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Chapter 12: Gravity

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Describe the movement of the moon towards the earth
-the moon is constantly falling towards the earth
Describe the movement of an object in uniform circular motion in relation to the center of the circle
-an object in uniform circular motion accelerates toward the center of the circle
What is the force responsible for the moon's centripetal acceleration?
-the Earth's gravitational attraction
What law did Newton propose to describe the force of gravity?
-the law of universal gravitation
What is the equation that describes the law of universal gravitation?
F = G (m1*m2/r^2)
What is F?
-the force of gravity between any two point objects of mass m1 and m2
What is r?
-the distance between the masses
What is G?
-the universal gravitation constant
What is the value of the universal gravitation constant?
6.67 e^-11 N*m^2/kg^2
Along what line is the force directed along?
-the line connecting the masses
Comparatively describe the force that each mass experiences
-each mass experiences a force of the same magnitude, but acting in opposite directions
As such, what does the force of gravity between two objects form?
-an action reaction pair
What is one of the key implications of the law of universal gravitation? (hint: related to attraction between objects in the universe)
-all objects in the universe attract all other objects in the universe by way of gravitational interaction
What does the fact that G is such a small number mean?
-that the force of gravity between objects of human proportions is imperceptibly small
Does the force of gravity increase or decrease with distance?
-decrease
Does the force of gravity ever vanish with distance?
-no it does not
-gravity is a force of infinite range
What is the relationship between F and distance?
F varies as 1 / r^2
Since F varies as 1 / r^2, what is F said to have?
-F is said to have an inverse square dependence on distance
For example, an increase in distance by a factor of 10 results in a decrease in the force by a factor of what?
10^2, or 100
Since the force of gravity between two masses depends on the product of the masses, what follows? (in terms of gravity)
-that if either mass is doubled, the force of gravity is doubled as well
If a given mass is acted on by gravitational interactions with a number of other maseses, what is the net force acting on a mass?
-a vector sum of each of the forces individually
What is the property of gravity referred to as?
-superposition
Does the acceleration due to gravity have a higher value at sea level or on the top of Mt. Everest?
-higher value at sea level
Does the universal gravitation constant to Mars? to the Moon?
-yes, the universal gravitation constant applies to any object in the universe
What does the law of universal gravitation describe?
-how gravity works everywhere in the universe
What is the distance of the "r" value that is used in Newton's Law of Universal Gravitation?
-the distance between two massess center-to-center
What are the units of the universal gravitation law?
N * m^2 / kg^2
What does the universal gravitation law actually say?
-if you take two 1 kg masses and put them 1 meter apart, then the strength of the attraction is equal to 6.67e^-11 N * m^2 / kg^2
What is one of the most important implications of G?
-every object in the universe is attracted to all other objects
Why?
-F of gravity will not equal zero unless r = infinity
-since the universe is not infinite, the case will never be met
-->thus, every object in the universe will always be attracted to other objects
What then is mass?
-a membership card to being attracted by other masses
If we experience attraction to everything in the universe, why do we only feel one attractive force (to that of the Earth)?
-because Earth is the biggest mass that is close by
Given the equation g = GMearth/r^2, what would g be if the radius was increased from 1 to 2?
1/4 g
If the radius was increased from 1 to 3?
1/9 g
What pattern do you see?
-whatever you do to r, you will do one over that factor squared to g
Given the equation q = (x√z)/y^2, what will q be if x becomes 3x?
-q will be 3q
If y becomes 4y?
-q will be 1/16 q
If z becomes 25 z?
-q will be 5q
Must you be outside of a body/mass to calculate the pull of gravity of that object?
-yes
Why?
-if you were to go inside of a body, you would have different parts of a body pulling on you differently
Are mass and weight the same thing?
-no they are not
What is mass?
-Ilka: "how much stuff" is in an object
-Book: a measure of the inertia of an object
Is mass an intrinsic or extrinsic property?
