2009

Tuesday, August 18, 2009

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Acceleration of gravity (g) universal gravitation

A body of mass m is attracted to Earth with a force that is worth its weight and P = mg. But under the law of universal gravitation, this force is also true: F = GmM/r2

, where M is the mass of Earth and r is the distance from the center of the Earth to the body of mass m. These forces being equal, is:

mM/r2 mg = G, ie g = GM/r2

Through this formula we can calculate the value of ga any distance from the center of the Earth, conocinedo M mass of it and the distance r.

This formula indicates that the farther from the center of the earth the acceleration of gravity is lower and, therefore, the bodies that they will fall uniformly accelerated motion, because as the body falls the value of g increases.

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The law of universal gravitation was released by Isaac Newton in 1686 and the myth says it was inspired by an apple falling from a tree. His statement is:

"Every body in the universe attracts the other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance that separates"

F = G m1 * M2 / r2, where G is a gravitational constant, put there by Cavendish (English, 1731-1810) using a torsion balance. G = 6.67 x10 (-11) (Mm2/Kg2) in MKS

This value of G means that two masses of 1 Kg 1 m are attracted by the power of 6.67 x10 (-11) N.

Friday, August 14, 2009

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Universal Gravitation Problems

1. Aceleracionde calculate gravity at the lunar surface if the dough is 1 / 81 the mass of Earth and its radius is 1738 km Mass of Earth = 6x10 (24) Kg
Answer: Done in class

2. At one point on Earth is a satellite of 500 kg on the Earth's gravitational field which acts with the force of 4000 Newton. What is the gravitational field strength and the acceleration of gravity at that distance?
A. Remember
gravitational field strength g = F / m, so 4000/500 = 8 N / kg .
The acceleration of gravity has the value mime 8 m/s2.

3. Calculate the gravitational field strength at 630 km from the earth's surface if the mass of Earth is 5.98 x 10 (24) kg and its radius 6370 km?
A. mM/r2
mg = G, the radius is 6370 km + 630 km = 7000 km, or 7 million m
is replaced in the equation and go: g = 8.14 m/s2 .

4. How far from the earth's surface rotates in a circular orbit sateliute if its mass is 1000 kg and the field acting on it with the force of 8000N?
A. Using F = GmM/r2, the radius is 6370 + d is squared. The 6370 km need to be transformed to meters. The result is d = 690 km approx.

Answer: 5. Calculate the gravitational field strength at a point located 3630 km from the earth's surface if the mass of Earth is 5.98 x 10 (24) kg and G = 6.67 x10-11
Answer:
The attractive force is equal weight, therefore we can equate P = G * mM/r2
if P = mg, mg = GmM/r2 say.
Masses are simplified and is g = GM/r2. replace the data, remember that the radius is 6370 km + 3630 = 10,000 km, that is 10 million meters from the center of the Earth. gives g = 4 N / kg or 4 m/s2 .

6. A 80-kg satellite rotates in a circular orbit. If the gravitational field acting on the satellite with a force of 16N. What is the gravitational field strength at that distance?
Answer:
gravitational field strength is expressed as g = F / m and its unit is N / Kg.
Then F = 16N m = 80kg, giving a g = 0.2 N / Kg .

Kepler

1. Revoluciuón period of Saturn is about 29.5 years. Calculate the distance from the sun. (Period of the earth = 1 and distance from the Sun = 1 AU) (1 AU = 1.5 x 10 (8) km)
Answer: Done in class.

2. The acceleration of gravity Mars relative to Earth is 0.37. Calculate the acceleration of gravity on Mars if Earth is m/s2 9.8 m/s2
Answer: aceleracionde
if Earth gravity is 9.8 m/s2 and that of Mars is 0.37 times that of Earth, then it says: g * g Mars = 0.37 Earth. The product gives a of 3.62 g on Mars m/s2.

3. The Earth's average density is 5.5 g/cm3 and that of Mars with relation to the Earth is 0.69. What is the density in g/cm3 Mars?
Answer:
take the density value of the Earth as 1 unit and that of Mars is 0.69 units. Then by rule 3 is obtained D = 3.79 g/cm3 Mars.

4. Calculate the acceleration of gravity at a point in the distance to the Moon is the Earth which is 60 Earth radii.
Answer:
g1 on the surface of the earth is GMt/r2 and g2 to the distance of the Moon is GMt / (60r) 2
by dividing both equations gives G1/G2 = (60r) 2/r2 = 3600 / 1
where g2 = 1 / 3600 * g1, g1 is taken as 9.8 m/s2 and you get g2 = 2.7 x10 (-3) m/s2.

