1. Describe each of Newton's 3 laws.
2. A 0.5 kg toy car is pushed with a 40 newton force. What is the car's acceleration?
3. Without calculating anything, what would be the effect (in problem 2) of increasing the mass of the car?
4. Give an example of Newton's 1st law in action.
5. Give an example of Newton's 3rd law in action.
6. Newton's "big book", what I claim is the most important non-religious book of all time is _____ and was published in _____.
7. What things are worth remembering about the so-called Scientific Revolution?
8. Have a basic idea of historical chronology between these fellows: Newton, Copernicus, Ptolemy, Galileo. And roughly, why their contributions are important.
9. What are epicycles and why are they important in the history of science?
10. What is precession (wobbling) and why is it important in the history of science?
11. Distinguish between weight and mass.
12. What is the SI unit of force? What is the English unit of force?
13. How does weight depend on gravitational acceleration?
14. Why do objects in freefall fall with the same acceleration? Give one of the arguments that appeals to you.
Gravitation problems:
1. Explain the meaning of "inverse square law".
2. Discuss each of Kepler's 3 laws.
3. At what point in its orbit is the Earth closest to the Sun?
4. At what point in its orbit is the Earth moving fastest?
5. What causes seasons?
6. What is a semi-major axis of orbit (a)?
7. What is an Astronomical Unit (AU)?
8. Consider Jupiter. It's orbit is 5 AU in size (roughly). How long should it take Jupiter to orbit the Sun once? Show how this calculation would be done.
9. What is the period of Earth's orbit around the Sun?
10. What is the size of Earth's orbit (in AU)?
11. When you stand on the Earth's surface, you experience your "normal" Earth weight. What would happen to your Earth weight if you were one Earth radius above the surface? (That's twice as far from the center as simply standing on the surface.)
12. What does gravitational force between 2 objects depend on?
General topics for exam 1. Be sure to review all assigned homework, blog posts and your notes.
You are permitted to have a sheet of notes for this test. I will NOT give equations.
pseudoscience
SI units (m, kg, s) - meanings, definitions
velocity
acceleration
related problems using the formulas
speed of light (c)
gravitational acceleration (g)
average vs. instantaneous velocity
the basics of flight
freefall problems
Newton's 3 laws
Kepler's 3 laws
inverse square law / Newton's law of universal gravitation
Monday, September 30, 2013
Kepler's laws and gravitation
First, the applets:
http://www.physics.sjsu.edu/tomley/kepler.html
http://www.physics.sjsu.edu/tomley/Kepler12.html
for Kepler's laws, primarily the 2nd law
http://www.astro.utoronto.ca/~zhu/ast210/geocentric.html
for our discussion on geocentrism and how retrograde motion appears within this conceptual framework
Cool:
http://galileo.phys.virginia.edu/classes/109N/more_stuff/flashlets/kepler6.htm
http://physics.unl.edu/~klee/applets/moonphase/moonphase.html
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Now, the notes.
Johannes Kepler, 1571-1630
Kepler's laws of planetary motion - of course, these apply equally well to all orbiting bodies
1. Planets take elliptical orbits, with the Sun at one focus. (If we were talking about satellites, the central gravitating body, such as the Earth, would be at one focus.) Nothing is at the other focus. Recall that a circle is the special case of the ellipse, wherein the two focal points are coincident. Some bodies, such as the Moon, take nearly circular orbits - that is, the eccentricity is very small.
2. The Area Law. Planets "sweep out" equal areas in equal times. See the applets for pictorial clarification. This means that in any 30 day period, a planet will sweep out a sector of space - the area of this sector is the same, regardless of the 30 day period. A major result of this is that the planet travels fastest when near the Sun.
3. The Harmonic Law. Consider the semi-major axis of a planet's orbit around the Sun - that's half the longest diameter of its orbit. This distance (a) is proportional to the amount of time to go around the Sun in a very peculiar fashion:
a^3 = T^2
That is to say, the semi-major axis CUBED (to the third power) is equal to the period (time) SQUARED. This assumes that we choose convenient units:
- the unit of a is the Astronomical Unit (AU), equal to the semi-major axis of Earth's orbit (approximately the average distance between Earth and Sun). This is around 150 million km or around 93 million miles
- the unit of time is the (Earth) year
e.g. Consider an asteroid with a semi-major axis of orbit of 4 AU. We can quickly calculate that its period of orbit is 8 years (since 4 cubed equals 8 squared).
