Sorry folks - I had a family emergency come up on the way to class this evening - I tried calling the campus offices, but was redirected to people who could not help me. I hope at least that you were able to work on labs with Mr. Scott.
For Monday, work on posted blog problems and be prepared to learn about voltage, current and resistance. In preparation, please investigate the meanings of these terms. You can also look up series circuits, parallel circuits and combination circuits.
Wednesday's test will cover lenses/mirrors, diffraction and interference and electrostatics (Coulomb's law and electric fields). Do take some time to play with the e-field applets.
See you Monday.
SL
Thursday, July 28, 2011
Problems in Diffraction / Electrostatics
1. Consider a diffraction grating, marked at 100 lines (slits) per mm. A 632nm laser hits it. A screen is 0.75-m away from the grating. Find the following:
a. the distance between slits (in mm)
b. the distance between slits (in m)
c. the diffraction angle for n=1
d. the distance between n=0 and n=1 on the wall (which is 0.75-m away)
e. the highest order (n) that you can get from this grating and laser combination
2. Repeat the above problem for a 450nm laser.
3. Explain superposition of waves.
4. Explain diffraction.
5. Two identical charges are 0.25-m apart. If the force between them is 25-N, what is the magnitude of each charge? Is this force attractive or repulsive? Can you tell the sign of the charges?
6. Consider a 100 uC (10^-6) charge, 0.01-m away from a -300 uC charge. Find the following:
a. the force between them
b. whether or not this force is attractive or repulsive
c. the new force, if the distance is doubled
d. draw the electric field between the charges
In preparation for next class:
7. Define voltage (electric potential), current, resistance and power. Also, give the units for each.
8. What is Ohm's Law?
9. If a 9-V battery is in series with a 25-ohm resistor, what current is drawn from the battery? How much charge "flows" during one minute? What is the power radiated (in heat) by the resistor?
a. the distance between slits (in mm)
b. the distance between slits (in m)
c. the diffraction angle for n=1
d. the distance between n=0 and n=1 on the wall (which is 0.75-m away)
e. the highest order (n) that you can get from this grating and laser combination
2. Repeat the above problem for a 450nm laser.
3. Explain superposition of waves.
4. Explain diffraction.
5. Two identical charges are 0.25-m apart. If the force between them is 25-N, what is the magnitude of each charge? Is this force attractive or repulsive? Can you tell the sign of the charges?
6. Consider a 100 uC (10^-6) charge, 0.01-m away from a -300 uC charge. Find the following:
a. the force between them
b. whether or not this force is attractive or repulsive
c. the new force, if the distance is doubled
d. draw the electric field between the charges
In preparation for next class:
7. Define voltage (electric potential), current, resistance and power. Also, give the units for each.
8. What is Ohm's Law?
9. If a 9-V battery is in series with a 25-ohm resistor, what current is drawn from the battery? How much charge "flows" during one minute? What is the power radiated (in heat) by the resistor?
Wednesday, July 27, 2011
Monday, July 25, 2011
Interference and Diffraction
http://www.falstad.com/ripple/index.html
This is the "ripple tank" applet I showed in class. Play around with 2-source interference and note locations of constructive and destructive interference. This also happens with light waves.
The mathematical relationship:
n lambda = d sin(theta)
n is the "image order number," going from 0 (central image, directly in line with the light source) to n=1 (first order image, the same on either side of the central image), to n=2, etc.
lambda is the wavelength of light
d is the distance of separation between "slits"
theta is the angle of diffraction
This is the "ripple tank" applet I showed in class. Play around with 2-source interference and note locations of constructive and destructive interference. This also happens with light waves.
The mathematical relationship:
n lambda = d sin(theta)
n is the "image order number," going from 0 (central image, directly in line with the light source) to n=1 (first order image, the same on either side of the central image), to n=2, etc.
lambda is the wavelength of light
d is the distance of separation between "slits"
theta is the angle of diffraction
Lens and Mirror problems
1. Compare and contrast convex and concave lenses.
2. Compare and contrast convex and concave mirrors.
3. Consider a lens, f = +12cm, with an object located 20cm in front of it. Find the following:
a. type of lens
b. di
c. type of image (real or virtual)
d. magnification of image
e. whether or not image is upside-down or right-side up
f. Where could you place object so that you get NO image?
g. Where could you place object so that you only get virtual images?
