http://www.youtube.com/watch?v=rbKcXkvw1bg&feature=related
http://www.youtube.com/watch?v=-XGds2GAvGQ
Rubens tube and Chladni plates from earlier classes:
http://www.youtube.com/watch?v=cqilJNsiqig&feature=channel
http://www.youtube.com/watch?v=kBmRNkM9saA&feature=channel
Thursday, March 29, 2012
Organ pipes - sound in tubes
We will be talking about waves in tubes/pipes (like brass instruments, woodwinds, etc.).
http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html
http://ralphmuehleisen.com/animations.html
Ultimately, I want you to see that waves in a tube are the same (mathematically) as waves on a string - the biggest differences:
the waves are longitudinal/compressional, NOT transverse
the waves have antinodes at each end, NOT nodes
When an organ pipe/tube is open on both ends, you have antinodes (in a longitudinal wave) on both ends. This becomes (mathematically) the same as a vibrating string (though the string has nodes on both ends). The math looks like the same, however:
lambda (l) = 2L/n
The lowest harmonic (f1, where n = 1) is still found by using v = f l, and dividing v by l. Successive harmonics are 2f1, 3f1, 4f1, ....
So, a tube has a lowest possible resonant tone, but if air is pushed through it harder, higher harmonics can be heard. Think about the recorder - you may have learned how to play one in your younger years. Keeping your fingers in the same positions, but blowing a bit harder, gives higher tones.
Some things to try:
Work your way through lessons on PhysicsClassroom.com
http://www.physicsclassroom.com/Class/sound/
PARTICULARLY LESSONS 5c and 2a.
Here is a problem to try:
1. Consider a tube that is 0.8-m long. The speed of sound is 345 m/s. Find the following:
a. the wavelengths of the first 4 harmonics
b. the frequencies of the first 4 harmonics
c. the wave shapes of the first 5 harmonics - see the applet, as well as my note sheet below
Note that the mathematics in this problem are IDENTICAL to those of the standing waves in the string - the speed, however, is the speed of sound.
http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html
http://ralphmuehleisen.com/animations.html
Ultimately, I want you to see that waves in a tube are the same (mathematically) as waves on a string - the biggest differences:
the waves are longitudinal/compressional, NOT transverse
the waves have antinodes at each end, NOT nodes
When an organ pipe/tube is open on both ends, you have antinodes (in a longitudinal wave) on both ends. This becomes (mathematically) the same as a vibrating string (though the string has nodes on both ends). The math looks like the same, however:
lambda (l) = 2L/n
The lowest harmonic (f1, where n = 1) is still found by using v = f l, and dividing v by l. Successive harmonics are 2f1, 3f1, 4f1, ....
So, a tube has a lowest possible resonant tone, but if air is pushed through it harder, higher harmonics can be heard. Think about the recorder - you may have learned how to play one in your younger years. Keeping your fingers in the same positions, but blowing a bit harder, gives higher tones.
Some things to try:
Work your way through lessons on PhysicsClassroom.com
http://www.physicsclassroom.com/Class/sound/
PARTICULARLY LESSONS 5c and 2a.
Here is a problem to try:
1. Consider a tube that is 0.8-m long. The speed of sound is 345 m/s. Find the following:
a. the wavelengths of the first 4 harmonics
b. the frequencies of the first 4 harmonics
c. the wave shapes of the first 5 harmonics - see the applet, as well as my note sheet below
Note that the mathematics in this problem are IDENTICAL to those of the standing waves in the string - the speed, however, is the speed of sound.
Music!
Music can be thought of (rather unartistically) as collections of frequencies. Here are the ways that we get notes.
In Western music, the standard is (generally) that a "Concert A" is tuned to 440 Hz. All other notes can be tuned with respect to that. Some orchestras tune to different standards, but we won't worry about those now.
An octave "above" a note is defined as twice the frequency of the note. Similarly, an octave "below" is taking a note and dividing it by two.
The tougher concept is - how do we get from one note on a piano (or any instrument) to the next note (and beyond)? The answer is wrapped up in the "equal tempered scale", a scale such that the ratio of one note to the previous note is always the same.
In short - to get from one note to its octave, multiply by two. But since there are 12 "jumps" or "semi-tones" or "half-steps" from one note to its octave, we ask ourselves (in an equal-tempered scale), what number multiplied by itself 12 times gives us two? The answer?
The twelfth root of 2, or 2 to the 1/12 power --- around 1.0594
This number to the 12th power is 2.
But wait, what did I mean by 12 "jumps"?
A A# B C C# D D# E F F# G G# A
That's 13 notes, but 12 "jumps" or piano keys from A to the next A.
To go from A to A#, multiply the frequency of A by 1.0594.
If you wanted to get to B instead, multiply A's frequency by 1.0594 twice (or by 1.0594^2). To get to C, multiply A by 1.0594^3.
In gory detail:
http://en.wikipedia.org/wiki/Equal_temperament
In Western music, the standard is (generally) that a "Concert A" is tuned to 440 Hz. All other notes can be tuned with respect to that. Some orchestras tune to different standards, but we won't worry about those now.