Likewise for Pluto: a = 40 AU. T works out to be around 250 years.
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Newton's take on this was quite different. For him, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is:
All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation:
F = G m1 m2 / d^2
or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared.
Big G = 6.67 x 10^-11, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces.
This is an INVERSE SQUARE law, meaning that:
- if the distance between the bodies is doubled, the force becomes 1/4 of its original value
- if the distance is tripled, the force becomes 1/9 the original amount
- etc.
Weight
Weight is a result of local gravitation. Since F = G m1 m2 / d^2, and the force of gravity (weight) is equal to m g, we can come up with a simple expression for local gravity (g):
g = G m(planet) / d^2
Likewise, this is an inverse square law. The further you are from the surface of the Earth, the weaker the gravitational acceleration. With normal altitudes, the value for g goes down only slightly, but it's enough for the air to become thinner (and for you to notice it immediately!).
Note that d is the distance from the CENTER of the Earth - this is the Earth's radius, if you're standing on the surface.
If you were above the surface of the earth an amount equal to the radius of the Earth, thereby doubling your distance from the center of the Earth, the value of g would be 1/4 of 9.8 m/s/s. If you were 2 Earth radii above the surface, the value of g would be 1/9 of 9.8 m/s/s.
The value of g also depends on the mass of the planet. The Moon is 1/4 the diameter of the Earth and about 1/81 its mass. You can check this but, this gives the Moon a g value of around 1.7 m/s/s. For Jupiter, it's around 2.5 m/s/s.
Flying Things
The amazing science of flight is largely governed by Newton's laws.
Consider a wing cross-section:
Air hits it at a certain speed. However, the shape of the wing forces air to rush over it and under it at different rates. The top curve creates a partial vacuum - a region "missing" a bit of air. So, the pressure (force/area) on top of the wing can become less than the pressure below. If the numbers are right, and the resulting force below the wing is greater than the weight of the plane, the plane can lift.
This is often embodied as the Bernoulli Principle:
Pressure in a moving stream of fluid (such as air) is less than the pressure of the surrounding fluid.
A related concept is the equation of continuity:
A1 v1 = A2 v2
Think about a garden hose with your thumb over the end - the water comes out faster, right? The product of the area (A) and speed (v) through a tube is constant - make the area smaller and the fluid comes out faster.
Yet another way to think of flight is to imagine the wing above, but slightly inclined upward (to exacerbate the effect). There is a downward deflection of air. The reaction force from the air below provides lift and the lift is proportional to the force on the wing.
In practice, it works out to be:
Lift = 0.3 p v^2 A
where p is the density of air, v (squared) is the speed of the plane, and A is the effective area.
Sunday, September 29, 2013
Newton problems
1. Know and understand Newton's laws of motion.
2. A 10-kg object is pushed on by a 200-N force. What will be the acceleration?
3. What is the weight of a 100-kg man?
4. Would the answer to 3 be different if he was on the moon? How so?
5. Consider yourself standing on a scale in an elevator. The scale reads your weight. Compared to being at rest, how would the scale reading change (if at all) if the elevator were:
A. Moving with constant velocity upward
B. moving with constant velocity downward
C. Moving with constant acceleration upward
D. Moving with constant acceleration downward
E. If the cable snapped (yikes!) and the elevator were falling
6. Give the name and publication on Newton's major book
Sunday, September 22, 2013
Consider these....
1. What are epicycles and why were they important? What is retrograde motion and what is *actually* going on when mars seems to move backward?
2. What contributions did Galileo make with his telescope? What got him into trouble?
3. What is Copernicus' main contribution to science?
4. Know and understand the demonstrations with the "ball dropping and launching" cart.
Wednesday, September 18, 2013
Newton's Laws
Newton and his laws of motion.
Newton, Philosophiae naturalis principia mathematica (1687) Translated by Andrew Motte (1729)
Lex. I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.
Lex. II. Mutationem motus proportionalem esse vi motrici impressae, & fieri secundum lineam rectam qua vis illa imprimitur.
The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.
Lex. III. Actioni contrariam semper & aequalem esse reactionent: sive corporum duorum actiones in se mutuo semper esse aequales & in partes contrarias dirigi.
To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other.
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Now, in better language:
Lex. I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.
Lex. II. Mutationem motus proportionalem esse vi motrici impressae, & fieri secundum lineam rectam qua vis illa imprimitur.