4. Repeat question 3 for a lens with f = -12cm.
5. Repeat question 3 for a mirror with f = +20cm.
6. Give a practical use for a convex lens, concave lens, convex mirror and concave mirror. (One for each.)
7. What is, in general, the effect of covering a lens or mirror in half?
2. Compare and contrast convex and concave mirrors.
3. Consider a lens, f = +12cm, with an object located 20cm in front of it. Find the following:
a. type of lens
b. di
c. type of image (real or virtual)
d. magnification of image
e. whether or not image is upside-down or right-side up
f. Where could you place object so that you get NO image?
g. Where could you place object so that you only get virtual images?
4. Repeat question 3 for a lens with f = -12cm.
5. Repeat question 3 for a mirror with f = +20cm.
6. Give a practical use for a convex lens, concave lens, convex mirror and concave mirror. (One for each.)
7. What is, in general, the effect of covering a lens or mirror in half?
Lens / Mirror Applet
http://www.phys.hawaii.edu/~teb/java/ntnujava/Lens/lens_e.html
Recall:
Lenses:
+f, convex lens (can form both real and virtual images, depending on do)
-f, concave lens (forms ONLY virtual images, since light rays always diverge)
Mirrors
+f, concave mirror (can form both real and virtual images, depending on do)
-f, convex mirror (forms ONLY virtual images, since light rays always diverge)
1/f = 1/di + 1/do
f = (theoretical) focal length
di = image distance (where image forms)
do = object distance (where object is located, relative to lens or mirror)
-di indicates a virtual image
+di indicates a real image
mag = -di/do
-mag indicates upside-down image
+mag indicates right-side up image
If absolute value of mag is > 1, image is larger than object.
If absolute value of mag is < 1, image is smaller than object.
Recall:
Lenses:
+f, convex lens (can form both real and virtual images, depending on do)
-f, concave lens (forms ONLY virtual images, since light rays always diverge)
Mirrors
+f, concave mirror (can form both real and virtual images, depending on do)
-f, convex mirror (forms ONLY virtual images, since light rays always diverge)
1/f = 1/di + 1/do
f = (theoretical) focal length
di = image distance (where image forms)
do = object distance (where object is located, relative to lens or mirror)
-di indicates a virtual image
+di indicates a real image
mag = -di/do
-mag indicates upside-down image
+mag indicates right-side up image
If absolute value of mag is > 1, image is larger than object.
If absolute value of mag is < 1, image is smaller than object.
Tuesday, July 19, 2011
Reflection and Refraction
REFLECTION
You may recall from class the simple, elegant Law of Reflection:
angle of incidence equals angle of reflection.
Think about pool balls hitting the side of a billiards table - angle in equals angle out.
The only tricky part is the way we measure angles - they are measured with respect to a "normal line", a line that is perpendicular to the surface where they hit.
REFRACTION
Refraction refers to a wave changing mediums - going from air to glass, air to water, water to air, glass to air, etc. We first begin by defining a new quantity, the index of refraction (n):
n = c/v
where c is the speed of light and v is the speed of light in the NEW medium. Indices of refraction are always greater than (or approximately equal to) one, and have NO units.
For example, if a substance (say, glass) slows down light to 2/3 of the speed of light (in a vacuum), its index is:
n = c/(2/3 c) = 1.5
A convenient relationship can be derived that relates the angle of incidence and the angle of refraction, along with the indices of refraction of the two mediums. It is called Snell's Law:
n1 sin(theta 1) = n2 sin(theta 2)
As before, the angles are measured with respect to a normal (perpendicular) line. It may be helpful to remember:
- When light goes from a lower density medium (n1) to a higher density medium (n2 > n1), the light ray is refracted TOWARD the normal line. And vice versa.
CRITICAL ANGLE
There is an angle, above which light can not leave the medium. Imagine a light ray trying to go from water into air. Clearly, the light ray will refract AWAY from the normal line. If you gradually increase the angle of incidence (theta 1), eventually the refracted angle (theta 2) will become 90 degrees - light "skating" across the surface.
Any theta 1 greater than this angle will result in "total internal reflection", wherein the light simply cannot leave the substance - it is reflected back inside the original medium. This is the secret of fiber optics. The mathematics come from Snell's Law:
n1 sin(theta 1) = n2 sin(90)
n1 sin(critical angle, ic) = 1 (1)
sin ic = 1/n
That is, the sine of the critical angle equals 1 over the index of refraction for that particular medium (assuming that medium 2 is air, so that n2 = 1).
Got it? Good!
You may recall from class the simple, elegant Law of Reflection:
angle of incidence equals angle of reflection.
Think about pool balls hitting the side of a billiards table - angle in equals angle out.