An octave "above" a note is defined as twice the frequency of the note. Similarly, an octave "below" is taking a note and dividing it by two.
The tougher concept is - how do we get from one note on a piano (or any instrument) to the next note (and beyond)? The answer is wrapped up in the "equal tempered scale", a scale such that the ratio of one note to the previous note is always the same.
In short - to get from one note to its octave, multiply by two. But since there are 12 "jumps" or "semi-tones" or "half-steps" from one note to its octave, we ask ourselves (in an equal-tempered scale), what number multiplied by itself 12 times gives us two? The answer?
The twelfth root of 2, or 2 to the 1/12 power --- around 1.0594
This number to the 12th power is 2.
But wait, what did I mean by 12 "jumps"?
A A# B C C# D D# E F F# G G# A
That's 13 notes, but 12 "jumps" or piano keys from A to the next A.
To go from A to A#, multiply the frequency of A by 1.0594.
If you wanted to get to B instead, multiply A's frequency by 1.0594 twice (or by 1.0594^2). To get to C, multiply A by 1.0594^3.
In gory detail:
http://en.wikipedia.org/wiki/Equal_temperament
Wednesday, March 28, 2012
Wave problems to try.
Wave problems.
1. Differentiate between mechanical and electromagnetic waves. Give examples.
2. Draw a wave and identify (or just define) the following parts: crest, trough, amplitude, frequency, period.
3. Consider a wave that travels with a speed of 25 m/s and a wavelength of 5-m. What is the frequency of this wave?
4. Differentiate between longitudinal and transverse waves. Give examples. You may have to look this up, as we did not yet discuss it.
5. Draw the first 3 harmonics for a string that is 3-m in length. Also, find the first 3 wavelengths (using 2L/n) and frequencies (using f = v/l), if the wave speed is 100 m/s.
6. The speed of sound (in air) is approximately 345 m/s. If you stand far from a mountainside and yell at it, the echo returns to your ear in 1.8 seconds. How far is the mountain from you?
7. Approximately how much greater is the speed of light than the speed of sound in air?
8. Discuss the physics of the Chladni plate.
9. Find the wavelength of a 89.7 MHz radio wave.
More practice, to try after the next class:
1. Consider a 2-m long string fixed at both ends. The speed of wave travel is 200 m/s in this string. Find the following:
a. wavelengths of the first 3 harmonics
b. frequencies of the first 3 harmonics
(4, 2, 4/3 meters; 50, 100, 150 Hz)
2. Now imagine an organ pipe, 1-m long. The speed of sound (which is the same as the speed of wave travel in an organ pipe) is 340 m/s. Find the same things as above.
(2, 1, 2/3 meters; 170, 340, 510 Hz)
3. What is the effect of capping one end of a tube?
4. Consider a C note, vibrating at 262 Hz. Find the following frequencies:
a. the next C, one octave above this one
b. a C, two octaves above 262 Hz
c. the note C#, one piano key ("semi-tone") above C
Plus more also!
Waves can be categorized into two broad types:
Mechanical waves
- those requiring a medium (something for the wave energy to "travel through", like air, water or steel)
Electromagnetic waves (EM)
- waves that do not require a medium. These waves can travel in a vacuum. This type includes visible light, x-rays, gamma rays, microwaves, radio waves, IR and UV. More about these to come when we get to light.
Also, all EM waves travel (in a vacuum) at the speed of light, c.
Mechanical waves
- those requiring a medium (something for the wave energy to "travel through", like air, water or steel)
Electromagnetic waves (EM)
- waves that do not require a medium. These waves can travel in a vacuum. This type includes visible light, x-rays, gamma rays, microwaves, radio waves, IR and UV. More about these to come when we get to light.
Also, all EM waves travel (in a vacuum) at the speed of light, c.
Wave notes.
Wave properties
A wave is essentially a traveling disturbance - motion of "energy", NOT the motion of stuff. Fundamentally, there are two varieties of these - one that requires a medium (mechanical) and one that does not require a medium (electromagnetic). An electromagnetic wave can often travel through a medium, but it always travels fastest (at the speed of light, c) where nothing gets in the way.
Properties of a wave:
Wavelength - the distance between 2 successive crests, or 2 successive troughs, or any 2 points "in phase" with each other. Wavelength is represented by the Greek letter lambda (which unfortunately I can't show here). The unit for wavelength is generally the meter, but it could be any unit of length.
Frequency is the number of waves/oscillations per second. It is represented by the letter f. The unit is the "cycle per second", usually called the hertz (Hz).
The period (T) is the amount of time for one oscillation. It is the inverse of the frequency. That is, if you have 2 oscillations/waves per second, the time for each is 1/2 second. In equation form:
T = 1/f or f = 1/T
Amplitude - the distance from equilibrium (the horizontal line) to the peak/crest of the wave, or to the trough/valley of the wave. The amplitude is usually a representation of the volume/loudness (if it's a sound wave) or intensity/brightness (if a light wave).