The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.
Lex. III. Actioni contrariam semper & aequalem esse reactionent: sive corporum duorum actiones in se mutuo semper esse aequales & in partes contrarias dirigi.
To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other.
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Now, in better language:
Newton's Laws redux.
1. Newton's First Law (Inertia)
An object will keep doing what it is doing, unless there is a reason for it to do otherwise.
That means, it will stay at rest OR it will keep moving (at a constant velocity) unless acted on by an unbalanced force.
2. Newton's Second Law
An unbalanced force (F) causes an object to accelerate (a).
That means, if you apply a force to an object (and the force is unbalanced - greater than any resisting forces), the object will accelerate.
Symbolically:
The Force (F) on a mass (m) produces acceleration (a), predicted by the above equation. In detail:
Greater F means greater a
If the Force is kept constant, but the mass is increased, the acceleration will be smaller:
a = F/m
That's an inverse relationship.
There is a new unit for Force - since Force = mass times acceleration, the units are:
kg m/s^2
We give this a new name, the newton (N). It's about 0.22 lb.
3. Newton's 3rd Law
To every action there is opposed an equal reaction. Forces always exist in pairs. Examples:
You move forward by pushing backward on the Earth - the Earth pushes YOU forward.
A rocket engine pushes hot gases out of one end - the gases push the rocket forward.
If you fire a rifle or pistol, the firearm "kicks" back on you.
Since the two objects experience the same force:
m A = M a
That's a little tricky to convey in letters but, the larger object (M) will experience the smaller acceleration (a) and the smaller object (m) will have a larger acceleration (A).
An object will keep doing what it is doing, unless there is a reason for it to do otherwise.
That means, it will stay at rest OR it will keep moving (at a constant velocity) unless acted on by an unbalanced force.
2. Newton's Second Law
An unbalanced force (F) causes an object to accelerate (a).
That means, if you apply a force to an object (and the force is unbalanced - greater than any resisting forces), the object will accelerate.
Symbolically:
F = m a
The Force (F) on a mass (m) produces acceleration (a), predicted by the above equation. In detail:
Greater F means greater a
If the Force is kept constant, but the mass is increased, the acceleration will be smaller:
a = F/m
That's an inverse relationship.
There is a new unit for Force - since Force = mass times acceleration, the units are:
kg m/s^2
We give this a new name, the newton (N). It's about 0.22 lb.
3. Newton's 3rd Law
To every action there is opposed an equal reaction. Forces always exist in pairs. Examples:
You move forward by pushing backward on the Earth - the Earth pushes YOU forward.
A rocket engine pushes hot gases out of one end - the gases push the rocket forward.
If you fire a rifle or pistol, the firearm "kicks" back on you.
Since the two objects experience the same force:
m A = M a
That's a little tricky to convey in letters but, the larger object (M) will experience the smaller acceleration (a) and the smaller object (m) will have a larger acceleration (A).
Galileo and Newton history, FYI
First, some history: epicycles
http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf
Worldviews:
http://www.stumbleupon.com/su/2jRGYC/dd.dynamicdiagrams.com/wp-content/uploads/2011/01/orrery_2006.swf/
http://www.solarsystemscope.com/
Some background details will be discussed in class. Here are some dates of note:
Nicolaus Copernicus
1473 - 1543
De Revolutionibus Orbium Celestium
Tycho Brahe
1546 - 1601
Johannes Kepler
1571 - 1630
Astronomia Nova
Galileo Galilei
1564 - 1642
Siderius Nuncius
Dialogue on Two Chief World Systems
Discourse on Two New Sciences
Isaac Newton
1642 - 1727
Philosophiae Naturalis Principia Mathematica (1687)
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Nicolaus Copernicus
1473 - 1543
De Revolutionibus Orbium Celestium
Tycho Brahe
1546 - 1601
Johannes Kepler
1571 - 1630
Astronomia Nova
Galileo Galilei
1564 - 1642
Siderius Nuncius
Dialogue on Two Chief World Systems
Discourse on Two New Sciences
Isaac Newton
1642 - 1727
Philosophiae Naturalis Principia Mathematica (1687)
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For Galileo:
http://galileo.rice.edu/
http://galileo.rice.edu/bio/index.html
I also recommend "Galileo's Daughter" by Dava Sobel. Actually, anything she writes is pretty great historical reading. See also Sobel's book "Longitude."
