Program assessment - we will fill this out during our final class

https://www.surveymonkey.com/s/GMHFQCJ

Newton and Gravitation

Newton

Newton's take on orbits 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 25 m/s/s.

Kepler's Laws

Kepler's Laws

Kepler's laws of planetary motion

http://astro.unl.edu/naap/ssm/animations/ptolemaic.swf

http://astro.unl.edu/naap/pos/animations/kepler.swf


Johannes Kepler, 1571-1630

Note that these laws apply equally well to all orbiting bodies (moons, satellites, comets, etc.)

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

The image below calls period P (rather than T), but the meaning is the same:

Example problem:  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.


The applets I referenced::

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

Homework due NEXT class!!!!

Also, make sure that your lab group has submitted the complete informal Mechanics lab.

This is due at the beginning of our first class next week.

Phinal Physics Phun-signment!  (Get it?)

1.  You have a model rocket with a mass of 0.050 kg.  It contains an engine that delivers a thrust force of 10-N for 0.8 seconds.  Answer the following questions based on this data.

a.  What is the weight of this rocket?

b.  What is the NET force acting on this rocket during the thrust period?  (Keep in mind that the engine pushes up, while the weight acts down.)

c.  What will be the acceleration of this rocket?

d.  If we assume that the rocket starts at rest, what will be the final velocity of the rocket before the engine stops burning?

e.  How high will the rocket go during this time period?

f.  Will the rocket continue to rise after the engine burns out?  If not, how far additionally will it rise?



2.  Consider standing on a scale in an elevator.  The scale has a spring inside of it, causing an "effective weight" measurement to be given.  A 130-lb (while at rest) woman stands on the scale in the elevator.  Answer the questions below thusly:  equal to 130 lb, less than 130 lb, greater than 130 lb, 0 lb.

a.  If the elevator is moving upward at a constant velocity, what will the scale read?

b.  If the elevator is moving downward at a constant velocity, what will the scale read?

c.  If the elevator is moving upward at a constant acceleration, what will the scale read?

d.  If the elevator is moving downward at a constant acceleration, what will the scale read?

e.  If the elevator were freely falling (uh oh....), what will the scale read?

3.  Pick one idea or topic that has captured your imagination during the motion/mechanics unit.  Describe or discuss it briefly.

Newton!

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.

>

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 trick 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).

F-block HW

Create two interesting units of speed - show how to create their conversion factors from m/s.

HW for Monday's A-block class

1.  Come up with a way/method to convert m/s to miles per hour.  Show all work.  You can check it by running it through a google converter, wherein you compare what google gives you to what your conversion factor does.

2.  Look up (or create!) any other interesting unit of speed - and show how to convert m/s to it.

Last minute practice

Find the time for a ball to fall 7-m from rest.  If the ball had been kicked horizontally at 4 m/s, how far would it have traveled?

Heading west in a motorboat at 15 m/s, you encounter a 5 m/s current north.  At the end of 400-m, how far off course are you?  And how much time did you spend to get there?

HW for Wednesday/ Thursday

1.  A ball is thrown horizontally off a building.  It takes 2 seconds to hit the ground, and it lands 15-m from the base of the building.  How tall is the building and what was is original horizontal velocity?

2.  This problem is a little different.  You're trying to cross a river which has a current of 8 m/s south.  You head directly across at 5 m/s east.  The river is 100-m wide.  How long does it take to cross and how far downstream do you land?

In this problem, the two velocities are acting simultaneously. There is no acceleration, so v=d/t is helpful here.

HW for Wednesday (F) and Thursday (A)

F:  These are the problems that were on the board yesterday.  Nothing new here.

1.  Consider a ball kicked off a 30-m tall cliff with an initial speed of 20 m/s.  How long does it take to hit the ground below?  (The quadratic formula, if you know how to use it, makes this problem a bit easier - or at least, then it can be done in step.)

2.  The drowsy cat.  A cat sits on a window sill (2-m in height).  It notices that a flowerpot sails up and past the top of the window (still moving up), then down and past the cat again (still moving down).  The total amount of time that the flowerpot is in sight is 1/2 a second (1/4 up and 1/4 down). How high ABOVE the top of the window frame does the flowerpot travel?  (Yes, this is a tricky problem.)

3.  Bonus, slightly less tricky problem.  A ball falls from rest.  It takes 1 second to fall the second half of its path downward.  From what height was it released and how long was it in air?

Reminder

Lab draft due and brief quiz next class (Friday A, Monday F)

HW for Monday (A) and Tuesday (F)

Use the equations of motion (where helpful) to solve the following problems.