Friday, May 22, 2009

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The free fall is uniformly retarded MUA

formulas are valid:
a) vf = gt
b) h = 1 / 2 g t2
c) VF2-VI2 = 2GH
and when you release the body from a height h, we have that vi = 0, then
2GH vf = Root

Note: In the fall of bodies of air resistance increases with the rate of fall. In the first few seconds the resistance is small and grows with increasing speed, until after a certain time is equal to the weight of the body and the acceleration vanishes, ie, from that moment the body reaches its limit speed, continuing the fall with uniform motion.

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Movement (MUR)

Al MUR is also called negative acceleration or retardation (-a)

If v (final) - v (initial) v (final) is less than vinicial, then -a = v (final) - v (initial) / t
hence v (final)-v (initial) =-a \u200b\u200b* t

If v (final) = 0 (stop), then the equation would -v ( initial) =-a \u200b\u200b* tmax
The time it takes for the body to stop is called "maximum time (tmax)
Therefore tmax = vi / a

The maximum space (dmax) is the path by phone from the moment that begins the delay until it stops.
If d = Vm * t ; vi-vf / 2 = Vm , then d = (vi + vf / 2) * t if vf = 0 and t = tmax = vi / a

Substituting d = vi / 2 * vi / 2 = vi2/2a , thus
dmax = vi2/2a
know that vf = vi-a * t ; d = Vm * t , replace in Vm = (Vi + Vf) / 2
Then d = (vi + vi-a * t) / 2 * t
d = (2vi - a * t / 2) * t , this means that the multiplication is: d = (2vi * t - a * t) / 2
ie d = vi * t - a / 2 * t2

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Uniformly Accelerated Motion (MUA)

A Mobile has a uniformly accelerated motion when the body increases or decreases speed kept pace.
if a = delta v / t, then V = V0 + at
The mobile photo ever experience the same gear.

average acceleration a = v (final) - v (initial) / t = delta v / delta t
the average speed is Vm = v (final) + v (initial) / 2
Space traveled during time t will d = Vm * t

know that d = Vm * t and Vm = (vi + vf) / 2 ie d = (vi + vf) / 2 * t , but
vf = vi + at , then
d = (vi + vi + at) / 2 * t , rearranging: d = (2 vi + at) / 2 * t
being d = (vi * t + t2) / 2
therefore d = vi * t + a / 2 * t2 We

other deduction:
know vf-vi = a * t ; d = Vm * t , then vf-vi = a * (d / Vm) Vm
(vf - vi) = a * d but as Vm = (vf + vi) / 2
then (vf + vi) / 2 * (vf-vi) = a * d , this equation is multiplied by 2
(vf + vi) ( vf-vi) = 2ad
VF2 - VI2 = 2ad if vi = 0, then VF2 = 2ad therefore 2ad vf = Root

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Movement Speed \u200b\u200bGraphic Acceleration vs time

accelerated or varied movement is called to any movement whose speed does not remain constant, ie a movement in which the speed increases, decreases (slow) or change direction. This movement is typical of a roller-coaster car.

Acceleration is the change of speed over a period of time: a = delta v / delta t
where v = v (final) - v (initial)
The acceleration of a mobile can be as distance graph vs. time or velocity vs. time.

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In this type of graph, the area under the curve corresponds to displacement (m) of a mobile and obtained by removing the total area dividing it into smaller areas such as squares, rectangles or triangles, which are easily calculable.

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uniform linear motion (MRU)

MUR = uniform rectilinear movement characterized by very regular and therefore predictable over time. Therefore a displacement body performs the same in equal time intervals. The graph distance (x) vs time (t) shows a straight line with equal slope. The slope in this type of graph corresponds to the speed.

The slope (n) is obtained as n = delta and / delta X

yes, we know that Vm = d (final) - d (initial) / t
applying the equation we have to d (final) = d (initial) + vt

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average speed (Vm): is defined as the ratio of the total distance traveled by a body (d) and total time (t) used in this way. Vm = d / t

Average speed (Vm vector): The average speed is the ratio between the movement performed and the total time.

Velocity is a vector quantity because it depends on one direction, while speed is a scalar quantity because it depends on the direction.

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Speed \u200b\u200band Movement Speed \u200b\u200band rest on Movement and Rest

The Movement is a change of body position relative to a reference. It is clear that the direction of motion is relative, because if we go on a plane, traveling companions are seen as at rest relative to us and we can say that they sleep in their seats with ease. However, transparent aircraft fuselage, a person who is outside would say that all passengers and make it move at lightning speed, to the observer outside the aircraft. Thus, the movement depends on the observer. Usually
our reference system is usually the earth and the mountains as the mountains of the Andes are clearly at rest, but if you look at the mountains from the moon would see that it moves at breakneck speed. Career

: the curve or road course that describes the body as it moves from point A to point B. Displacement

: The shift experienced by the body from point A to point B, regardless of the way through. Is represented as a straight line or arrow from A to B

Distance traveled: the path length or distance actually traveled by a mobile.