The velocity/speed (v) of a wave is the rate at which the energy travels. Simply, v is given by:
v = d/T
Since the wavelength is the distance in question, and T = 1/f, the equation can be written more conveniently for a wave:
v = d/T = wavelength * 1/T = wavelength * f
So.....
v = wavelength * frequency
We can imagine waves that travel outward from the origin - maybe in one direction (like sending a pulse on a spring) or in 3 dimensions (like a sound wave).
However, often waves interfere with other waves - to produce NEW waves. Sometimes waves interfere with themselves. This is the case with "standing waves", or waves on a string. It will also be the case with music in tubes or organ pipes.
Consider this applet, where the fundamental (lowest) possible resonant frequency is 25 Hz. The resonant frequency is that frequency that generates the largest possible amplitude for the energy investment. Think of it as the "just right" rate at which you'd need to "pump" a swing to get it higher and higher. Too little and you go nowhere. Too much and you also go nowhere. There is a "just right" amount of frequency - that's the resonant frequency.
http://ngsir.netfirms.com/englishhtm/StatWave.htm
Note what happens when you move the frequency to multiples of the resonant frequency: 50 Hz, 75 Hz, etc. This same sort of thing happens routinely on stringed instruments, as we shall see in class.
Tuesday, March 27, 2012
Harmonics on a String
Since the string is fixed at both ends, it must have nodes (points of NO disturbance) at both ends. However, other possible modes of vibration can satisfy this condition. The wavelength must be satisfied by:
wavelength (lambda) = 2L / n
where n is the so-called "harmonic number," or if you prefer, the number of HALF-waves.
So, the wavelengths can be given by:
n wavelength
1 2L
2 L
3 2L/3
4 2L/4, or L/2
5 2L/5
6 2L/6, or L/3
The frequencies that correspond to these "harmonics" are given by:
v = f * lambda
or...
f = v/lambda
It is also important to note that the frequencies increase LINEARLY. That is, the frequency for n=2 is twice that of n=1. The frequency for n=3 is three times that of n=1. Got it?
This turns out to have musical significance.
Doubling a frequency generates something called and OCTAVE. For those of you who do NOT speak music, an octave is the difference between DO and DO, if you sing:
DO RE MI FA SO LA TI DO
Note that there are 8 notes here, thus the term octave.
Tripling the frequency also gives something of musical significance - it is 3/2 times greater than n=2. In music, a frequency multiple of 3/2 is defined as a "fifth", so named since it is the difference between DO and SO (5 notes).
But don't worry about that business, please - I mention it for your interest.
Play with this:
http://zonalandeducation.com/mstm/physics/waves/standingWaves/understandingSWDia1/UnderstandingSWDia1.html
This one is ok, but the pictures are a little misleading:
http://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaveDiagrams1/StandingWaveDiagrams1.html
A word on terminology:
The lowest harmonic (n=1) is called the fundamental. Any other n-value above 1 is called an overtone. So, the second harmonic (n=2) is called the first overtone.
Got it?
Next up.... how to translate these ideas to sounds in tubes/pipes, and how to construct musical scales.
Energy.
I stole my energy story from the famous American physicist Richard Feynman. Here is a version adapted from his original energy story. He used the character, "Dennis the Menace." The story below is paraphrased from the original Feynman lecture on physics (in the early 1960s).
Dennis the Menace
Adapted from Richard Feynman
Imagine Dennis has 28 blocks, which are all the same. They are absolutely indestructible and cannot be divided into pieces.
His mother puts him and his 28 blocks into a room at the beginning of the day. At the end of each day, being curious, she counts them and discovers a phenomenal law. No matter what he does with the blocks, there are always 28 remaining.
This continues for some time until one day she only counts 27, but with a little searching she discovers one under a rug. She realises she must be careful to look everywhere.
One day later she can only find 26. She looks everywhere in the room, but cannot find them. Then she realises the window is open and two blocks are found outside in the garden.
Another day, she discovers 30 blocks. This causes considerable dismay until she realises that Bruce has visited that day, and left a few of his own blocks behind.
Dennis' mother removes the extra blocks, gives the remaining ones back to Bruce, and all returns to normal.
We can think about energy in this way (except there are no blocks!). We can use this idea to track energy transfers during changes. We need to be careful to look everywhere to ensure that we can account for all of the energy.
Some ideas about energy
Energy is stored in fuels (chemicals).
Energy can be stored by lifting objects (potential energy).
Moving objects carry energy (kinetic energy).
Electric current carries energy.
Light (and other forms of radiation) carries energy.
Heat carries energy.
Sound carries energy.
Harmonic motion
SHM refers to a regular oscillation, such as you might see with a pendulum or mass bobbing up and down (or back and forth) on a spring.
http://www.walter-fendt.de/ph14e/pendulum.htm
Note in this applet that while the "bob" swings back and forth, the displacement (elongation) changes SINUSOIDALLY, as shown on the graph. The velocity and acceleration of the bob also changes in a similar fashion.