It is also worth reading about Copernicus and the Scientific Revolution.
For those of you interested in ancient science, David Lindberg's "Beginnings of Western Science" is amazing.
In general, John Gribbin's "The Scientists" is a good intro book about the history of science, in general. I recommend this for all interested in the history of intellectual pursuits.
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More historical information regarding Newton:
http://en.wikipedia.org/wiki/Isaac_Newton
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More historical information regarding Newton:
http://en.wikipedia.org/wiki/Isaac_Newton
This is really exhaustive - only for the truly interested.
This one is a bit easier to digest:
http://galileoandeinstein.physics.virginia.edu/lectures/newton.html
We'll return to Newton's gravitation (along with Kepler) later in the course.
Monday, September 16, 2013
Gravity problems
1. Define the acceleration due to gravity (g).
2. A ball is dropped from rest from a great height. After 2.5 seconds, how fast is it traveling? How far did it fall in this time?
3. Consider dropping this same ball from a 10-m tower. How long will it take to hit the ground? This may require a little algebra.
4. Revisit problem 3. If this has been done on the Moon, would it take more, less or the same time to fall to the ground? How about on Jupiter?
The acceleration due to gravity!
We discussed the acceleration due to gravity in class. It is a value (g), and it is approximately equal to 9.8 m/s/s, near the surface of the Earth. At higher altitudes, it becomes lower - a related phenomenon is that the air pressure becomes less (since the air molecules are less tightly constrained), and it becomes harder to breathe at higher altitudes (unless you're used to it). Also, the boiling point of water becomes lower - if you've ever read the "high altitude" directions for cooking Mac n Cheese, you might remember that you have to cook the noodles longer (since the temperature of the boiling water is lower).
On the Moon, which is a smaller body (1/4 Earth radius, 1/81 Earth mass), the acceleration at the Moon's surface is roughly 1/6 of a g (or around 1.7 m/s/s). On Jupiter, which is substantially bigger than Earth, the acceleration due to gravity is around 2.2 times that of Earth. All of these things can be calculated without ever having to visit those bodies - isn't that neat?
Consider the meaning of g = 9.8 m/s/s. After 1 second of freefall, a ball would achieve a speed of .....
9.8 m/s
After 2 seconds....
19.6 m/s
After 3 seconds....
29.4 m/s
We can calculate the speed by rearranging the acceleration equation:
vf = vi + at
In this case, vf is the speed at some time, a is 9.8 m/s/s, and t is the time in question. Note that the initial velocity is 0 m/s.
Got it?
The distance is a bit trickier to figure. This formula is useful - it comes from combining the definitions of average speed and acceleration.
d = vi t + 0.5 at^2
Since the initial velocity is 0, this formula becomes a bit easier:
d = 0.5 at^2
Or....
d = 0.5 gt^2
Or.....
d = 4.9 t^2
(if you're near the surface of the Earth, where g = 9.8 m/s/s)
This is close enough to 5 to approximate.
So, after 1 second, a freely falling body has fallen:
d = 5 m
After 2 seconds....
d = 20 m
After 3 seconds....
d = 45 m
After 4 seconds...
d = 80 m
This relationship is worth exploring. Look at the numbers for successive seconds of freefall:
0 m
5 m
20 m
45 m
80 m
125 m
180 m
If an object is accelerating down an inclined plane, the distances will follow a similar pattern - they will still be proportional to the time squared. Galileo noticed this. Being a musician, he placed bells at specific distances on an inclined plane - a ball would hit the bells. If the bells were equally spaced, he (and you) would hear successively quickly "dings" by the bells. However, if the bells were located at distances that were progressively greater (as predicted by the above equation, wherein the distance is proportional to the time squared), one would hear equally spaced 'dings."
Check this out:
Equally spaced bells:
http://www.youtube.com/watch?v=06hdPR1lfKg&feature=related
Bells spaced according to the distance formula:
http://www.youtube.com/watch?v=totpfvtbzi0
Furthermore, look at the numbers again:
0 m
5 m
20 m
45 m
80 m
125 m
180 m
Each number is divisible by 5:
0
1
4
9
16
25
36
All perfect squares, which Galileo noticed - this holds true on an inclined plane as well, and its easier to see with the naked eye (and time with a "water clock.")
Look at the differences between successive numbers:
1
3
5
7
9
All odd numbers. Neat, eh?
