Gravity & Gravity & MotionMotion

Chapter 10 Section 2Chapter 10 Section 2

GravityGravity Force that pulls objects towards Force that pulls objects towards

each othereach other Galileo Galilee and Isaac Galileo Galilee and Isaac

NewtonNewton Law of Universal GravitationLaw of Universal Gravitation

-Gravity acts between all objects -Gravity acts between all objects in the universein the universe

Differences between Galileo & AristotleDifferences between Galileo & Aristotle

In the early 1600s,Galileo did experiments In the early 1600s,Galileo did experiments to figure out the laws (or rules) followed to figure out the laws (or rules) followed by objects in motion.by objects in motion.The prevailing ideas on physics at the The prevailing ideas on physics at the time were still those of Aristotle (from time were still those of Aristotle (from 350 BC).350 BC).Galileo proved that most of Aristotle’s Galileo proved that most of Aristotle’s ideas on physics were wrong! He proved ideas on physics were wrong! He proved it by doing experiments.it by doing experiments.Aristotle believed that moving objects Aristotle believed that moving objects naturally slow and stop on their own (the naturally slow and stop on their own (the stars? He said that there were different stars? He said that there were different rules for heavenly objects.)rules for heavenly objects.)Galileo said that moving objects naturally Galileo said that moving objects naturally want to continue moving at the same want to continue moving at the same speed in the same direction, they only speed in the same direction, they only slow if something forces them to slow slow if something forces them to slow down. (Newton’s 1down. (Newton’s 1stst Law) Law)

If I push a chair across the If I push a chair across the floor…floor…

Aristotle says it continues a little while due to Aristotle says it continues a little while due to inertiainertia but then slows to its natural state of but then slows to its natural state of rest.rest.

Galileo says the chair wants to continue moving Galileo says the chair wants to continue moving ((inertiainertia) but is being slowed down by a ) but is being slowed down by a forceforce, , (sliding friction with the floor).(sliding friction with the floor).

On ice, the chair would have the same inertia On ice, the chair would have the same inertia but the friction force would be less, hence it but the friction force would be less, hence it will slide further.will slide further.

On ice, Aristotle’s ideas do not explain why it On ice, Aristotle’s ideas do not explain why it takes longer for the chair to eventually stop.takes longer for the chair to eventually stop.

Galileo: same rule Galileo: same rule applies in spaceapplies in space

In space (the ‘heavens’), Aristotle says things In space (the ‘heavens’), Aristotle says things are made out of a special fifth element are made out of a special fifth element (quintessence) which does not naturally slow (quintessence) which does not naturally slow down.down.

In space, Galileo says there must be little or In space, Galileo says there must be little or no resisting forces (no air or fluid friction) no resisting forces (no air or fluid friction) which allows the object to keep up its natural which allows the object to keep up its natural motion - the same rules that apply on Earth.motion - the same rules that apply on Earth.

Planets can move around the Sun without Planets can move around the Sun without slowing down because nothing is making slowing down because nothing is making them slow down.them slow down.

Galileo’s ExperimentGalileo’s Experiment Aristotle had claimed that Aristotle had claimed that

heavier objects fell faster heavier objects fell faster than lighter ones. Twice the than lighter ones. Twice the weight would fall twice as weight would fall twice as fast he said.fast he said.

Galileo did experiments that Galileo did experiments that easily proved this was not easily proved this was not true (although that he did true (although that he did the experiments at the the experiments at the Leaning Tower of Pisa may Leaning Tower of Pisa may be a myth).be a myth).

Falling ObjectsFalling Objects If we include the force due to air-If we include the force due to air-

resistance, we would find that - all resistance, we would find that - all other things being equal - heavier other things being equal - heavier objects do fall faster. Anything with objects do fall faster. Anything with more surface area will also fall more surface area will also fall slower, due to more fluid friction.slower, due to more fluid friction.

But when air resistance is minimal, But when air resistance is minimal, all objects fall on the Earth at 9.81 all objects fall on the Earth at 9.81 m/sm/s22 or 32.2 ft/s or 32.2 ft/s22 or (22 mph)/s. or (22 mph)/s.

Notes about accelerationNotes about acceleration If either the speed or direction of an If either the speed or direction of an

object changes, we say that it is object changes, we say that it is acceleratingaccelerating..

Speeding up, slowing down, or Speeding up, slowing down, or turning a corner are all turning a corner are all accelerationsaccelerations..

AnyAny change in velocity (magnitude change in velocity (magnitude or direction) is an acceleration.or direction) is an acceleration.