Note the similar behavior for a mass on a spring:
http://www.walter-fendt.de/ph14e/springpendulum.htm
This type of motion is called "Simple Harmonic Motion," and it assumes the following reasonable conditions:
- the initial amount of pull (as long as it is "small") does not matter
- the mass of the string (for a pendulum) is small compared to the bob
- there are no significant frictional losses or effects
If these conditions are not met, the oscillator would likely be a complex harmonic oscillator, and there are different rules for those!
I introduce the idea of SHM, as it leads us nicely into the concept of a wave. If you imagine a mass bobbing up and down on a spring, and can imagine a pen attached to the mass, it could draw out the shape of the graph above. You would have to have the pen hit a piece of paper that is being moved at a constant speed horizontally.
In this case, a sine wave would be generated. You can see a little of this here:
http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html
exam
Physics 100
Exam 1
For the acceleration due to gravity, let g = 10 m/s/s for calculations.
Useful equations:
v = d/t
a = (vf - vi)/t
d = vi t + 0.5 at2
vf = vi + at
d = 0.5(vi + vf) t
F = m a
F = G m1 m2 / d2
g = G m / d2
a3 = T2
c = 3 x 108 m
1. Which could be a unit for acceleration?
a. m/s
b. m/s/s
c. mile/hr/s
d. m/s2
e. all but a
2. Consider an object in freefall with no air resistance. How fast will it be traveling (approximately) after 2.5 seconds of falling?
a. 2.5 m/s
b. 25 m/s
c. 30 m/s
d. 27.5 m/s
e. there is not enough information
3. You are seated at a baseball game and you notice that the ball leaves the bat BEFORE you hear the crack of the bat. Why is this?
a. the speed of sound is greater than the speed of light
b. the speed of light is greater than the speed of sound
c. the speed of light equals the speed of sound in air
d. your view of the game is blocked by some jerk with big hair
e. this actually can NOT possibly happen - you must be mistaken, or perhaps there is an echo
4. Seasons on Earth are the result of:
a. the tilt of the the Earth's axis
b. Earth getting closer and further from the Sun
c. Kepler's 3rd law
d. the variable output of the Sun's radiation
e. the Earth's magnetosphere
5. Consider dropping a heavy object on the Moon from rest. How does the time to fall compare with the same object dropped from the same height on Earth? Assume no air resistance.
a. it is less
b. it is the same
c. it is more
d. the answer depends on the mass of the object
6. The SI unit of mass is the ____ and it is currently based on _____.
a. gram, chunk of metal
b. gram, water
c. kilogram, water
d. kilogram, speed of light
e. kilogram, chunk of metal
7. The SI unit of length is the _____ and it is currently based on _____.
a. meter, distance from North pole to equator
b. meter, two lines on a platinum-iridium bar
c. kilometer, speed of light
d. meter, speed of light
e. mile, speed of light
8. Consider the following situation: a ball is dropped from rest. At the SAME time, another identical ball is shot horizontally from the same height. Which ball lands first? There is no air resistance.
a. the horizontally shot ball
b. the dropped ball
c. they land at the same time
d. there is not enough information to tell
9. What is the celestial sphere?
a. the path of the Earth around the Sun
b. a model of the universe with the Earth at the center
c. a model of the universe with the Sun at the center
d. the Sun
e. an epicycle
10. Consider a person standing on a large steel cart with low-friction wheels. This person is holding a pole - this pole suspends a giant magnet a constant distance from the front of the cart. Assuming that this magnet normally attracts steel, will this make the cart move?
a. yes - Newton's third law demands it
b. no - the action and reaction forces cancel each other on the cart
c. yes, but only if the magnet weighs more than the cart and person
d. no - because the magnet does not affect the rubber tires
e. yes, but only enough to barely make the cart move at a constant speed
11-12. Consider the planet Jupiter traveling around the Sun.
11. If Jupiter is 5 AU from the Sun, how long (in years) does it take to orbit the Sun once?
a. 5
b. 10
c. 53
d. 25
e. square root of 53
12. What is the shape of Jupiter's orbit?
a. figure 8
b. circle
c. hyperbola
d. ellipse
e. parabola
13. What is an Astronomical Unit?
a. the amount of time required for Earth to orbit once
b. the amount of time required for Earth to rotate once
c. the size of Earth's semi-major axis (in orbit around the Sun)
d. the average distance to the Moon
e. the diameter of the Solar System
14. What is an epicycle?
a. the elliptical path that every planet takes
b. the circular path that every planet takes
c. the apparent path of the Sun through the sky
d. a concept used to explain retrograde motion
e. a device used to measure the distance to a star
15. Consider an extremely sensitive electronic scale that measures weight. You have a tightly sealed jar of live flies on the scale. Will the scale reading change, based on the flies' position?
a. yes - it will read the most when the flies are moving around
b. no - it will not change at all, regardless of the flies' motion
c. yes - it will read the most when the flies are resting on the bottom of the jar
d. yes - it will read the most when the flies are attached to the sides of the jar
e. yes - it will read the most if the flies are on the top of inside of the lid (upside-down)
16. During what month is the Earth nearest the Sun?
a. June
b. September
c. March
d. January
e. It's actually different every year
17. Which statement is true about the Earth's speed as it moves around the Sun?
a. it is fastest when nearest the Sun
b. it is unchanging, more or less
c. it is fastest when farthest from the Sun
18. Consider a see-saw, initially at rest. A 20 kg child sits 1.5-m from the fulcrum on the left. Where should a 30 kg child sit so that the see-saw is balanced?
a. 3-m from the fulcrum on the right
b. 2-m from the fulcrum on the right
c. 1-m from the fulcrum on the right
d. the 30 kg child can not balance the 20 kg child
e. 2.5-m from the fulcrum on the right
19. Imagine balancing a broom horizontally on your finger. Which end is heaviest?
a. A
b. B
c. both ends weigh the same
20-21. Consider standing on a scale that measures your weight. You and the scale are in an elevator.
