Tuesday, May 31, 2016
Tuesday, May 24, 2016
Some reading before class
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
(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).
Tuesday, May 10, 2016
Saturday, May 7, 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, after you've had some class time to work on it. 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. We're talking about a couple of introductory paragraphs or so.
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) - percent error.
10. General concluding remarks
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. We're talking about a couple of introductory paragraphs or so.
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) - percent error.
10. General concluding remarks
It is ok to have 7-9 in one large section.
Tuesday, May 3, 2016
Practice problems
Here are two more practice problems for the equations of motion:
1. A car starts from rest and accelerates at 5 m/s/s. After 8 seconds of continual acceleration:
a. how fast is it moving?
b. how far has it gone?
(40 m/s, 160 m)
2. This one may require a bit of algebra. If you were to drop a ball (from rest) from a 50-m tall tower, find:
a. how long it takes to hit the ground?
b. how fast it will be traveling right before it hits?
(3.19 seconds, 31.3 m/s)
Don't forget to review the new lab stuff, too! (It is just below this on the blog.)
Also, answers to the recent quiz:
1. 3.65 days
2. approx. 9, 612,173
3. on the order of 140 million (or somewhere in the 10^8 range)
4. 27,273
1. A car starts from rest and accelerates at 5 m/s/s. After 8 seconds of continual acceleration:
a. how fast is it moving?
b. how far has it gone?
(40 m/s, 160 m)
2. This one may require a bit of algebra. If you were to drop a ball (from rest) from a 50-m tall tower, find:
a. how long it takes to hit the ground?
b. how fast it will be traveling right before it hits?
(3.19 seconds, 31.3 m/s)
Don't forget to review the new lab stuff, too! (It is just below this on the blog.)
Also, answers to the recent quiz:
1. 3.65 days
2. approx. 9, 612,173
3. on the order of 140 million (or somewhere in the 10^8 range)
4. 27,273
The New Lab!
Hey everybody!
As discussed in class, the new lab will have you trying to determine the acceleration due to gravity. We have heard that this should be close to 9.8 m/s/s, but how can we be sure? Here are some techniques for finding this value.
1. The dropped object method.
Drop an object from a measured height (d) and record the time (t) for it to fall. Calculate the acceleration (a) from this. You can try a large height (such as in the atrium, using a stopwatch), or you can use a small height with a photogate (and shut-off switch) set-up.
2. The pendulum method.
You know from earlier in the year that the period of a pendulum (T) is given by an equation:
In this equation, T is period/time for one swing (in seconds), L is length (in meters), and g is the acceleration due to gravity.
3. The ticker-tape method.
This is maybe the most novel method, and it gives you a lot of data. However, the analysis is probably the longest. A ticker-tape timer will vibrate 60 times per second (60 Hz is the frequency), which will give 60 dots per second on a piece of "ticker tape." By measuring the distance between dots and calculating the increasing speeds - details to be discussed in class - you can, in principle, determine the acceleration.
4. The single photogate method.
In this method, you will release a ball from rests and allow it to fall a measured distance (d). It will achieve a certain velocity (Vf) at the bottom of the fall - the photogate should give you the final velocity, if used correctly.
So there you have it - 4 methods for finding g. There are others, of course, but these 4 can be done in our classroom.
Consider these 4 methods and decide which one is most interesting to you. You will perform the experiment during the next class.
In preparation, start to write-up a tentative outline of how you plan to collect data. It is ok to leave out the technical details at this point, since you probably don't know how to use the new equipment yet.
In your final lab report, you will have a detailed procedure - something that a total stranger could conceivably follow - and a materials list. You will have other lab report things as well.
As discussed in class, the new lab will have you trying to determine the acceleration due to gravity. We have heard that this should be close to 9.8 m/s/s, but how can we be sure? Here are some techniques for finding this value.
1. The dropped object method.
Drop an object from a measured height (d) and record the time (t) for it to fall. Calculate the acceleration (a) from this. You can try a large height (such as in the atrium, using a stopwatch), or you can use a small height with a photogate (and shut-off switch) set-up.
2. The pendulum method.
You know from earlier in the year that the period of a pendulum (T) is given by an equation:
In this equation, T is period/time for one swing (in seconds), L is length (in meters), and g is the acceleration due to gravity.
3. The ticker-tape method.
This is maybe the most novel method, and it gives you a lot of data. However, the analysis is probably the longest. A ticker-tape timer will vibrate 60 times per second (60 Hz is the frequency), which will give 60 dots per second on a piece of "ticker tape." By measuring the distance between dots and calculating the increasing speeds - details to be discussed in class - you can, in principle, determine the acceleration.
4. The single photogate method.
In this method, you will release a ball from rests and allow it to fall a measured distance (d). It will achieve a certain velocity (Vf) at the bottom of the fall - the photogate should give you the final velocity, if used correctly.
So there you have it - 4 methods for finding g. There are others, of course, but these 4 can be done in our classroom.
Consider these 4 methods and decide which one is most interesting to you. You will perform the experiment during the next class.
In preparation, start to write-up a tentative outline of how you plan to collect data. It is ok to leave out the technical details at this point, since you probably don't know how to use the new equipment yet.
In your final lab report, you will have a detailed procedure - something that a total stranger could conceivably follow - and a materials list. You will have other lab report things as well.
Friday, April 29, 2016
Equations of motion HW
The equations of motion are given above. Try these problems. Solutions will be coming over the weekend. Thanks!
1. (From last homework.) How far will a freely-falling body fall in 4 seconds? There is no air resistance.
2. A car starts from rest and achieves a speed of 30 m/s in 4 seconds. Find:
a. the acceleration
b. the distance that it goes in the 4 seconds
Now the same car applies the brakes once it has achieved 30 m/s. If the car stops in 2 seconds, find:
a. the acceleration
b. how far the car travels in the 2 seconds
3. Consider throwing a ball up in the air with an initial speed of 30 m/s. I suggest that you call up positive (which makes gravity negative).
a. How long will it take for the ball to reach apogee (the top)?
b. How high will it go?
b. How high will it go?
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