FYI:
http://www.mcm.edu/academic/galileo/ars/arshtml/mathofmotion1.html
Wednesday, September 11, 2013
Homework problems in motion.
Woo Hoo – it’s physics problems and questions! OH YEAH!!
You will likely be able to do many of these problems, but possibly not all. Fret not, physics phriends! Try them all.
1. Determine the average velocity of your own trip to school: in miles per hour. Use GoogleMaps or something similar to get the distance, and try to recall the time from your last trip. Use your trip from home to Towson, or something that makes sense to you. If possible, do it in miles per hour AND m/s.
2. Consider an echo-y canyon. You stand 200-m from the canyon wall. How long does it take the echo of your scream (“Arghhhh! Curse you Physics!!!”) to return to your ears, if the speed of sound is 340 m/s? (Sound travels at a constant speed in a given environment.) Also, keep in mind that the sound has to travel away from AND back to the source.
3. What is the difference between traveling at an average speed of 65 mph for one hour and a constant speed of 65 mph for one hour? Will you go further in either case?
4. What is the meaning of instantaneous velocity? How can we measure it?
5. What is the acceleration of a toy car, moving from rest to 6 m/s in 4 seconds?
6. How far will a light pulse (say, a cell phone radio wave) travel in 1 second? In one minute? In one year? You don't have to work this out, but you should show HOW it would be calculated. Keep in mind that the light pulse travels AT the speed of light.
7. What does a negative acceleration indicate?
8. Consider an automobile starting from rest. It attains a speed of 30 m/s in 8 seconds. What is the car’s acceleration during this period?
1. Determine the average velocity of your own trip to school: in miles per hour. Use GoogleMaps or something similar to get the distance, and try to recall the time from your last trip. Use your trip from home to Towson, or something that makes sense to you. If possible, do it in miles per hour AND m/s.
2. Consider an echo-y canyon. You stand 200-m from the canyon wall. How long does it take the echo of your scream (“Arghhhh! Curse you Physics!!!”) to return to your ears, if the speed of sound is 340 m/s? (Sound travels at a constant speed in a given environment.) Also, keep in mind that the sound has to travel away from AND back to the source.
3. What is the difference between traveling at an average speed of 65 mph for one hour and a constant speed of 65 mph for one hour? Will you go further in either case?
4. What is the meaning of instantaneous velocity? How can we measure it?
5. What is the acceleration of a toy car, moving from rest to 6 m/s in 4 seconds?
6. How far will a light pulse (say, a cell phone radio wave) travel in 1 second? In one minute? In one year? You don't have to work this out, but you should show HOW it would be calculated. Keep in mind that the light pulse travels AT the speed of light.
7. What does a negative acceleration indicate?
8. Consider an automobile starting from rest. It attains a speed of 30 m/s in 8 seconds. What is the car’s acceleration during this period?
9. In the above problem, how far has it traveled in the 8 seconds?
10. Review these ideas. Write down answers, if it would be helpful.
a. standards for the m, kg, and s. Know the original meaning of the standard, and the current standard (approximate meaning - don't worry about the crazy numbers)
b. indicators of pseudoscience
11. Review your notes and the blog entries. Is anything especially unclear at this point?
Monday, September 9, 2013
Velocity and Acceleration
Motion!
THE EQUATIONS OF MOTION!
First, let's look at some definitions.
Average velocity
v = d / t
That is, displacement divided by time.
Another way to compute average velocity:
v = (vi + vf) / 2
where vi is the initial velocity, and vf is the final (or current) velocity.
Average velocity should be distinguished from instantaneous velocity (what you get from a speedometer):
v(inst) = d / t, where t is a very, very, very tiny time interval. There's more to be said about this sort of thing, and that's where calculus begins.
Now this idea (velocity) is pretty useful if you care about the velocity at a specific time OR the average velocity for a trip.
Approximately....
Keep in mind that 1 m/s is approximately 2 miles/hour.
Your walking speed to class - 1-2 m/s
Running speed - 5-7 m/s
Car speed (highway) - 30 m/s
Professional baseball throwing speed - 45 m/s
Terminal velocity of skydiver - 55 m/s
Speed skiing - 60 m/s
Speed of sound (in air) - 340 m/s
Bullet speed (typical) - 900 m/s
Satellite speed (in orbit) - 6200 m/s
Escape velocity of Earth - 11,200 m/s
(That's around 7 miles per second, or 11.2 km/s)
Speed of light (in a vacuum) -
This number is a physical constant, believed to be true everywhere in the universe. The letter c is used to represent the value being of constant celerity (speed).