20. If the elevator were accelerating upward, what would be true of your weight reading?
a. it would be less than normal
b. it would be zero
c. it would be greater than normal
21. If the cable snapped (yikes!), what would the scale read?
a. your normal weight
b. greater than your normal weight
c. less than your normal weight, but not zero
d. zero
e. 9.8 m/s/s
22. Newton's major work was _____ and was published in _____.
a. Principia Mathematica, 1787
b. Principa Mathematica, 1687
c. De Revolutionibus, 1543
d. De Revolutionibus, 1687
e. Almagest, 1687
23. Imagine if you had a baseball somehow equipped with a speedometer. If the ball were dropped, how would the reading on the speedometer change (if at all)?
a. it would reach 9.8 m/s and stay there
b. it would increase by 9.8 m/s every second
c. it would decrease by 9.8 m/s every second
d. it would increase by an amount less than 9.8 m/s every second
e. it would increase by an amount greater than 9.8 m/s every second
24. Which is the longest day of the year?
a. autumnal equinox
b. vernal equinox
c. summer solstice
d. winter solstice
e. none of these
25. If you were standing on the Moon, which statement would be true?
a. your mass and weight would be less than on Earth
b. your mass would be less than your Earth mass, but your weight would remain unchanged
c. your weight would be less than your Earth weight, but your mass would remain unchanged
d. your mass would be greater than your Earth mass, but your weight would remain unchanged
e. your mass and weight would both remain unchanged
26. What is the approximate value for g at a distance above sea level equal to one Earth radius?
a. 10 m/s/s
b. 5 m/s/s
c. 1 m/s/s
d. 0 m/s/s
e. 2.5 m/s/s
27. How far (in m) would a light pulse travel in 10 seconds?
a. (3 x 108) x 10
b. 3 x 108
c. (3 x 108) x 100
d. (3 x 108) x 1000
e. (3 x 108) x 0.1
28. The Moon is approximately how far from us?
a. one light-second
b. one light-year
c. one light-day
d. one light-month
e. one light-nanosecond
29. How long have we known/believed that the Earth was spherical?
a. since the time of Columbus
b. since the Scientific Revolution and Galileo
c. since the ancient Greeks lived
d. since we were able to see it from space
e. since the 1800s
30. Consider 2 massive bodies in space. The distance between is changed to 4 times the original distance. What happens to the gravitational force between the bodies?
a. it is 16 times greater
b. it is 1/16 as much
c. it remains the same
d. it is quadrupled
e. it is ¼ as much
31. A car is accelerating at a rate of 2 m/s/s. If it starts from rest, how fast will it be traveling after 7 seconds?
a. 7 m/s
b. 9 m/s
c. 2/7 m/s
d. 7/2 m/s
e. 14 m/s
32. In the above problem, how far will the car travel during this time?
a. 14 m
b. 49 m
c. 7 m
d. 98 m
e. 25 m
33. To measure the size of the Earth, Eratosthenes:
a. walked from the equator to the North Pole
b. used sticks and shadows
c. compared the Earth to the Moon
d. compared the Earth to Mars
e. watched a lunar eclipse
34. What is the weight of a 65 kg woman?
a. 65 kg
b. 65 N
c. 650 kg
d. 650 N
e. 650 lb
35. If you were to push on a 10-kg box with a force of 50-N, what would happen? Assume no friction.
a. it would accelerate
b. it would move at a constant speed of 5 m/s
c. it would move at a constant speed of 0.2 m/s
d. it would not move
e. it is impossible to say
36. Imagine a spring scale - it has a hook at the top for hanging up, and a spring-loaded hook at the bottom for weighing things. Now this spring scale is placed horizontally with two equal 10-N weights attached to each side by strings. The weights are draped over frictionless pulleys as shown. What does the scale read?
a. 20-N
b. 0-N
c. 5-N
d. 10-N
e. some other value
37. Consider throwing a ball straight up in the air. At the top of its path:
a. the speed is 9.8 m/s
b. the speed is the same as it was in your hand
c. the acceleration is 9.8 m/s/s upward
d. the acceleration is 0
e. the speed is 0
38. Consider a horizontal curved piece of hose. Water is sent out of the tube. Which path does the water take?
a. A
b. B
c. C
39. Recall the balancing guy demonstration. Where is the center of mass likely to be located? See diagram.
a. A
b. B
c. C
d. D
e. E
40. Traveling to Philadelphia, you could either drive at a constant 65 mph or an average 65 mph. In general, which method will get you to Philadelphia sooner?
a. Constant speed
b. Average speed
c. They are the same time for both
d. Why would you want to go to Philadelphia?