-intrinsic
Therefore, does it change based on location?
-no it does not
What is weight?
-the force of gravity on an object (due to another body's pull)
Is weight an intrinsic or extrinsic property?
-extrinsic property
What is it defined by?
Therefore, does it change based on location?
-most definitely
Are mass and weight related?
-yes
How?
Force of gravity = mg = W
Therefore, what impact does increasing the mass of an object have?
-if you increase the mass of an object (while your location stays the same), then weight will correspondingly increase
Therefore, what does having more mass mean?
-you participate more in the gravitation club/phenomena
If you traveled from the Earth to the Moon (and ate a typical/healthy amount on the way), would your mass stay the same?
-yes
-mass is an intrinsic property that is not dependent upon location
If you traveled from the Earth to the Moon (and ate a typical/healthy amount on the way), would your weight stay the same?
-no it would not
Why?
-because weight is an extrinsic property that is dependent upon location
-since the moon's gravitational force is less than that of the Earth's, weight will decrease when mass is held constant
What is the SI unit for mass?
-kg
What is the English unit for mass?
-slugs
What is the SI unit for weight?
-newtons
What is the English unit for weight?
-pounds
Therefore, what do you compare when you compare kilos and pounds?
-mass vs. weight
Therefore, what is the relationship between kilos and pounds?
-1 kg of mass only weighs 2.2 lbs on the Earth's surface
-comparison values will be dependent upon location
Is a comparison between kilos and slugs dependent upon location?
-no
Why not?
-because kilos and slugs are both units of mass
Is a comparison between newtons and pounds dependent upon location?
-no
Why not?
-because newtons and pounds are both units of weight
When an object is in orbit around another body, how does the force required to keep the object in circular motion compare to the actual force supplied?
force required = force actual
Describe the relationship between orbital speed and distance
-as the distance between two object increases, the necessary orbital speed decreases
-->as you go farther away, you can slow down and still maintain circular motion
Is orbital speed dependent on mass?
-no
Describe the moon's position when it is not visible in the sky
-the moon is between the Earth and the sun
-as such, it is not illuminated from our perspective and we cannot see it
Describe the moon's position when it is "half moon"
-moon and Earth at an equal x distance from the sun
-as a result, only half of the moon is illuminated by the sun from our perspective
Describe the moon's position when it is full moon
-Earth is between moon and sun
-all of moon is illuminated from our perspective
The orbital period of the moon around the Earth is calculated to be 27.4 days. Why is the actual period greater than this value?
-as the moon is travelling around the Earth, after 27 days the Earth has changed position
-when the Earth's movement is accounted for, the phases of the moon are more than one Earth period
What is the orbital period of the Earth around the sun?
-365.24220 days
What calendar system is based off of this calculation?
-Julian calendar
What is wrong with this calculation?
-actual rotation is equal to 365.25 days minus 11 minutes
By 1582, how many days was the calendar off by?
-11 days
What was ordered?
-rectification by pope gregory
What calendar system is now used?
-Gregorian
What has been instituted to ensure that we do not develop further inaccuracies?
-currently, we do not have a leap year every year
-leap years do not occur during turn-of-century years that are not divisible by 400
It is often said that astronauts in orbit experience weightless ness because they are beyond the pull of Earth's gravity. Is this statement correct? Explain.
-no it is not
-->the force of Earth's gravity is practically as strong in orbit as it is on the surface of the earth
Why then do astronauts experience weightlessness?
-because they are inconstant free fall
Why can't gravitational force be dependent upon the sum of two masses?
-because it would predict a nonzero force even when one of the masses is zero
-->this is certainly not observed
An astronaut orbits the Earth in a space capsule whose height above the surface is one Earth radius. If m is her mass on the surface of the Earth, then at her current location, her mass is...?
-m
An alien moon orbits around an alien planet at speed v, at an orbital radius R. The correct value for the universal gravitation constant could be obtained by what equation?
G = v2(R) / Mp