On the other hand, if you care about the details of velocity, if and when it changes, then we need to introduce a new concept: acceleration.
Now this idea (velocity) is pretty useful if you care about the velocity at a specific time OR the average velocity for a trip.
Some velocities to ponder....
Keep in mind that 1 m/s is approximately 2 miles/hour.
Your walking speed to class - 1-2 m/s
Running speed - 5-7 m/s
Car speed (highway) - 30 m/s
Professional baseball throwing speed - 45 m/s
Terminal velocity of skydiver - 55 m/s
Speed skiing - 60 m/s
Speed of sound (in air) - 340 m/s
Bullet speed (typical) - 900 m/s
Satellite speed (in orbit) - 6200 m/s
Escape velocity of Earth - 11,200 m/s
(That's around 7 miles per second, or 11.2 km/s)
Speed of light (in a vacuum) -
c = 299,792,458 m/s
This number is a physical constant, believed to be true everywhere in the universe. The letter c is used to represent the value being of constant celerity (speed).
On the other hand, if you care about the details of velocity, if and when it changes, then we need to introduce a new concept: acceleration.
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Acceleration, a
a = (change in velocity) / time
a = (vf - vi) / t
The units here are m/s^2, or m/s/s.
Acceleration is a measure of how quickly you change your speed - that is, it's a measure of 'change in speed' per time. Imagine if you got in a car and floored it, then could watch your speedometer. Imagine now that you get up to 10 miles/hr (MPH) after 1 second, 20 MPH by the 2nd second, 30 MPH by the 3rd second, and so on. This would give you an acceleration of:
10 MPH per second. That's not a super convenient unit, but you get the idea (I hope!).
Acceleration is a measure of how quickly you change your speed - that is, it's a measure of 'change in speed' per time. Imagine if you got in a car and floored it, then could watch your speedometer. Imagine now that you get up to 10 miles/hr (MPH) after 1 second, 20 MPH by the 2nd second, 30 MPH by the 3rd second, and so on. This would give you an acceleration of:
10 MPH per second. That's not a super convenient unit, but you get the idea (I hope!).
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Today we will chat about the equations of motion. There are 5 useful expressions that relate the variables in questions:
vi - initial velocity. Note that the i is a subscript.
vf - velocity after some period of time
a - acceleration
t - time
d - displacement
Now these equations are a little tricky to come up with - we can derive them in class, if you like. (Remember, never drink and derive. But anyway....)
We start with 3 definitions, two of which are for average velocity:
v (avg) = d / t
v (avg) = (vi + vf) / 2
and the definition of acceleration:
a = (change in v) / t or
a = (vf - vi) / t
Through the miracle of algebra, these can be manipulated (details shown, if you like) to come up with:
vf = vi + at
d = 0.5 (vi + vf) t
d = vi t + 0.5 at^2
vf^2 = vi^2 + 2ad
d = vf t - 0.5 at^2
Note that in each of the 5 equations, one main variable is absent. Each equation is true - indeed, they are the logical result of our definitions - however, each is not always helpful or relevant. The expression you use will depend on the situation.
In general, I find these most useful:
vf = vi + at
d = 0.5 (vi + vf) t
d = vi t + 0.5 at^2
d = 0.5 (vi + vf) t
d = vi t + 0.5 at^2
By the way, note that the 2nd equation above is the SAME THING as saying distance equals average velocity [0.5 (vi + vf)] multiplied by time.
Let's look at a sample problem:
Consider a car, starting from rest. It accelerates uniformly (meaning that the acceleration remains a constant value) at 1.5 m/s^2 for 7 seconds. Find the following:
- the speed of the car after 7 seconds
- how far the car has traveled after 7 seconds
Then, the driver applies the brakes and brings the car to a halt in 3 seconds. Find:
- the acceleration of the car in this time
- the distance that the car travels during this time
Got it? Hurray!
There is another way to think about motion - graphically. That is, looking (pictorially) at how the position or velocity changes with time. We'll talk about this in class, and use a motion detector to "see" the motion a little better.
Physics - YAY!
SI Units
Some comments on standards. I use SI units a great deal in my classes. To inform you:
Mass is measured based on a kilogram (kg) standard.