41. The speed of light is so fast that a pulse could travel:
a. around the Earth's equator once in a second
b. around the Earth's equator 1000 times in one second
c. from New York to Los Angeles in 1 second
d. from the North Pole to the South Pole in 1 second
e. around the Earth's equator 7 times in 1 second
42. A bowling ball and a golf ball are dropped simultaneously from the same height. There is no air resistance. Which lands first?
a. bowling ball
b. golf ball
c. same time for each
43. Consider an airplane flight. You toss a bag of airline snacks straight up as the plane cruises along at 500 miles/hr. Where do the snacks land?
a. behind you
b. in front of you
c. to the left OR right of you
d. in your hands
e. it is impossible to say
44. This is a graph of distance versus time for a car. What is the car doing in this interval?
a. Nothing - it is stopped
b. Accelerating
c. Moving with constant speed
d. Slowing down
e. speeding up, then slowing down
45. Which historical ordering of scientists is correct:
a. Copernicus, Newton, Galileo
b. Newton, Galileo, Copernicus
c. Copernicus, Galileo, Newton
d. Galileo, Copernicus, Newton
e. Newton, Copernicus, Galileo
Bonus. On March 31, 2012, what awesome thing is happening in DC?
Exam 1
For the acceleration due to gravity, let g = 10 m/s/s for calculations.
Useful equations:
v = d/t
a = (vf - vi)/t
d = vi t + 0.5 at2
vf = vi + at
d = 0.5(vi + vf) t
F = m a
F = G m1 m2 / d2
g = G m / d2
a3 = T2
c = 3 x 108 m
1. Which could be a unit for acceleration?
a. m/s
b. m/s/s
c. mile/hr/s
d. m/s2
e. all but a
2. Consider an object in freefall with no air resistance. How fast will it be traveling (approximately) after 2.5 seconds of falling?
a. 2.5 m/s
b. 25 m/s
c. 30 m/s
d. 27.5 m/s
e. there is not enough information
3. You are seated at a baseball game and you notice that the ball leaves the bat BEFORE you hear the crack of the bat. Why is this?
a. the speed of sound is greater than the speed of light
b. the speed of light is greater than the speed of sound
c. the speed of light equals the speed of sound in air
d. your view of the game is blocked by some jerk with big hair
e. this actually can NOT possibly happen - you must be mistaken, or perhaps there is an echo
4. Seasons on Earth are the result of:
a. the tilt of the the Earth's axis
b. Earth getting closer and further from the Sun
c. Kepler's 3rd law
d. the variable output of the Sun's radiation
e. the Earth's magnetosphere
5. Consider dropping a heavy object on the Moon from rest. How does the time to fall compare with the same object dropped from the same height on Earth? Assume no air resistance.
a. it is less
b. it is the same
c. it is more
d. the answer depends on the mass of the object
6. The SI unit of mass is the ____ and it is currently based on _____.
a. gram, chunk of metal
b. gram, water
c. kilogram, water
d. kilogram, speed of light
e. kilogram, chunk of metal
7. The SI unit of length is the _____ and it is currently based on _____.
a. meter, distance from North pole to equator
b. meter, two lines on a platinum-iridium bar
c. kilometer, speed of light
d. meter, speed of light
e. mile, speed of light
8. Consider the following situation: a ball is dropped from rest. At the SAME time, another identical ball is shot horizontally from the same height. Which ball lands first? There is no air resistance.
a. the horizontally shot ball
b. the dropped ball
c. they land at the same time
d. there is not enough information to tell
9. What is the celestial sphere?
a. the path of the Earth around the Sun
b. a model of the universe with the Earth at the center
c. a model of the universe with the Sun at the center
d. the Sun
e. an epicycle
10. Consider a person standing on a large steel cart with low-friction wheels. This person is holding a pole - this pole suspends a giant magnet a constant distance from the front of the cart. Assuming that this magnet normally attracts steel, will this make the cart move?
a. yes - Newton's third law demands it
b. no - the action and reaction forces cancel each other on the cart
c. yes, but only if the magnet weighs more than the cart and person
d. no - because the magnet does not affect the rubber tires
e. yes, but only enough to barely make the cart move at a constant speed
11-12. Consider the planet Jupiter traveling around the Sun.
