very low temperature. A certain 15 g sample has a specific heat given by

C = aT^{3}

where a = 2.5 x 10^{-5} J/kg-K^{4}.

a. Find the heat needed to warm the sample from 10 K to 35 K.

b. Find the change in entropy of the sample during the warming process.
Two rods with the same diameter are connected with their ends together. One of the rods is three times as long as the other. The longer rod has a thermal conductivity that is four times that of the shorter rod. The longer rod has its free end held at a constant temperature of 100^{o}C while the shorter rod has its free end held at a constant temperature of 0^{o}C.

a. Find the temperature at the boundary between the two rods.

b. If the cross sectional area of the rods is 3 cm^{2}, the length of the short rod is 50 cm, and the thermal conductivity of the short rod is 385 W/m-K, how long would it take to melt 3.5 kg of ice connected to the cold end of the shorter rod.

A certain gas is at a temperature of 27^{o}C. What would the temperature
of the gas have to be to increase the rms speed of the molecules in the
gas by 12 percent?

**Physics 4C--Exam 3 Sample Problems**

Two thin lenses are separated by 12 cm. The lens on the left has a focal
length of -10 cm and the one on the right has a focal length of +30 cm.
An object is placed 15 cm to the left of the -10 cm focal length lens.

a. Make a careful ray diagram and locate (approximately) the final image
formed.

b. Calculate the location of the final image. Is it real or virtual?

c. Find the magnification of the system.

A circular fringe pattern is set up using a Michelson interferometer with light of wavelength 580 nm. A thin sheet of transparent plastic 2.5 x 10^{-6}m thick is placed in front of one of the mirrors perpendicualr to the light rays. An oberver counts a shift of six fringes while the sheet is inserted. What is the index of refraction of the sheet?

a. Explain what is meant by the Rayleigh criterion.

b. If the pupil of your eye is dilated to a diameter of 5 mm, what is the minimum distance between two point sources that your eye can distinguish at a distance of 40 m from the eye?

A cylindrical coffee can is 17 cm in diameter. When an observer's eye is place above and to the side of the can, she can just see the far edge of the bottom of the can. When the can is filled with water, she (with her eye at the same position) can now see a spot at the center of the bottom of the can. Find the height of the can.

Two sources of electromagnetic waves are in phase and located one above the
other along the y-axis. S_{2} is placed at the origin and S_{1}
is a distance of three wavelengths away in the positive y direction. The
sources have equal intensities, I_{o}, when they arrive at a point
P on the x-axis. Point P is five wavelengths away from the origin.

a. Find the phase difference between the two waves when they arrive at
P.

b. Find the intensity of the resultant wave at P. Hint: Make a phasor
diagram and find the resultant wave amplitude graphically. Note that point
P is not a "distant" point in this problem.

A mu meson (mass = 1.89 x 10-28 kg) is moving at v = 0.97 c with respect to the earth.
a. Calculate the kinetic energy of the mu meson. Find the percent error that would occur if you instead used the classical calculation for the kinetic energy.
If the half life of the mu meson is 2.2 ms, how far will it travel on average, before decaying, as determined by an earth based observer?

Superman is playing baseball and hits a home run. His bat is moving forward at 0.6 c as the ball leaves the bat. If the ball is moving forward at 0.8 c with
respect to the bat, how long (on an earth based clock) does it take for the baseball to cover the 20 m between home plate and the pitcher’s mound? (Treat
the motion as one dimensional)

The Bohr model predicts that the allowed energy levels for the electron in a hydrogen atom are given by
En = -13.6 ev/n2 , n = 1,2,3…
Calculate the longest and the shortest wavelengths (two answers) for photons that can be emitted by a hydrogen atom for an electron transition ending on the n = 2 level. Show these transitions on an energy level diagram.

Electrons are ejected from a metallic surface with speeds ranging up to 4.8 x 105 m/s when light with a vavelength of 580 nm is incident on the surface.
a. What is the work function of this metal?
b. What is the cutoff (threshold) wavelength?

A proton is moving at v = .96 c with respect to the earth.
a. Calculate the kinetic energy of the proton. Find the percent error that would occur if you instead used the classical calculation for the kinetic energy.
b. If an observer were riding along with the proton, how long would it take the proton to travel from the earth to the sun (1.49 x 108 km) on the observer's clock?

You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line away from the Earth for 6 months and then returning home at the same constant speed. You wish , on your return, to find Earth as it will be 1000 years in the future.
a. How fast, relative to Earth, must you travel?
b. If you and your space craft have a rest mass of 10,000 kg, how much kinetic energy would the spaceship need to travel at the speed found in part a?
c. Considering the fact that the annual US consumption of energy is about 1017 J, comment on the feasibility of accomplishing such a trip.

What is the DeBroglie wavelength for an electron whose kinetic energy is 8 ev?

The average threshold of vision (weakest light detectable by the human eye) is 4.0 x 10-11 W/m2 at a wavelength of 550 nm. If light having this intensity and wavelength
enters the eye and the pupil is open to its maximum diameter of 8.5 mm, how may photons per second enter the eye?