Length (or displacement or position) is based on a meter (m) standard.
Time is based on a second (s) standard.
How do we get these standards?
Length - meter (m)
- originally 1 ten-millionth the distance from north pole (of Earth) to equator
- then a distance between two fine lines engraved on a platinum-iridium bar
- (1960): 1,650,763.73 wavelengths of a particular orange-red light emitted by atoms of Kr-86 in a gas discharge tube
- (1983, current standard): the length of path traveled by light during a time interval of 1/299,792,458 seconds
That is, the speed of light is 299,792,458 m/s. This is the fastest speed that exists. Why this is is quite a subtle thing. Short answer: the only things that can travel that fast aren't "things" at all, but rather massless electromagnetic radiation. Low-mass things (particles) can travel in excess of 99% the speed of light.
Long answer: See relativity.
Time - second (s)
- Originally, the time for a pendulum (1-m long) to swing from one side of path to other
- Later, a fraction of mean solar day
- (1967): the time taken by 9,192,631,770 vibrations of a specific wavelength of light emitted by a cesium-133 atom
Mass - kilogram (kg)
- originally based on the mass of a cubic decimeter of water
- standard of mass is now the platinum-iridium cylinder kept at the International Bureau of Weights and Measures near Paris
- secondary standards are based on this
- 1 u (atomic mass unit, or AMU) = 1.6605402 x 10^-27 kg
- so, the Carbon-12 atom is 12 u in mass
Volume - liter (l)
- volume occupied by a mass of 1 kg of pure water at certain conditions
- 1.000028 decimeters cubed
- ml is approximately 1 cc
Temperature - kelvin (K)
- 1/273.16 of the thermodynamic temperature of the triple point of water (1 K = 1 degree C)
- degrees C + 273.15
- 0 K = absolute zero
For further reading:
http://en.wikipedia.org/wiki/SI_units
http://en.wikipedia.org/wiki/Metric_system#History
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In addition, we spoke about the spherocity of the Earth and how we know its size. I've written about this previously. Please see the blog entries below:
http://howdoweknowthat.blogspot.com/2009/07/how-do-we-know-that-earth-is-spherical.html
http://howdoweknowthat.blogspot.com/2009/07/so-how-big-is-earth.html
Topics for the class
http://www.youtube.com/watch?v=oSCX78-8-q0
Just because it is cool.
8.28 Introduction; course philosophy
9.4 How things (don't) work
9.9 How things move, part 1: velocity, acceleration and the math of motion (1.1, 1.2)
9.11 How things move, part 2: Newton’s laws (1.2)
9.16 How things move, part 3: Newton's laws redux (1.3)
9.18 How things move, part 4: kites and planes, Bernoulli’s principle (6.2, 6.3)
9.23 How things move in space, part 1: center of gravity; keeping time (4.1)
9.25 No class
9.30 How things move in space, part 2: gravitation; Earth and Moon (4.2)
10.2 How things move in space, part 3: orbits (4.2)
10.7 Exam 1
10.9 How things sound, part 1: waves and music (9.1, 9.2)
10.14 How things sound, part 2: musical instruments (9.2)
10.16 How things sound, part 3: Doppler effect (9.2)
10.21 How things look, part 1: light, lasers, polarization (13.1, 14.1, 14.3)
10.23 How things look, part 2: lenses, mirrors, telescopes (15.1)
10.28 How things look, part 3: 3-d, optical illusions (15.1)
10.30 How things look, part 4: holograms
11.4 How things tick, part 1: particles, static electricity (10.1, 10.2)
11.6 How things tick, part 2: circuits (10.3)
11.11 Exam 2
11.13 How things tick, part 3: magnetism, electromagnetism (speakers, etc.) (11.1)
11.18 How things tick, part 4: induction (microphones, pickups) (11.2)
11.20 How things tick, part 5: weirdo electrical stuff (touchscreens, digital stuff, etc.) (11.2)
11.25 How things (might) work, part 1: relativity
12.2 How things (might) work, part 2: time travel
12.4 TBA
12.9 TBA
12.11 TBA - Last day of class
12.16 Final exam
Pseudoscience fun, FYI
Alien Autopsy film - when you watch it, consider what makes it believable or NOT believable.
If you ever have an hour to kill - the definitive documentary on pseudoscience and psychic stuff, in general.
Skepticism 101
Related to our brief foray into all things skeptical.