1.  Consider a sports car, capable of accelerating from rest at 5 m/s/s.  If it accelerates uniformly for 8 seconds, find:

a.  the velocity after 8 seconds
b.  how far the car has gone in this time

Now assume that the driver applies the brakes and the car uniformly comes to a halt in 3 seconds.

c.  What is the acceleration during this braking time?
d.  How far does the car go during this time?

Draw two graphs that represent:

a.  the displacement vs. time for the entire trip
b.  the velocity vs. time for the entire trip


2.  Imagine that a falling body accelerates at 10 m/s/s.  It is released from a high tower:

a.  If it takes 3.5 seconds to hit the ground, how fast is it traveling immediately before hitting the ground?
b.  If it took 3.5 seconds to hit the ground, how tall was the tower from which it was released?

Keep working on your lab report.  Expect a draft to be due by Friday.

HW

As mentioned in class:

Use Google maps, etc. to "map out" your trip to school.  Find the following:

distance

time - you should probably use your own approximate time to school in the morning.  Convert to hours (dividing minutes by 60)

displacement - measure on the screen (start to end) and use the scale to convert to miles

Then calculate:

speed
velocity

Please work in miles and hours.

Arduino links

Here is a download link for code for several Arduino projects in the Sik guide:

sparkfun.com/sikcode

And the guide is here:

http://dlnmh9ip6v2uc.cloudfront.net/datasheets/Kits/SFE03-0012-SIK.Guide-300dpi-01.pdf

HW for Thursday (A) and Friday (F)

THIS WILL BE COLLECTED.

Static electricity review:

1.  Consider a chunk of charge equal to 5 coulombs.

a.  How many protons is this?

b.  If another chunk of charge equal to -5 coulombs is brought to a point 0.1-m away from the first charge, what is the force between the two chunks of charge?

c.  Draw the electric field between these two chunks of charge.


2.  In the circuit below, find the total resistance, battery current and fill in the chart.

3.  In this collection of equal-resistance light bulbs below, list the bulbs in order of brightness (brightest first).

Lab update

Draft due Friday (A) and Monday (F).


Lab calculations

You've (ideally) finished the calculations for the series part of the experiment:

total resistance
percent difference from the theoretical (65 ohms)

If you haven't yet done the parallel calculations, do them:

- total experimental resistance (battery voltage divided by battery current)
- total theoretical resistance - use this formula:
   1/Rp = 1/R1 + 1/R2

The easiest way to proceed is to use the x^-1 key on your calculator.  Don't forget to take the inverse of the sum of the inverses.

- percent difference between theoretical resistance and experimental resistance

Keep working on lab.  You'll still need the usual things:

title
purpose
data table(s)
calculations
conclusion (use the lab questions as a 'jumping off' point - make sure you answer the questions in bold)
sources of error, ways to improve, etc.

HW

In addition to working on the lab, here are circuit questions to think about (A block - Wednesday; F-block - Thursday):

1.  Consider 3 resistors in series with a 12-V battery, with resistances equal to 1, 2 and 3 ohms.  Find the following:

a.  total resistance
b.  current from battery
c.  current through each resistor
d.  voltage over each resistor

2.  Consider 3 resistors in parallel with a 12-V battery, with resistances equal to 1, 2 and 3 ohms.  Find the following:

a.  total resistance
b.  current from battery
c.  current through each resistor
d.  voltage over each resistor

3.  Imagine if you had a circuit with a 12-V battery in series with a 4-ohm resistor - and this is in series with a parallel combination of resistors (3 and 6 ohms).  How would you treat this circuit, if you wanted to determine the total resistance, and all currents and voltages?  Give this a shot, if you have time.

Lab writeup questions

Folks,

You have some data for a series circuit and a parallel circuit.  I will give you some "leading questions" to help you frame your formulation of Kirchoff's Rules.  The questions in bold are to be answered in your lab report.

I.  Series Circuit

Think about these things: 

- What do you find to be true about the voltages?  

- What do you find to be true about the currents?  

- How do the individual voltages compare to the battery voltage?

- How do the individual currents compare to the battery current?

Write a general rule about voltages in a series circuit.

Write a general rule about currents in a series circuit.

Calculations (you may have to wait until next class for these):

What is the total resistance of this circuit (according to the values of the resistors given in class from the stripes)?

What is the total resistance of this circuit according to calculation?  (R = battery voltage divided by battery current)

II.  Parallel Circuit

- What do you find to be true about the voltages?

- What do you find to be true about the currents?  

- How do the individual voltages compare to the battery voltage?

