Tuesday, May 31, 2016
Tuesday, May 24, 2016
Some reading.
Brief history
From last class:
Ancient science highlights:
Epicycles
Precession
From class:
http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf
http://astro.unl.edu/naap/motion3/animations/sunmotions.swf
The most important things to get out of this were:
- Epicycles were a very useful way to (wrongly) explain why retrograde motion happened with planets.
- Precession (the wobbling of the Earth) causes us to have different North Stars (or no North Star) at various points over the course of thousands of years. Thus, star maps are not accurate after several hundred years. However, this was not understood until the time of Newton and others.
From class:
http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf
http://astro.unl.edu/naap/motion3/animations/sunmotions.swf
The most important things to get out of this were:
- Epicycles were a very useful way to (wrongly) explain why retrograde motion happened with planets.
- Precession (the wobbling of the Earth) causes us to have different North Stars (or no North Star) at various points over the course of thousands of years. Thus, star maps are not accurate after several hundred years. However, this was not understood until the time of Newton and others.
Scientific Revolution
N. Copernicus, d. 1543
De Revolutionibus Orbium Celestium
Galileo Galilei, 1564-1642
Siderius Nuncius
Dialogue on Two World Systems
http://galileo.rice.edu/sci/observations/sunspot_drawings.html
(J. Kepler, C. Huygens, R. Descartes, et. al.)
Isaac Newton, 1642-1727
Principia Mathematica, 1687
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.
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.
>
And now, in more contemporary language:
1. Newton's First Law (inertia)
An object will keep doing what it is doing, unless there is reason for it to do otherwise.
The 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 that force is unbalanced (greater than any resisting force), the object will accelerate.
Symbolically:
That's a linear relationship.
Greater F means greater a. However, if the force is constant, but the mass in increased, the resulting acceleration will be less:
a = F / m
That's an inverse relationship.
We have a NEW unit for force. Since force = mass x acceleration, the units are:
kg m / s^2
which we define as a newton (N). It's about 0.22 lb.
There is a special type of force that is important to mention now - the force due purely to gravity. It is called Weight. Since F = m a, and a is the acceleration due to gravity (or g):
W = m g
Note that this implies that: weight can change, depending on the value of the gravitational acceleration. That is, being near the surface of the Earth (where g is approximately 9.8 m/s/s) will give you a particular weight value, the one you are most used to. However, at higher altitudes, your weight will be slightly less. And on the Moon, where g is 1/6 that of the Earth's surface, your weight will be 1/6 that of Earth. For example, if you weight 180 pounds on Earth, you'll weight 30 pounds on the Moon!
3. Newton's Third 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. Strange, isn't it?
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 (m and M, let's say) 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), while the smaller object (M) experiences the larger acceleration (A).
And now, in more contemporary language:
1. Newton's First Law (inertia)
An object will keep doing what it is doing, unless there is reason for it to do otherwise.
The 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 that force is unbalanced (greater than any resisting force), the object will accelerate.
Symbolically:
F = m a
That's a linear relationship.
Greater F means greater a. However, if the force is constant, but the mass in increased, the resulting acceleration will be less:
a = F / m
That's an inverse relationship.
We have a NEW unit for force. Since force = mass x acceleration, the units are:
kg m / s^2
which we define as a newton (N). It's about 0.22 lb.
There is a special type of force that is important to mention now - the force due purely to gravity. It is called Weight. Since F = m a, and a is the acceleration due to gravity (or g):
W = m g
Note that this implies that: weight can change, depending on the value of the gravitational acceleration. That is, being near the surface of the Earth (where g is approximately 9.8 m/s/s) will give you a particular weight value, the one you are most used to. However, at higher altitudes, your weight will be slightly less. And on the Moon, where g is 1/6 that of the Earth's surface, your weight will be 1/6 that of Earth. For example, if you weight 180 pounds on Earth, you'll weight 30 pounds on the Moon!
3. Newton's Third 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. Strange, isn't it?
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 (m and M, let's say) 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), while the smaller object (M) experiences the larger acceleration (A).
Thursday, May 19, 2016
Fun practice
1. A rock is dropped from a 100-m high cliff. How long does it take to fall the first 50-m, and the second 50-m?
2. A juggler usually tosses balls vertically to a height H. To what height must they be tossed if they are to spend twice as much time in the air?
3. Two objects are begin a free fall from rest from the same height, 1 second apart. How long after the first object begins to fall are the 2 objects 10 m apart?
4. A hot air balloon is ascending at a rate of 12 m/s and is 80-m above the ground when a package is dropped over the side. How long does it take the package to hit the ground, and with what speed does it hit the ground?