Saturday, April 11, 2009

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that was years ago, a scientist initiated a conference on the move giving two blows with his fist on the table, with an interval of 2 seconds between them. After that he told the crowd: "I can assure you that the two previous hits have given them in different places. In fact, the blows were given in points are located several miles from each other."
How about this statement?

Monday, March 16, 2009

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Magic Squares - Exercises

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Monday, February 23, 2009

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Serway book copies

Here are a few copies of the book Physics of Serway

on the subject of Newton's second law F = ma (the subject of partial examination)

I hope they can

Download here

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PHYSICAL REVIEW !!!!! Copies of Physics II

YOUNG GOOD THIS WEEK IS THE PHYSICAL REVIEW, SO AS CONCEPTUAL PHYSICS II, (I think that another physicist IV and VI) AS A STUDY

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Partners These are copies of my book Physics II, for the consideration of this

Saturday, if you have any questions asked. This relatively easy

review must take this first review

Download PDF copy from here

Thursday, February 19, 2009

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Here is the problem of the average speed a vehicle

A car travels a certain road with an average speed of 40km / h, and returns for her with an average speed of 60km / h. calculates the average speed on the round trip (not 50km / h) ...

Care !!!!! the first thing that would happen we would add the speed and divide into 2 which would give us 50kms / h

but this way is wrong. The first thing to do is remind us of the speed equation

is speed = distance / time, this we can deduce the time, time = distance / speed.

time round we do not know, but we deduce the equation that is distancia/40 (see page) and return time distancia/60 the same way, time is the sum total trip time over time back.

resulting t = D/24. Now this time we replace the rate equation (see fact sheet).

and then we realize that the average speed is 48Kms / h

Wednesday, February 11, 2009

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Average Speed \u200b\u200bCollaboration Minoldo Gramajo

DIEGO

Minoldo Gramajo Gonzalez .

After finishing my morning classes, I walked hurriedly towards the staff room for lunch, when I saw in the hallway. I expected lying over the railing. Being close he came to me and said:

_ Teacher: I said if I bring some chocolates, you give me some points.

I looked surprised and the first intention was to ask who had told such a thing, but I did and said

_ Ah! You want points in math to pass the course in this period.

_ Yes _Me said.

For a moment I thought to take coordination to report it, but was a good boy, though a bit naive and I decided to give me time to decide what to do. _

know

Diego, for the best talk I proposed this time tomorrow, because today I have hunger and want to go to lunch.

_ Okay, I'll look tomorrow at this time.

The next day there was time. not wait to talk to me I said

_ You want points, right?

_ Yes

_ Why?

_ is to go a little wrong with Matt and I are going to end the quarter and would be better.

understand, only we'll do it my way, because I am the Professor of Mathematics. You want points, I'm willing to give 70 points full area, but that if shhhht! (I said putting the index on the lips).

_ Do not worry Professor _Dijo a smile.

I took a calendar on the wall of such large numbers that are in banks and spoke thus:

_ September and you will start I will for the first day of an ounce of chocolate _le said pointing to the numeral 1_ day two will give me twice, or two grams, three twice previous day and so on until the end of the month. All this notes on a calendar and when you have all the sums he has given me the sum. This will give the number of grams of chocolate for me. " To convert to chocolates, divide this number by the grams in a chocolate and brings me.

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course and with his bow _le said. Note _le indicated to make sure comprendiera_: The one: one gram, the two: two grams, three, four grams, the four: Eight grams, five: 16 grams ; if you add up to where we are 31 grams in five days.

He left happy and I returned to my lunch.

took three days and gave no sign. the fourth I called:

Diego _le dije_ are my chocolates?

_ Ahhh! _ Profe dijo_ me ... if they are bastantitos thousand ...

_ Come, bring paper, pencil and calculator, let's calculate.

I took the calendar and put it on a desk, I pointed and said,

_ On day one, a gram is not it, .. the two , twice ... _ Yes

_ What a day to day?

_ the amount is doubled.

_ This is expressed mathematically: t n = 2 n-1 where n is the number of days. September has 30 days, so the last two days should be allocated 29 grams of chocolate, right?

_ Yes

_ The sum of thirty days is S n = 2 ³⁰ - 1, which gives us _S n = 1073741823 grams of chocolate. How many grams of chocolate is thought to bring me?

_ 40.

_ Good: (1 073 741 823) / 40 = 26,843,545. 58 chocolates.

_ How much does your factory produce one of those chocolates?

_ Maybe a quetzal.

_ Well, then we would approximately 27 million quetzales.

_ How many newspapers can produce the chocolate factory?

_ Maybe ... 50 000 chocolates.

_ Well, if in a day are 50 000, to produce my chocolates 536.87 would be needed, working six days a week, it takes 89.5 weeks and if we do a year, equivalent to 52 weeks, it will take 1.72 years to make my chocolates.