1) 1) Mass & Mass & DistanceDistance: Force of gravity : Force of gravity between objects…between objects…Increases withIncreases with greater massgreater massDecreases with less massDecreases with less mass

Increases with closer distance.Increases with closer distance.Decreases with greater distance.Decreases with greater distance.

2) 2) Gravity & WeightGravity & Weight--Weight =Weight = Gravitational force Gravitational force exerted exerted on a person towards earth.on a person towards earth.--Objects with greater mass have Objects with greater mass have greater weightgreater weight

Weight = Mass x Acceleration due to Weight = Mass x Acceleration due to GravityGravity

Acceleration due to Gravity = Acceleration due to Gravity = 9.81 m/s9.81 m/s22

What is the SI Unit for Mass? KgWhat is the SI Unit for Mass? Kg

Math PracticeMath PracticeLeroy has a mass of 60 kg and is Leroy has a mass of 60 kg and is

hanging out on earth. What is hanging out on earth. What is Leroy’s weight?Leroy’s weight?

First write the equation:First write the equation:Weight = Mass X Acceleration due to Weight = Mass X Acceleration due to

gravitygravityWeight = 60 kg x 9.8 m/sWeight = 60 kg x 9.8 m/s22

Leroy’s Weight = 588 NewtonsLeroy’s Weight = 588 Newtons

Gravity & MotionGravity & Motion1) 1) Free FallFree Fall::

When Gravity is the When Gravity is the ONLYONLY force acting on force acting on object.object.Object Object acceleratesaccelerates (speeds up)(speeds up) downward downward

Acceleration due to Gravity = 9.81 m/sAcceleration due to Gravity = 9.81 m/s22

Same for ALL objects…regardless of Mass!Same for ALL objects…regardless of Mass!What does that mean?What does that mean?

Velocity increases 9.8 m/s each second it falls.Velocity increases 9.8 m/s each second it falls.After 1 second, velocity has increased to 9.8 m/s After 1 second, velocity has increased to 9.8 m/s

After 2 seconds, velocity has increased to 19.6 After 2 seconds, velocity has increased to 19.6 m/sm/s

(9.8 +9.8)(9.8 +9.8)

2) 2) Air ResistanceAir Resistance::Fluid Friction (air) acts in Fluid Friction (air) acts in OPPOSITEOPPOSITE direction to motion.direction to motion.Upward force exerted on falling objectsUpward force exerted on falling objects

Which object will experience greater air Which object will experience greater air resistance?resistance? An object with a large surface An object with a large surface

area or a small surface area?area or a small surface area? What is an example?What is an example?

Greater Surface Area = Greater Air Greater Surface Area = Greater Air ResistanceResistance

Are the sky divers going to Are the sky divers going to fall at the same rate of fall at the same rate of

acceleration?acceleration?Are they in true Free Fall?Are they in true Free Fall?

Terminal VelocityTerminal Velocity

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force (Fd) and buoyancy equals the downward force of gravity(FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration.

Based on wind resistance, the terminal velocity of a skydiver in a belly-to-earth (i.e. face down) position is about 195 km/h (122 mph or 54 m/s).Higher speeds can be attained if the skydiver pulls in his or her limbs. In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s), which is almost the terminal velocity of the Peregrine Falcon diving down on its prey. Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 1,357.6 km/h (843.6 mph /Mach 1.25) by Felix Baumgartner who skydived from 38,969.4m (127,852.4ft) above earth on 14 October 2012. The record was set due to the high altitude where the lesser density of the atmosphere decreased drag.

3) 3) Projectile MotionProjectile MotionAn object that is thrown is a projectileAn object that is thrown is a projectile

If the only force acting on two objects is Gravity…If the only force acting on two objects is Gravity…and one object is dropped and another is thrown and one object is dropped and another is thrown

horizontally…which will hit the ground first?horizontally…which will hit the ground first?

Gravity continues to act on both objects Gravity continues to act on both objects at the same rate. They will hit the at the same rate. They will hit the

ground at the same time.ground at the same time.

DESPITE MASS!!DESPITE MASS!!

Enter Isaac Newton, Enter Isaac Newton, Orbital Motion and Orbital Motion and

GravityGravity Newton extended the study of motion begun by Newton extended the study of motion begun by Galileo.Galileo.

Newton summarized his work on motion in three laws.Newton summarized his work on motion in three laws. A A forceforce is any kind of push or pull exerted by one is any kind of push or pull exerted by one

object on another.object on another. Besides contact, friction, electric, magnetic, elastic, Besides contact, friction, electric, magnetic, elastic,

pressure, etc. forces, Newton said that objects also pressure, etc. forces, Newton said that objects also exert a exert a gravitationalgravitational force on each other. force on each other.