2. A juggler usually tosses balls vertically to a height H. To what height must they be tossed if they are to spend twice as much time in the air?
3. Two objects are begin a free fall from rest from the same height, 1 second apart. How long after the first object begins to fall are the 2 objects 10 m apart?
4. A hot air balloon is ascending at a rate of 12 m/s and is 80-m above the ground when a package is dropped over the side. How long does it take the package to hit the ground, and with what speed does it hit the ground?
Tuesday, May 10, 2016
Test and Lab due dates
May 16: Lab draft due
May 18: Complete lab due
May 20: Test on Motion
Also, try this fun problem: The Drowsy Cat
A drowsy cat is sleeping on a window sill (2-m tall). Someone throws a ball up past the window, and the cat (being a keen observer, as all cats are) notices that the ball is in view for a total of 0.5 seconds (up and down). How far ABOVE the top of the window does the ball actually go?
May 18: Complete lab due
May 20: Test on Motion
Also, try this fun problem: The Drowsy Cat
A drowsy cat is sleeping on a window sill (2-m tall). Someone throws a ball up past the window, and the cat (being a keen observer, as all cats are) notices that the ball is in view for a total of 0.5 seconds (up and down). How far ABOVE the top of the window does the ball actually go?
Monday, May 2, 2016
the new Lab
OK, it's time to start thinking about your lab write-up. This will ultimately be due next week some time. Here is what your lab will need:
1. Introduction - with purpose and discussion of the "problem" - this is more than just the purpose. Give some background to what you are trying to do/measure.
2. Detailed equipment list
3. Detailed procedure, as you did it - make sure that a total stranger can follow your method.
4. Data table - with all calculations done
5. Graphs, if relevant
6. Sample of calculation - you need to do them all, but you only need to SHOW one sample
7. Discussion of error - the things that you really can not control
8. Discussion of other errors - things that could conceivably be eliminated (and how to do so)
9. Discussion of how close you are to the accepted value of g (9.8 m/s/s)
10. General conclusion
It is ok to have 7-9 in one large section.
1. Introduction - with purpose and discussion of the "problem" - this is more than just the purpose. Give some background to what you are trying to do/measure.
2. Detailed equipment list
3. Detailed procedure, as you did it - make sure that a total stranger can follow your method.
4. Data table - with all calculations done
5. Graphs, if relevant
6. Sample of calculation - you need to do them all, but you only need to SHOW one sample
7. Discussion of error - the things that you really can not control
8. Discussion of other errors - things that could conceivably be eliminated (and how to do so)
9. Discussion of how close you are to the accepted value of g (9.8 m/s/s)
10. General conclusion
It is ok to have 7-9 in one large section.
Thursday, April 21, 2016
Tuesday, April 12, 2016
HW for Thursday
1. Consider a car starting from rest. If it has an acceleration of 4 m/s/s, find the following:
a. how fast the car is moving after 7 seconds
b. how far the car has gone in this time
2. Consider a falling object, subject only to gravity (a = 9.8 m/s/s, with no air resistance).
a. How fast is a falling ball moving after 3 seconds of freefall?
b. How far will it have fallen in this time?
3. If a ball is dropped from 15 m, how long does it take to hit the ground? Assume that the acceleration is due only to gravity and that there is no air resistance.
4. Consider a baseball pitch, starting from rest and accelerating up to 45 m/s in a 0.5 m pitching arc. Find:
a. the acceleration of the ball
b. the time that the pitcher is in contact with the ball
5. Try this: Derive a "5th equation of motion," in which initial velocity (Vi) is absent.
ALSO - WE WILL HAVE A QUIZ IN 2 CLASSES. Units, unit conversions, speed....
a. how fast the car is moving after 7 seconds
b. how far the car has gone in this time
2. Consider a falling object, subject only to gravity (a = 9.8 m/s/s, with no air resistance).
a. How fast is a falling ball moving after 3 seconds of freefall?
b. How far will it have fallen in this time?
3. If a ball is dropped from 15 m, how long does it take to hit the ground? Assume that the acceleration is due only to gravity and that there is no air resistance.
4. Consider a baseball pitch, starting from rest and accelerating up to 45 m/s in a 0.5 m pitching arc. Find:
a. the acceleration of the ball
b. the time that the pitcher is in contact with the ball
5. Try this: Derive a "5th equation of motion," in which initial velocity (Vi) is absent.
ALSO - WE WILL HAVE A QUIZ IN 2 CLASSES. Units, unit conversions, speed....
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