The only tricky part is the way we measure angles - they are measured with respect to a "normal line", a line that is perpendicular to the surface where they hit.
REFRACTION
Refraction refers to a wave changing mediums - going from air to glass, air to water, water to air, glass to air, etc. We first begin by defining a new quantity, the index of refraction (n):
n = c/v
where c is the speed of light and v is the speed of light in the NEW medium. Indices of refraction are always greater than (or approximately equal to) one, and have NO units.
For example, if a substance (say, glass) slows down light to 2/3 of the speed of light (in a vacuum), its index is:
n = c/(2/3 c) = 1.5
A convenient relationship can be derived that relates the angle of incidence and the angle of refraction, along with the indices of refraction of the two mediums. It is called Snell's Law:
n1 sin(theta 1) = n2 sin(theta 2)
As before, the angles are measured with respect to a normal (perpendicular) line. It may be helpful to remember:
- When light goes from a lower density medium (n1) to a higher density medium (n2 > n1), the light ray is refracted TOWARD the normal line. And vice versa.
CRITICAL ANGLE
There is an angle, above which light can not leave the medium. Imagine a light ray trying to go from water into air. Clearly, the light ray will refract AWAY from the normal line. If you gradually increase the angle of incidence (theta 1), eventually the refracted angle (theta 2) will become 90 degrees - light "skating" across the surface.
Any theta 1 greater than this angle will result in "total internal reflection", wherein the light simply cannot leave the substance - it is reflected back inside the original medium. This is the secret of fiber optics. The mathematics come from Snell's Law:
n1 sin(theta 1) = n2 sin(90)
n1 sin(critical angle, ic) = 1 (1)
sin ic = 1/n
That is, the sine of the critical angle equals 1 over the index of refraction for that particular medium (assuming that medium 2 is air, so that n2 = 1).
Got it? Good!
Waves and Sound notes
Here is a skeleton outline of the notes from the past few classes.
Waves - a periodic disturbance, typically oscillating with sinusoidal behavior. Imagine a simple harmonic oscillator moving through space.
Types of waves (in general):
mechanical - require medium
electromagnetic - do not require a medium, and travel at the speed of light (in a vacuum)
c = 3 x 10^8 m/s
Types of wave (by geometry):
transverse - disturbance is perpendicular to wave speed
longitudinal - disturbance is parallel to wave speed
Wave speed, v = frequency x wavelength
Standing waves on a string:
There are harmonics - "standing" waves which occur at points where the energy maximizes the displacement of the string. A string can typically vibrate at any frequency, but some are dramatically better than others. These frequencies are called harmonics.
wavelength = 2L / n
This is an expression for the wavelength of given harmonic (with harmonic number n)
To find the frequency (or speed), use the wave speed expression above.
For organ pipes open at both ends, the mathematical treatment is very similar. The waves, however, are NOT transverse - they are longitudinal. That is, the sound jiggles back and forth, NOT up and down. However, we can represent the motion of the particles (in terms of particle density inside the tube) as a sine function with anti-nodes on both ends. This gives rise to the pictures we saw in class (and on the applets posted earlier).
If the tube is capped at one end, the wavelengths are given by 4L/n. Furthermore, due to this geometry, the tube can only generate ODD numbered harmonics.
The Doppler Effect
The changed in perceived/detected frequency, due to relative motion between source and observer. See previously posted applets.
f' = f [(v +/- vd) / (v -/+ vs)]
where v is the speed of sound, vd is the speed of the detector, and vs is the speed of the source.
Waves - a periodic disturbance, typically oscillating with sinusoidal behavior. Imagine a simple harmonic oscillator moving through space.
Types of waves (in general):
mechanical - require medium
electromagnetic - do not require a medium, and travel at the speed of light (in a vacuum)
c = 3 x 10^8 m/s
Types of wave (by geometry):
transverse - disturbance is perpendicular to wave speed
longitudinal - disturbance is parallel to wave speed
Wave speed, v = frequency x wavelength
Standing waves on a string:
There are harmonics - "standing" waves which occur at points where the energy maximizes the displacement of the string. A string can typically vibrate at any frequency, but some are dramatically better than others. These frequencies are called harmonics.
wavelength = 2L / n
This is an expression for the wavelength of given harmonic (with harmonic number n)
To find the frequency (or speed), use the wave speed expression above.
For organ pipes open at both ends, the mathematical treatment is very similar. The waves, however, are NOT transverse - they are longitudinal. That is, the sound jiggles back and forth, NOT up and down. However, we can represent the motion of the particles (in terms of particle density inside the tube) as a sine function with anti-nodes on both ends. This gives rise to the pictures we saw in class (and on the applets posted earlier).
