PHYS 402 Bossier Parish Community College Unit Breakdowns and Conversions Problems this is hw 4, be sure they aren’t right due on 12pm July

PHYS 402 Bossier Parish Community College Unit Breakdowns and Conversions Problems this is hw 4,

be sure they aren’t right

due on 12pm July 25,

.thanks for your help!

Boston time.

Thanks! Homework 4
PHYS 402 Sec 01
Summer 2020
Thursday, July 23, 2020
Due Date/Time: Saturday, 25 July, 2020 at 12:00PM (Noon)
This is to be completed and submitted individually; collaboration is NOT allowed. Show all of your work – and be
detailed about it! My primary concern is that you can show that you understand the material. The only way I can see
what you are thinking is for you to write it down. So, write down your thoughts – especially if you are stuck.
Feel free to use Desmos (https://www.desmos.com/calculator (Links to an external site.)) to aid in problem solving, if you
find it to be a helpful tool.
Note: Any and all requested sketches should be hand drawn!
If you have questions about the exam please email both the instructor (Matt: mkr2007@wildcats.unh.edu)
and learning assistant (Devony: dnw1002@wildcats.unh.edu) so that we can address your question as
quickly as possible!
Universal Constants
• Avogadro’s Number: NA = 6.022 × 1023 molecules/mol
• Boltzmann’s Constant: kB = 1.38 × 10?23 J/K
• Universal Gas Constant: R = NA kB = 8.31 J/(mol K)
• Stefan-Boltzmann Constant: ? = 5.67 × 10?8 J/(s m2 K 4 )
• Threshold of Human Hearing: I0 = 1.00 × 10?12 W/m2
• Fundamental Charge: e = 1.6 × 10?19 C
• Permittivity of Free Space: 0 = 8.85 × 10?12 (C 2 · s2 )/(kg · m3 )
• Coulomb’s Constant: k =
1
4?0
= 8.99 × 109 (kg · m3 )/(s2 · C 2 )
• Speed of Light in a Vacuum: c = 3.00 × 108 m/s
Unit Breakdowns and Conversions
Base Units: mass in kilograms (kg), length in meters (m), time in seconds (s), charge in Coulombs (C).
Newton: 1 N = 1
kg·m
s2
N
m2
=1
Pascal: 1 P a = 1
Joule: 1 J = 1 N · m = 1
Watt: 1 W = 1
J
s
Volt: 1 V = 1
J
C
Farad: 1 F = 1
Ohm: 1 ? = 1
V
A
C
s
=1
C
V
kg·m2
s2
kg·m2
s3
=1
Ampere: 1 A = 1
kg
m·s2
kg·m2
C·s2
=1
=1
C 2 ·s2
kg·m2
kg·m2
s·C 2
Electron Volt to Joule: 1 eV = 1.6 × 10?19 J
Volt from Electron Volt: 1 V = 1
eV
e
Useful Tables
Problem 1.
A large bedroom contains about 1 × 1027 molecules of air. Suppose the temperature in the room is initially
measured to be 20o C.
(a.) Treating the air in the room as an ideal gas, estimate the energy required to raise the temperature of the
air in the room by 5o C (from 20o C to 25o C).
(b.) When the room temperature is 30o C, there is some average kinetic energy associated with the gas
molecules. What is the speed of an air molecule with that average kinetic energy? Note that the average molar mass of air is 28.97 g/mol = 0.02897 kg/mol.
Problem 2.
(a.) A pure metal ingot of mass 25kg is heated from room temperature (20 o C) to 100 o C by the addition of
4.7 × 105 J of energy. Calculate its specific heat and, using the given table of Specific Heats of Various
Substances, identify the substance of which it is composed.
(b.) How much additional heat is required to change this solid metal ingot at 100 o C into liquid metal at the
melting point? (Consult the given Heats of Fusion and Vaporization table for the melting point and latent
heat of fusion of the substance you identified in part (a.))
Problem 3. A spider spins a web with silk threads of mass density µ = 9.18 × 10?9 kg/m. A typical tension
in the long radial threads of such a web is 0.007 N . Suppose a fly hits the web, sending a wave pulse down a
radial thread toward a spider sitting 0.5 m away from the point of impact. Which will reach the spider first:
the very slight sound of the impact or the disturbance traveling along the radial thread of the web? Assume
the air temperature is 20 o C.
Problem 4.
Sound is detected by the human ear when a sound wave causes the eardrum to vibrate, as described in the
figure below:
The eardrum lies at the end of the ear canal and transmits vibrations to sensory organs in your ear. Typically,
in adults humans, the ear canal is about 2.5 cm = 0.025 m in length and the diameter of the eardrum is about
8.4 mm = 0.0084 m. When someone speaks to you in a normal tone of voice, the sound intensity at your ear
is approximately 1.0 × 10?6 W/m2 .
(a.) What is the sound intensity level (in dB) of a normal conversation?
(b.) How much energy is delivered to your eardrum each second during normal conversation? Assume the area
2
A of the eardrum of diameter d is A = ?d4
(c.) Assume the temperature inside the ear canal is 98.6o F = 37o C. At what frequencies in the audible range
(20 Hz ? 20000 Hz) will an adult human have increased hearing sensitivity? (In other words, what
frequency standing waves can occur within the ear canal that are within the audible range?) Model the
ear canal as an open-closed tube.
Problem 5.