Good books, sites, etc.
by Michael Shermer:
Why people believe weird things
The believing brain
The science of good and evil
Science friction
Why Darwin matters
Skeptic Magazine
James "The Amazing" Randi
Flim Flam
Conjuring
The Faith Healers
An encyclopedia of claims, frauds and hoaxes of the occult and supernatural
Skeptical Inquirer
Skeptic's Dictionary
Richard Feynman - "Cargo Cult Science" essay
Martin Gardner
Fads and fallacies in the name of science
Carl Sagan
The demon-haunted world
Richard Dawkins
Climbing mount improbable
Schick/Vaughn
How to think about weird things
Other good essays and sites:
Wednesday, September 4, 2013
Pseudoscience
What Is Pseudoscience?
Distinguishing between science and pseudoscience is problematic
By Michael Shermer
Climate deniers are accused of practicing pseudoscience, as are intelligent design creationists, astrologers, UFOlogists, parapsychologists, practitioners of alternative medicine, and often anyone who strays far from the scientific mainstream. The boundary problem between science and pseudoscience, in fact, is notoriously fraught with definitional disagreements because the categories are too broad and fuzzy on the edges, and the term “pseudoscience” is subject to adjectival abuse against any claim one happens to dislike for any reason. In his 2010 book Nonsense on Stilts (University of Chicago Press), philosopher of science Massimo Pigliucci concedes that there is “no litmus test,” because “the boundaries separating science, nonscience, and pseudoscience are much fuzzier and more permeable than Popper (or, for that matter, most scientists) would have us believe.”
It was Karl Popper who first identified what he called “the demarcation problem” of finding a criterion to distinguish between empirical science, such as the successful 1919 test of Einstein’s general theory of relativity, and pseudoscience, such as Freud’s theories, whose adherents sought only confirming evidence while ignoring disconfirming cases. Einstein’s theory might have been falsified had solar-eclipse data not shown the requisite deflection of starlight bent by the sun’s gravitational field. Freud’s theories, however, could never be disproved, because there was no testable hypothesis open to refutability. Thus, Popper famously declared “falsifiability” as the ultimate criterion of demarcation.
The problem is that many sciences are nonfalsifiable, such as string theory, the neuroscience surrounding consciousness, grand economic models and the extraterrestrial hypothesis. On the last, short of searching every planet around every star in every galaxy in the cosmos, can we ever say with certainty that E.T.s do not exist?
Princeton University historian of science Michael D. Gordin adds in his forthcoming book The Pseudoscience Wars (University of Chicago Press, 2012), “No one in the history of the world has ever self-identified as a pseudoscientist. There is no person who wakes up in the morning and thinks to himself, ‘I’ll just head into my pseudolaboratory and perform some pseudoexperiments to try to confirm my pseudotheories with pseudofacts.’” As Gordin documents with detailed examples, “individual scientists (as distinct from the monolithic ‘scientific community’) designate a doctrine a ‘pseudoscience’ only when they perceive themselves to be threatened—not necessarily by the new ideas themselves, but by what those ideas represent about the authority of science, science’s access to resources, or some other broader social trend. If one is not threatened, there is no need to lash out at the perceived pseudoscience; instead, one continues with one’s work and happily ignores the cranks.”
I call creationism “pseudoscience” not because its proponents are doing bad science—they are not doing science at all—but because they threaten science education in America, they breach the wall separating church and state, and they confuse the public about the nature of evolutionary theory and how science is conducted.
Here, perhaps, is a practical criterion for resolving the demarcation problem: the conduct of scientists as reflected in the pragmatic usefulness of an idea. That is, does the revolutionary new idea generate any interest on the part of working scientists for adoption in their research programs, produce any new lines of research, lead to any new discoveries, or influence any existing hypotheses, models, paradigms or worldviews? If not, chances are it is pseudoscience.
We can demarcate science from pseudoscience less by what science is and more by what scientists do. Science is a set of methods aimed at testing hypotheses and building theories. If a community of scientists actively adopts a new idea and if that idea then spreads through the field and is incorporated into research that produces useful knowledge reflected in presentations, publications, and especially new lines of inquiry and research, chances are it is science.
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http://www.randi.org/site/index.php/encyclopedia.html
http://www.quackwatch.com/01QuackeryRelatedTopics/pseudo.html
http://en.wikipedia.org/wiki/Pseudoscience
http://www.skepdic.com/pseudosc.html
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