If the tube is capped at one end, the wavelengths are given by 4L/n. Furthermore, due to this geometry, the tube can only generate ODD numbered harmonics.
The Doppler Effect
The changed in perceived/detected frequency, due to relative motion between source and observer. See previously posted applets.
f' = f [(v +/- vd) / (v -/+ vs)]
where v is the speed of sound, vd is the speed of the detector, and vs is the speed of the source.
Problems in Snell's Law
1. Define index of refraction.
2. Is it possible for an index of refraction to be less than one? Why or why not?
3. Consider a light beam hitting a block of plexiglas (index = 1.6). It hits at an angle of 25 degrees, with respect to a normal line at the surface. Find the angle of refraction inside the material.
4. A light ray hits the side of an equilateral prism on its left side, striking it at an angle of 30 degrees with respect to a normal line. If it refracts at an angle of 20 degrees inside the prism, what is the index of refraction of the prism? Also, draw an diagram that represents this problem.
5. What is a critical angle of refraction?
2. Is it possible for an index of refraction to be less than one? Why or why not?
3. Consider a light beam hitting a block of plexiglas (index = 1.6). It hits at an angle of 25 degrees, with respect to a normal line at the surface. Find the angle of refraction inside the material.
4. A light ray hits the side of an equilateral prism on its left side, striking it at an angle of 30 degrees with respect to a normal line. If it refracts at an angle of 20 degrees inside the prism, what is the index of refraction of the prism? Also, draw an diagram that represents this problem.
5. What is a critical angle of refraction?
Friday, July 15, 2011
Applets and sites worth your time
A good source for general help.
Organ Pipe
http://www.walter-fendt.de/ph14e/stlwaves.htm
http://www.astro.ubc.ca/~scharein/a311/Sim/doppler/Doppler.html
(Enable "source motion" to make the source move.)
http://www.fisica.uniud.it/~deangeli/applets/Multimedia/Waves_java/Doppler/doppler.htm
http://www.falstad.com/ripple/ex-doppler.html
Waves on a string
Wave addition
http://www.smaphysics.ca/phys30s/waves30s/waveadd1.html
Interference
http://www.walter-fendt.de/ph14e/interference.htm
http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html
Sound and Wave problems
1. Consider a string vibrating on a guitar at 320 Hz (E note). If the string length is 0.6-m, find the following:
a. wavelength of first 3 harmonics
b. frequency of first 3 harmonics
c. speed of first 3 harmonics
2. Now imagine an organ pipe, open on both ends. The speed of sound is 340 m/s. Find the following:
a. length of tube needed to create a resonant frequency of 150 Hz.
b. frequencies and wavelengths of first 3 harmonics
c. wave shapes of first 3 harmonics
d. the effect of capping the tube at one end
3. Most instruments in western music are tuned to a 440 Hz (A) standard. That is, the note middle A is defined as 440 Hz. Find the following frequencies:
a. one octave below
b. two octaves below
c. 1 semi-tone (piano key) above
d. 3 semi-tones above
4. (In advance of next class) Consider a police car, traveling at 35 m/s, with a siren at 1000 Hz. Find the frequencies when the car does the following:
a. approaches you (with you at rest)
b. passes you (with you at rest)
c. approaches you (with you traveling toward the car at 15 m/s)
d. passes you (with you traveling away from the car at 15 m/s)
5. Distinguish between mechanical and electromagnetic waves, giving examples.
6. Distinguish between transverse and longitudinal waves, giving examples.
7. What is the frequency of a 120 x 10^-11 m X-ray?
Tuesday, July 12, 2011
Harmonics on a string
Simple harmonic motion:
http://positron.ps.uci.edu/~dkirkby/music/html/demos/SimpleHarmonicMotion/index.html
Harmonics on a stretched string/spring - "standing waves"
http://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html
Superposition (adding) of waves:
http://www.phy.ntnu.edu.tw/ntnujava/index.php?PHPSESSID=83b90d00c3a8b37a065ec5abe61acb7f&topic=19.msg124#msg124
Adding harmonics with instruments:
http://www13.fisica.ufmg.br/~wag/transf/TEACHING/ONDAS/Library_thinkquest/Harmonics.html
http://positron.ps.uci.edu/~dkirkby/music/html/demos/SimpleHarmonicMotion/index.html
Harmonics on a stretched string/spring - "standing waves"
http://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html
Superposition (adding) of waves:
http://www.phy.ntnu.edu.tw/ntnujava/index.php?PHPSESSID=83b90d00c3a8b37a065ec5abe61acb7f&topic=19.msg124#msg124
Adding harmonics with instruments:
http://www13.fisica.ufmg.br/~wag/transf/TEACHING/ONDAS/Library_thinkquest/Harmonics.html
Thursday, July 7, 2011
Einstein references
- John Norton's "Einstein for Everyone" e-book:
- Supplementary readings:
- J. Schwartz and M. McGuinness, Einstein for Beginners. New York: Pantheon.