A 0.6 m guitar string under a tension of 50 N has a mass per unit length of 0.01 kg/m.
(a.) The figure below shows one of the standing wave modes of this string. What is the frequency of this
standing wave?
(b.) What is the fundamental frequency of this guitar string
(i.) under the given tension?
(ii.) if the tension is halved?
(c.) What is the highest resonant frequency that can be heard by a person capable of hearing frequencies
between 20 Hz and 20, 000 Hz when
(i.) under the given tension?
(ii.) if the tension is halved?
Problem 6.
In the figure below, charge q2 experiences no net electric force.
(a.) What is q1 ? (Note: 10 cm = 0.1 m and ?2 nC = ?2 × 10?9 C.)
(b.) What is the strength of the electric field 0.2 m from the charge q1 ?
(c.) What is the electric potential due to the point charge q1 at a distance 0.5 m away from the charge?
Problem 7.
Human nerve cells are surrounded by a cell membrane (or cell wall), an insulating layer of lipids that separates
regions of conducting fluid inside and outside the cell. Embedded in these cell walls are ion exchange pumps
which act much like the charge escalator of a battery, using chemical energy to separate charge by transporting
ions. The transport and subsequent diffusion of charged ions lead to a separation in charge across the cell
membrane. Consequently, a living cell generates an emf.
The potential inside a nerve cell is typically 70 mV less than that outside the cell. (This is called the cell’s
resting potential.) Therefore, a potential difference of ?V = 70 mV = 0.07 V exists between the inside and the
outside of the cell, as shown below:
(a.) The thickness of a typical nerve cell membrane is approximately 7 nm = 7 × 10?9 m. What is the electric
field inside the membrane (due to the resting potential difference) of a resting nerve cell?
(b.) Charges can move across the cell membrane, so it is not a perfect insulator; the cell membrane will
have a certain resistance. Suppose the resistivity of the cell membrane is measured to be approximately
3.6 × 107 ? · m. What is the resistance of the 7.0-nm-thick membrane of a spherical cell with diameter
5 × 10?5 m?
Note: Recall that the surface-area of a sphere is given by A = 4?r2 , where r is the radius of the sphere.
Problem 8.
Consider the following circuit diagram:
Note that SW1 denotes a switch.
(a.) Find the equivalent resistance for the collection of resistors in this circuit.
Note: Since I did not give you explicit values for the resistors, your result will be algebraic rather than
numerical.
(b.) Find the equivalent capacitance for the collection of resistors in this circuit.
Note: Since I did not give you explicit values for the capacitors, your result will be algebraic rather than
numerical.
(c.) Re-draw this circuit by replacing all the resistors with the equivalent resistance found in part (a.) and
replacing all the capacitors with an equivalent capacitor. What is the time constant of the resulting RC
Circuit? Your result will again be algebraic rather than numerical.
(d.) Let C1 = C2 = C3 = C4 = 5 µF = 5 × 10?6 F and let R1 = R2 = R3 = R4 = R5 = 100 ?. Then what is
the numerical value for the time constant from part (c.)? (That is, plug these values into your result from
part (c.))
Hint: I know this circuit diagram looks horrifying at first. Take it one step at a time.
Problem 9.
A digital cell phone emits 0.60 W atts of 1.9 GHz = 1.9 × 109 Hz radio waves. (Assume the waves are passing
through air so that their speed is effectively the vacuum speed of light). At a distance of 10 cm = 0.1 m from
the cell phone,
(a.) What is the amplitude of the electric field?
(b.) What is the amplitude of the magnetic field?
(c.) What is the wavelength?
(d.) Considering what you know (intensity, frequency, wavelength), etc. about these EM waves emitted by the
cell phone, do you think the EM waves radiating from your phone are capable of causing bodily harm to
a cell phone user?
Hint: Use the Electromagnetic Spectrum Rules of Thumb we gave in class to argue about how the
frequency, wavelength, energy, etc. of the waves might contribute to this scenario.
Problem 10.
To see a flower better, you hold a 6.0-cm-focal-length magnifying glass (converging lens) 4.0 cm from the flower.
(Note: 1 cm = 0.01 m.)
(a.) Draw a ray-tracing diagram for this scenario to locate the virtual image produced, making sure to follow
the appropriate ray-tracing rules. (Clearly label focal points, object and image distances, object and image
heights.)
(b.) What is the magnification?
Problem 11.
A laser beam is aimed at a 1.0-cm-thick sheet of glass at an angle 30o above the glass. (Note: 1 cm = 0.01 m.)
(a.) What is the laser beam’s direction of travel in the glass?
(b.) What is its direction in the air on the other side of the glass (as the beam exits)?

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