11. If Jupiter is 5 AU from the Sun, how long (in years) does it take to orbit the Sun once?
a. 5
b. 10
c. 53
d. 25
e. square root of 53
12. What is the shape of Jupiter's orbit?
a. figure 8
b. circle
c. hyperbola
d. ellipse
e. parabola
13. What is an Astronomical Unit?
a. the amount of time required for Earth to orbit once
b. the amount of time required for Earth to rotate once
c. the size of Earth's semi-major axis (in orbit around the Sun)
d. the average distance to the Moon
e. the diameter of the Solar System
14. What is an epicycle?
a. the elliptical path that every planet takes
b. the circular path that every planet takes
c. the apparent path of the Sun through the sky
d. a concept used to explain retrograde motion
e. a device used to measure the distance to a star
15. Consider an extremely sensitive electronic scale that measures weight. You have a tightly sealed jar of live flies on the scale. Will the scale reading change, based on the flies' position?
a. yes - it will read the most when the flies are moving around
b. no - it will not change at all, regardless of the flies' motion
c. yes - it will read the most when the flies are resting on the bottom of the jar
d. yes - it will read the most when the flies are attached to the sides of the jar
e. yes - it will read the most if the flies are on the top of inside of the lid (upside-down)
16. During what month is the Earth nearest the Sun?
a. June
b. September
c. March
d. January
e. It's actually different every year
17. Which statement is true about the Earth's speed as it moves around the Sun?
a. it is fastest when nearest the Sun
b. it is unchanging, more or less
c. it is fastest when farthest from the Sun
18. Consider a see-saw, initially at rest. A 20 kg child sits 1.5-m from the fulcrum on the left. Where should a 30 kg child sit so that the see-saw is balanced?
a. 3-m from the fulcrum on the right
b. 2-m from the fulcrum on the right
c. 1-m from the fulcrum on the right
d. the 30 kg child can not balance the 20 kg child
e. 2.5-m from the fulcrum on the right
19. Imagine balancing a broom horizontally on your finger. Which end is heaviest?
a. A
b. B
c. both ends weigh the same
20-21. Consider standing on a scale that measures your weight. You and the scale are in an elevator.
20. If the elevator were accelerating upward, what would be true of your weight reading?
a. it would be less than normal
b. it would be zero
c. it would be greater than normal
21. If the cable snapped (yikes!), what would the scale read?
a. your normal weight
b. greater than your normal weight
c. less than your normal weight, but not zero
d. zero
e. 9.8 m/s/s
22. Newton's major work was _____ and was published in _____.
a. Principia Mathematica, 1787
b. Principa Mathematica, 1687
c. De Revolutionibus, 1543
d. De Revolutionibus, 1687
e. Almagest, 1687
23. Imagine if you had a baseball somehow equipped with a speedometer. If the ball were dropped, how would the reading on the speedometer change (if at all)?
a. it would reach 9.8 m/s and stay there
b. it would increase by 9.8 m/s every second
c. it would decrease by 9.8 m/s every second
d. it would increase by an amount less than 9.8 m/s every second
e. it would increase by an amount greater than 9.8 m/s every second
24. Which is the longest day of the year?
a. autumnal equinox
b. vernal equinox
c. summer solstice
d. winter solstice
e. none of these
25. If you were standing on the Moon, which statement would be true?
a. your mass and weight would be less than on Earth
b. your mass would be less than your Earth mass, but your weight would remain unchanged
c. your weight would be less than your Earth weight, but your mass would remain unchanged
d. your mass would be greater than your Earth mass, but your weight would remain unchanged
e. your mass and weight would both remain unchanged
26. What is the approximate value for g at a distance above sea level equal to one Earth radius?
a. 10 m/s/s
b. 5 m/s/s
c. 1 m/s/s
d. 0 m/s/s
e. 2.5 m/s/s
27. How far (in m) would a light pulse travel in 10 seconds?
a. (3 x 108) x 10
b. 3 x 108
c. (3 x 108) x 100
d. (3 x 108) x 1000
e. (3 x 108) x 0.1
28. The Moon is approximately how far from us?
a. one light-second
b. one light-year
c. one light-day
d. one light-month
e. one light-nanosecond
29. How long have we known/believed that the Earth was spherical?
a. since the time of Columbus
b. since the Scientific Revolution and Galileo
c. since the ancient Greeks lived
d. since we were able to see it from space
e. since the 1800s
30. Consider 2 massive bodies in space. The distance between is changed to 4 times the original distance. What happens to the gravitational force between the bodies?
a. it is 16 times greater
b. it is 1/16 as much
c. it remains the same
d. it is quadrupled
e. it is ¼ as much
31. A car is accelerating at a rate of 2 m/s/s. If it starts from rest, how fast will it be traveling after 7 seconds?
a. 7 m/s
b. 9 m/s
c. 2/7 m/s
d. 7/2 m/s
e. 14 m/s
32. In the above problem, how far will the car travel during this time?
a. 14 m
b. 49 m
c. 7 m
d. 98 m
e. 25 m
33. To measure the size of the Earth, Eratosthenes:
a. walked from the equator to the North Pole
b. used sticks and shadows
c. compared the Earth to the Moon
d. compared the Earth to Mars
e. watched a lunar eclipse
34. What is the weight of a 65 kg woman?
a. 65 kg
b. 65 N
c. 650 kg
d. 650 N
e. 650 lb
35. If you were to push on a 10-kg box with a force of 50-N, what would happen? Assume no friction.
a. it would accelerate
b. it would move at a constant speed of 5 m/s
c. it would move at a constant speed of 0.2 m/s
d. it would not move
e. it is impossible to say
36. Imagine a spring scale - it has a hook at the top for hanging up, and a spring-loaded hook at the bottom for weighing things. Now this spring scale is placed horizontally with two equal 10-N weights attached to each side by strings. The weights are draped over frictionless pulleys as shown. What does the scale read?