- J. P. McEvoy and O. Zarate, Introducing Stephen Hawking. Totem.
- J. P. McEvoy, Introducing Quantum Theory. Totem.
Wednesday, July 6, 2011
Pre-Final Problems
1. Consider a 7-m long pendulum (a Foucault pendulum, typically used to demonstrate the revolution of the Earth). Find its period on Earth, and on the Moon.
2. How long must a pendulum be such that its period is 0.5 seconds?
3. A spring-mass oscillator has a period of 0.8 seconds. What are the first 3 times where the oscillator will have its maximum speed?
4. What is the acceleration due to gravity at a point above the surface of the Earth equal to the radius of the Earth?
5. Mercury orbits the Sun once every 88 days. What is the size of its orbit (semi-major axis) and what is its average speed around the Sun (in km/hr)?
6. What is the angular velocity of a 33 1/3 album? If it takes 0.5 seconds to accelerate up to this speed, what is the angular acceleration and how many turns does it take to get up to this speed?
*7. Two masses (2 kg and 8 kg) are 5-m apart. Where is the center of mass located (as measured from the 2 kg mass)? Hint: consider one distance as x and the other distance as (5-x), then solve for x.
8. A meter stick is set up such that the fulcrum is located at the 25-cm mark. If a 100-g mass is at the 15-cm mark, what is the mass of the meter stick (assuming that it is at the 50-cm mark).
Sunday, July 3, 2011
Practice Problems
Gravitation
1. Consider Jupiter, which has an orbital size (a) of 5 AU.
- How long does it take to orbit the Sun once?
- What exactly is 5 AU, in this problems?
2. If an asteroid were discovered that took 2.5 years to orbit the Sun once, how far away from the Sun must it be (on average)?
3. Consider the planet Mars, with mass 1/10 that of Earth and a radius 1/2 as much. What is its acceleration due to gravity? Also, if it is 1.8 AU from the Sun, how long does it take to orbit the Sun? Finally, what is its average speed (in km/sec) around the Sun? To do this, you'll need to convert AU to km first.
Torque and Center of Mass
4. On a see-saw, a 40-kg child is located 1.5-m away from the fulcrum. Where must a 75-kg adult be located, to balance with the child?
5. In the above problem, the 40-kg child now moves twice as far away from the fulcrum as she originally was. A third child (25-kg) wanders in. If the adult remains in the same location as above, where can the third child sit to balance the see-saw?
Rotation
6. If a cd can go from rest to 400 revolutions per minute in 4 seconds, find the following:
a. the final angular velocity (in radians/sec) - this is a conversion
b. the angular acceleration required to get to this angular velocity
c. the linear speed of a point at the edge of the cd (radius = 0.06 m)
11 - Gravitation -- Kepler and Newton
As discussed in class, Kepler's laws were based on Tycho Brahe's massive amount of data. The laws can be summarized as follows:
1. Planetary orbits are elliptical with the Sun at one focus.
2. Planets sweep out equal areas in equal amounts of time.
3. The square of the period of orbit is proportional to the cube of the semi-major axis. If the units are years and AUs, this is an equality:
T^2 = a^3
e.g, Consider an asteroid with a 4 AU semi-major axis of orbit. How long does it take to orbit once?
Answer: 8 years
>
Several decades after Kepler, Newton derived (from geometry) his law of universal gravitation. The derivation is prohibitive to discuss here, but it can be found in Principia (prop. 71). I don't recommend that you read it - many key points are omitted by Newton. In modern language:
F = G m1 m2 / r^2
That is, the force of gravitational attraction is equal to a constant (6.67 x 10^-11 Nm^2/kg^2) times the product of the masses, divided by the distance between the masses squared.
Setting this equal to the local force of gravity (weight) yields a simple expression for local gravitation:
g = G m(planet) / r^2
Finally, we saw in class how Newton's law of gravitation, along with the expression for centripetal acceleration (v^2 / r) can yield Kepler's third law. That is, Newton's law was powerful enough to predict anything known before it, as well as make predictions about the future.
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