UniversalGravitation

Gravity is the way in which masses communicate with each

other

• Newton had the insight to see that the force on the moon has the same nature as the force on a falling apple – they are both pulled by earth’s gravity. The apple is pulled more by Earth’s gravity

because it is so close to Earth’s surface.

The Falling Moon

• Newton hypothesized that the moon was simply a projectile circling the earth under the attraction of gravity.

• Newton generalized his moon finding to all objects, and stated that all objects in the universe attract each other.

The Falling Earth• The planets continually fall around the sun in

closed paths, known as orbits. The planets do not crash into the sun because they have tangential (sideways) velocity.

Tangential velocity:Tangential velocity: the “sideways” the “sideways” velocity-the component of velocity velocity-the component of velocity perpendicular to the pull of gravityperpendicular to the pull of gravity If the tangential velocity of the planets was

reduced to zero, they would move straight towards the sun and crash into it.

SI Unit: m/s Ex: The proper amount of tangential velocity

allows Earth to orbit the sun w/o flying into it or flying off into the vacuum of space

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Since the moon is gravitationally Since the moon is gravitationally attracted to Earth, why does it not attracted to Earth, why does it not simple crash into Earth?simple crash into Earth?

Because the moon has enough tangential velocity.

Family Guy Gravity Clip

http://www.mediazine.net/view/family_guy_peter_gravity

Newton’s Law of Universal Newton’s Law of Universal GravitationGravitation

Newton’s Law of Universal Gravitation:Newton’s Law of Universal Gravitation: every object attracts every other object every object attracts every other object with a force that for any two objects is with a force that for any two objects is directly proportional to the mass of directly proportional to the mass of each other.each other. The greater the masses, the greater the

attraction between them; the greater the distance between the objects, the weaker the force of gravity.

The force of gravity is the weakest of the presently four known fundamental forces.

SI Unit: Newton (N)

Equation: FFGG = G m = G m11 m m22 / d / d22

• FG = Force of gravity (N)

• G = universal gravitation constant (6.67 x 10-11 Nm2/kg2)

• m1 = mass of object 1 (kg)

• m2 = mass of object 2 (kg)

• d = distance (m)

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How is the gravitational force between a How is the gravitational force between a pair of planets altered when the mass pair of planets altered when the mass of one of the planets is doubled?of one of the planets is doubled?

Double mass = Double FG

When both masses are doubled?When both masses are doubled?Double both masses = Quadruple FG

(2)(2) = 4

Check Your UnderstandingCheck Your UnderstandingWhen the masses are not changed, but they When the masses are not changed, but they

are twice as far apart?are twice as far apart? Increase d by 2 = Decrease in FG by ¼

1/ 22

When they are three times further apart?When they are three times further apart? Increase d by 3 = Decrease FG by 1/9

1/32

When they are five times further apart?When they are five times further apart? Increase d by 5 = Decrease FG by 1/25

1/52

• Because gravitational forces are the weakest forces found in nature, the force of attraction between you and a classmate is unnoticeable.

• In addition to your mass, your weight also depends on the distance from the center of earth. At the top of a mountain, your mass is the

same as it is anywhere else, but your weight is slightly less because you are further from earth’s center.

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If there is an attractive force between all If there is an attractive force between all objects, why do we not feel ourselves objects, why do we not feel ourselves gravitating toward massive buildings in gravitating toward massive buildings in our vicinity?our vicinity?

Because the masses are small compared to the mass of the earth

• The further away an object is from Earth’s center, the less the force of gravity acting on the object

• The force of gravity will NEVER go to ZERO!!!! You can never be completely weightless in space

• There is always some mass in the universe creating a gravitational force

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What’s Wrong with These Statements??

The moon and planets are beyond the The moon and planets are beyond the pull of Earth’s gravity.pull of Earth’s gravity.

All objects in the universe attract each other.

Gravity gets stronger with altitude, as Gravity gets stronger with altitude, as evidenced by objects carried up a evidenced by objects carried up a flight of stairs feeling heavier.flight of stairs feeling heavier.

Gravity decreases with altitude because the distance from the center of the Earth is increased

Gravitational Fields

• A force field exerts a force on an object in its vicinity.– Ex: gravity, electricity, magnetism

• Field lines represent a force field.

Gravitational field: the kind of force field that surrounds massive objects. Where the lines are close together, the field

is stronger; further away, where the field lines are farther apart, the field is weaker.

Ex: the force of gravity exerted by Earth

• The gravitational field of earth exists inside the earth as well as outside.

• If you were to fall from the North Pole to the South Pole through the center of earth, you’d lose speed moving toward the center, and gain speed moving away from the center.

• In a cavity at the center of Earth your weight would be zero, because you would be pulled equally by gravity in all directions.

• At the center of the earth, the gravitational field strength is zero.

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Halfway to the center of Earth, would Halfway to the center of Earth, would gravity pull on you more strongly or gravity pull on you more strongly or less strongly than at the surface of less strongly than at the surface of Earth?Earth?

Less strongly

So would you weigh more or less?So would you weigh more or less?Less b/c the overall net force of gravity

is less

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If you dropped a rock into a tunnel through Earth what would happen to its speed as it approached the center?

Speed would decrease

In the above question, what would happen to its speed as it moved away from the center?

Speed would increase

Weight and Weightlessness

• Objects under the influence of gravity are pulled toward each other and accelerate. The pressing against earth is the sensation we interpret as weight.

• What keeps us from accelerating into the earth is the Earth’s surface The force of the earth pushing back up on you

is a support force called the normal force A scale actually tells you your normal force,

not your weight

• If you were to weigh yourself in an elevator accelerating up, compared to your ordinary weight, the scale would say you weigh more.

• If you were to weigh yourself in an elevator accelerating down, compared to your ordinary weight, the scale would say you weigh less.

• If you were to weigh yourself in an elevator in free fall, compared to your ordinary weight, you weigh zero.

• Weightlessness is NOT the absence of gravity; it is the absence of the normal force.

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If you are in an elevator that is accelerating If you are in an elevator that is accelerating upward, will the scale say you are heavier upward, will the scale say you are heavier or lighter than normal?or lighter than normal?

It would say you weigh more than usual b/c your normal force is greater. The ground is pushing up on you more, thus making the scale have a larger reading.

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If you are in an elevator that is moving at a constant speed upward, will the scale say you are heavier or lighter than normal?

Neither! Your weight would be the same as if the elevator were standing still because there is no acceleration, and therefore no change in force (and no change in your weight reading). Only when an elevator is accelerating do you notice a difference.