a. 20-N
b. 0-N
c. 5-N
d. 10-N
e. some other value
37. Consider throwing a ball straight up in the air. At the top of its path:
a. the speed is 9.8 m/s
b. the speed is the same as it was in your hand
c. the acceleration is 9.8 m/s/s upward
d. the acceleration is 0
e. the speed is 0
38. Consider a horizontal curved piece of hose. Water is sent out of the tube. Which path does the water take?
a. A
b. B
c. C
39. Recall the balancing guy demonstration. Where is the center of mass likely to be located? See diagram.
a. A
b. B
c. C
d. D
e. E
40. Traveling to Philadelphia, you could either drive at a constant 65 mph or an average 65 mph. In general, which method will get you to Philadelphia sooner?
a. Constant speed
b. Average speed
c. They are the same time for both
d. Why would you want to go to Philadelphia?
41. The speed of light is so fast that a pulse could travel:
a. around the Earth's equator once in a second
b. around the Earth's equator 1000 times in one second
c. from New York to Los Angeles in 1 second
d. from the North Pole to the South Pole in 1 second
e. around the Earth's equator 7 times in 1 second
42. A bowling ball and a golf ball are dropped simultaneously from the same height. There is no air resistance. Which lands first?
a. bowling ball
b. golf ball
c. same time for each
43. Consider an airplane flight. You toss a bag of airline snacks straight up as the plane cruises along at 500 miles/hr. Where do the snacks land?
a. behind you
b. in front of you
c. to the left OR right of you
d. in your hands
e. it is impossible to say
44. This is a graph of distance versus time for a car. What is the car doing in this interval?
a. Nothing - it is stopped
b. Accelerating
c. Moving with constant speed
d. Slowing down
e. speeding up, then slowing down
45. Which historical ordering of scientists is correct:
a. Copernicus, Newton, Galileo
b. Newton, Galileo, Copernicus
c. Copernicus, Galileo, Newton
d. Galileo, Copernicus, Newton
e. Newton, Copernicus, Galileo
Bonus. On March 31, 2012, what awesome thing is happening in DC?
Tuesday, March 6, 2012
test
What should I know for the test?
How to use the formulas (which will be given):
v = d/t
a = (vf - vi)/t
vf = vi + at
d = 0.5(vi + vf) t
d = vi t + 0.5at^2
F = ma
W = mg
F = G m1 m2 / d^2
g = G M / d^2
a^3 = T^2
v = d/t
a = (vf - vi)/t
vf = vi + at
d = 0.5(vi + vf) t
d = vi t + 0.5at^2
F = ma
W = mg
F = G m1 m2 / d^2
g = G M / d^2
a^3 = T^2
the meaning of velocity, acceleration
gravitational acceleration, g
center of gravity
universal gravitation
Newton's laws
Kepler's laws
basic science history (Copernicus, Kepler, Newton)
epicycles and retrograde motion
speed of light (meaning, etc.)
inverse square law
weightlessness
Expect a test that is multiple-choice, with somewhere in the neighborhood of 20% numerical problems - a calculator is permitted but not really needed.
Also expect that there will be 40-50 questions, though more are possible. You will have the entire class to finish the test.
If you've attended class, reviewed the notes, understood the demonstrations and worked the problems, you should be fine.
Lever practice
1. What IS a center of mass (CM)?
2. Is the CM necessarily ON the body? If not, why not? Where else could it be?
3. What does it mean for something to be stable? That is, what does it say about the location of the CM?
4. Why is a tall SUV more likely to tip over rounding a curve than, say, a low-riding sports car?
5. Consider a see-saw, initially balanced. A 100-lb person sits 2 feet to the right of the fulcrum. Where could a 150-lb person sit to keep the see-saw balanced?
6. Consider a cantilever - a 8-ft long board with a fulcrum 2-ft from the left end. There is a 40-lb child sitting 1-ft to the left of the fulcrum, balancing the board. Considering that the CM of the board is located exactly in the middle of the board, what is the weight of the board? Draw this out first.
7. Review some of the CM demonstrations done in class - consider what makes one thing stable or unstable.
2. Is the CM necessarily ON the body? If not, why not? Where else could it be?
3. What does it mean for something to be stable? That is, what does it say about the location of the CM?
4. Why is a tall SUV more likely to tip over rounding a curve than, say, a low-riding sports car?
5. Consider a see-saw, initially balanced. A 100-lb person sits 2 feet to the right of the fulcrum. Where could a 150-lb person sit to keep the see-saw balanced?
6. Consider a cantilever - a 8-ft long board with a fulcrum 2-ft from the left end. There is a 40-lb child sitting 1-ft to the left of the fulcrum, balancing the board. Considering that the CM of the board is located exactly in the middle of the board, what is the weight of the board? Draw this out first.
7. Review some of the CM demonstrations done in class - consider what makes one thing stable or unstable.
Thursday, March 1, 2012
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