- How do the individual currents compare to the battery current?

Write a general rule about voltages in a parallel circuit.

Write a general rule about currents in a parallel circuit.

Calculations (you may have to wait until next class for these):

What is the total resistance of this circuit (according to the values of the resistors given in class from the stripes)?

What is the total resistance of this circuit according to calculation?  (R = battery voltage divided by battery current)

Other general questions to answer:

Did you notice if resistors got hot?  Why might this be?

What exactly is Ohm's Law?  Does it apply to all electrical components?

What do you think "tolerance" is, as applied to resistors.  For example, if a resistor is said to have a 10% tolerance, what can that mean?

Give sources of error in this experiment.

A block HW

Graph your lab data:

I vs. R

That is, I (on the y-axis) vs. R (on the x-axis).

What do you make of this relationship?  Does it make sense in light of the definition of resistance?

Also, draw an electrical schematic for your circuit, using the symbols for battery, resistance and wire.  You may have to look up the symbols online.

Also, try the F-block problems posted earlier, if you have time.

HW for F-block

Please review definitions of voltage, current, and resistance (along with their units).

1.  How long would it take a circuit carrying 4 amps to pass 50 coulombs of charge?

2.  A 9-V battery is attached to a resistor.  As a result, 0.1-A of current passes through it.  What is the resistance of the resistor?

3.  Look up the schematic symbols for battery, wire and resistor.  Draw a basic circuit which depicts the bulb and battery arrangement we made in class.

For next class (Friday and Monday)

Find definitions for:

- current 

- resistance

Thank you.

HW

Come to class with a definition of energy that is better than my "blocks" analogy.

HW

How do batteries work?  Find out and write about it in your notes.

HW - electric fields (for Thurs/Fri)

Draw electric fields for each of the following:

a.  big hunk of negative charge
b.  big hunk of positive charge
c.  negative charge and positive charge separated by a short distance
d.  positive charge and identical positive charge separated by a short distance
e.  negative charge and identical negative charge separated by a short distance

Play around with this.  It should run on most machines:

http://phet.colorado.edu/en/simulation/charges-and-fields

Place charges on the screen and click "show E-field" and "direction only".

Start simple and go crazy.

If your computer will allow, these are great:

http://www.falstad.com/emstatic/

http://www.falstad.com/vector3de/

HW

For Tuesday/Wednesday class;

Look up (in physics classroom or elsewhere) information about electric fields.

If your computer allow it, play around with this applet:

http://www.falstad.com/emstatic/

Coulomb's law HW

1.  What are each of the quantities in the Coulomb's law equation, and what are their units?

2.  a.  Calculate the force that exists between two clusters of charge (each 10 micro coulombs), 0.1-m apart.  The prefix "micro" means x 10^-6.
b.  Is this force attractive or repulsive?  How do you know?

3.  If you have a cluster of charge that is 5 C in magnitude, how many protons is this?

4.  Thinking about the inverse square law - if the distance between two charges is changed to five times the original distance, what exactly happens to the force between them (compared to the original force)?

5.  If the distance between two charges is changed to half the original distance, what exactly happens to the force between them (compared to the original force)?

6.  The radius of a typical Hydrogen atom is 53 pm (5.3 x 10^-11 m) -- the distance between a proton and electron in "orbit" around it.  What is the force between these two particles?

HW

Find out something about:

Coulomb's law (including the equation)
Electric fields

HW to turn in Thursday (F) or Friday (A)

1.  Find out about a few examples of how holography is used today.  Or if you're feeling ambitious, suggest some uses for it.

2.  Diffraction question

You are sending light through a diffraction grating that has 300,000 slits/openings per meter.  You aim a blue laser at it (wavelength = 475 x 10^-9 m).  The laser and grating is 1-m from a wall.  Find:

a.  the value for d (the distance between the slits)
b.  the diffraction angle for a first order (n = 1) image
c.  the distance between the central image (n = 0) and the first (n = 1) image.  Use trig here.
d.  Draw this situation.
e.  How many dots would you see on the wall?
f.  If you used a red laser, would the dot spacing change?  If so, how?

HW

F block - come to class with some type of definition of "charge" (the electrical type).

A block - come to class with some understanding/definition of holography (if you haven't yet done this).  Also, look into x-ray diffraction, if you have not yet done this.

Happy weekend!

late update (for F block).

For Friday's F-block class -- Look into x-ray diffraction a bit more.  And also find out a little about holography.  Sorry for the delay.

HW

Please do a little reading about light diffraction.  Find out what it is, and if possible, find a mathematical expression that represents it.