_ You gave me a gift box, right?

_ Yes

_ Assume a chocolate has dimensions of 5 cm * 10cm * 0.5cm and whether it translates to cubic meters, gives approximately 671 m ³ as total volume of my chocolates. need to compute the box that will contain this volume. cubic If we consider would be a cube of side 8.76 m side approx.

_ What do you think?

only smiles.

_ not calculate the crest, it must go back to school, but I think you learned four things:

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not accept deals that do not know that it will go.

learned math, that's why I'm here.

it remains only to consider whether it wants to win the course.

Since that time again not to lose a test and although it was a brilliant student, always got the grades needed to pass. In college, they say that doing well.

Sunday, February 1, 2009

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Lic Class III

For those who do not get to math class III is now on the third floor of Tower 1 room 315

class this as a pdf file and can be downloaded from

http://www.scribd.com/share/upload/8441847/7hx6pocgmn6hgvvdb5u

down so that it can have to subscribe to the site, just ask them simple email and password but only read

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mathematical physics class II

do you think if the days after classes Saturdays 4: 00 to 5:30 we were in the U.S. to resolve questions of Physics II, is more difficult to be on Saturday but it is the only day we can all, but I think we can use ½ hours but to clarify some questions that have not been clarified during the day, I for now I sign anyone else?

Tuesday, January 27, 2009

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Discussion Educational Psychology

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Saturday newly past, within the educational psychology class came to light the issue of the national teachers. When we read the newspapers and see that are on strike, who took to the roads and schools, we quickly they are lazy, they are freeloaders that is an excuse for not working.

But the reality of our education, we live in the capital, know little or nothing of what happens inside, we give many advantages for certain inside do not exist. For example, I study in public schools here in the capital, where the facilities, maybe not the best, but can get very good students who attend (I went back because there touch me vote.)

However, the reality of the interior is different, that those teachers who must walk miles , on roads where it enters vehicle but can only be explored on foot, where the facilities if they exist, are homeless, or even think of bathroom walls, where students are taught in pastures, on bricks, standing in the sun, etc.

Many of them work without the certainty that they were paid, and the saddest thing is a salary that gives shame .

I know little about, but I see both sides of the coin before the judge, at least they are organizing to reclaim what they feel is fair (judge you if you is) while we do nothing, when should claim security and assurance system legal .

What do you think? complain to this blog maybe we do not agree on everything, but that is, to live together and tolerate those who think differently

Monday, January 26, 2009

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A teacher like no! My buddies

Rafael Santiago Engineer
students rarely have the opportunity to have a good teacher, many of us throughout our life we \u200b\u200bhave seen all kind of professor, who never prepares This class, or the lazy, the not know the course (ironic really) and so on. But we must not distort at all, We have the privilege of having a great teacher (and not because we are snakes or commies , because if anything, engineer Santiago is known to separate the professional friendship, I mean we enyucado if we are).

During all this time has shown us daily capacity, the knowledge of the subject, has the ability to reduce difficult problems the easy problems (that does not mean that we should not look to win their class)

repeatedly has said "Physics is my passion" and anyone who has taken classes with him will prove us right. Our greetings and admiration to the master Santiago (it really is a teacher), we look forward to your continued friendship during the duration of our career, and I hope some time Dr. Bernardo Morales, also can be part of our Teachers group of little people like them .....

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the beginning as any group we started to look for people who were related to us, and the embarrassment that characterizes not know someone started asking name, and the typical "What do you do?. Then we were two sides that began to lose soldiers in its ranks, some for family reasons, others for monetary issues, some more because the way of physics and mathematics were asked an uphill battle that could not travel. But we were running we began to strengthen ties friendship ties so strong that we begin to remove members of other groups.

Saturdays have become these days in which the 8-hour day goes by so fast because we are of what they expect to arrive on Saturday to go to the "U", but to see the guys.

We are a group where you can hear the most vulgar jokes, we can draw some comfort the mother, we can outwit each other until doubled over with laughter, with the consequent to the next to fall the fun will be one, nicknames come and go and comparisons with animals and other objects is typical of the day. But that is not important, what matters is that we have also found a helping hand, a sincere hug, a simple text message and support when necessary.

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nuevooo, nuevooo

For those who had the opportunity to be in the USAC was like to be reminded again, all the old days came to fuck to shoot rockets into the classroom and threatened with scissors and machinery for the hair. TRUTH WOULD BE VERY HAPPY !!!!! WELCOME

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What happened mates!

Here are some of our colleagues in educational psychology, with some already knew, this is the case of the peasants. Now we feel a bit disjointed because they are 2 classes Diaz followed with the lic. also we have to adjust to our new location in the classroom, and just are not the darlings of the lic .....( we ever can)