The force of The force of gravitygravity causes causes allall bodies to bodies to attractattract all all other bodies.other bodies.

Gravity, coupled with laws of motion, enabled Newton Gravity, coupled with laws of motion, enabled Newton to explain exactly how orbits work.to explain exactly how orbits work.

The Moon and the EarthThe Moon and the Earth the Earth will exert the Earth will exert

a gravitational a gravitational forces on the Moon forces on the Moon pulling the Moon pulling the Moon towards the Earth.towards the Earth.

So, So, what holds the what holds the Moon up?Moon up?

Why doesn’t it fall Why doesn’t it fall down like if you down like if you drop a rock?drop a rock?

Moon

Earth

The Moon and the EarthThe Moon and the Earth If the Moon was just sitting If the Moon was just sitting

up there, it up there, it wouldwould fall fall straight down onto the straight down onto the Earth.Earth.

But the Moon is moving, But the Moon is moving, “sideways” at a pretty high “sideways” at a pretty high speed.speed.

The Moon The Moon does fall downdoes fall down, , but it is moving sideways at but it is moving sideways at the same time.the same time.

Just like if I throw a Just like if I throw a baseball, it moves across baseball, it moves across the room while falling the room while falling downwardsdownwards

gg

earthearth

Moon

Moon’s velocity

The Moon and the EarthThe Moon and the Earth Without gravity, the Moon Without gravity, the Moon

would move in a straight would move in a straight line, flying away from the line, flying away from the Earth.Earth.

The orbit is a balance The orbit is a balance between the natural between the natural straight-line motion and straight-line motion and the attractive pull towards the attractive pull towards the Earth.the Earth.

The Moon is always falling The Moon is always falling towards the Earth but it is towards the Earth but it is also always shooting away also always shooting away from the Earthfrom the Earth

gg

earthearth

Moon

Moon’s velocity

Path followed by the Moon

The Sun and PlanetsThe Sun and Planets

Orbits of planets around the Sun work just Orbits of planets around the Sun work just like the Moon’s orbit around the Earth.like the Moon’s orbit around the Earth.

If the gravitational force and orbital speed If the gravitational force and orbital speed are exactly balanced, a planet will orbit in a are exactly balanced, a planet will orbit in a perfect circle.perfect circle.

If the planet’s speed is a little faster or If the planet’s speed is a little faster or slower, a non-circular orbit results.slower, a non-circular orbit results.

If the planet’s speed is much too fast or If the planet’s speed is much too fast or slow it may escape the Sun altogether or slow it may escape the Sun altogether or fall into the Sun.fall into the Sun.

Discovery of planetsDiscovery of planets Uranus was discovered in the 1700’s but Uranus was discovered in the 1700’s but

never followed exactly the expected orbit.never followed exactly the expected orbit. Some astronomers guessed that the pull Some astronomers guessed that the pull

of gravity from an 8of gravity from an 8thth planet could be planet could be causing the deviationcausing the deviation

A French astronomer in 1846, calculated A French astronomer in 1846, calculated where the 8th planet could be to explain where the 8th planet could be to explain Uranus’s motion and sent his calculations Uranus’s motion and sent his calculations to a German astronomer friend.to a German astronomer friend.

Discovery of NeptuneDiscovery of Neptune Minutes after starting his search at the Minutes after starting his search at the

given coordinates, the astronomer found given coordinates, the astronomer found Neptune.Neptune.

Neptune is sometimes referred to as the Neptune is sometimes referred to as the “first planet discovered by mathematics”.“first planet discovered by mathematics”.

The most impressive thing a theory can do The most impressive thing a theory can do is correctly predict something totally is correctly predict something totally unknown before. unknown before.

Newton’s Laws did that here and have Newton’s Laws did that here and have continued to do so for centuries.continued to do so for centuries.

Discovery of PlutoDiscovery of Pluto Now let’s just watch Neptune and if it goes off course we’ll do Now let’s just watch Neptune and if it goes off course we’ll do

a ‘little’ math and find a new planet.a ‘little’ math and find a new planet. Neptune went of course, calculations were made, no planet Neptune went of course, calculations were made, no planet

was discovered.was discovered. Pluto eventually discovered in 1930 but far too small for the Pluto eventually discovered in 1930 but far too small for the

measured perturbations.measured perturbations. Pluto was a lucky accident.Pluto was a lucky accident. Neptune had not gone off course, we had incorrect masses for Neptune had not gone off course, we had incorrect masses for

some planets which made the calculated path incorrect.some planets which made the calculated path incorrect. Planets currently show zero deviation from the expected paths Planets currently show zero deviation from the expected paths

based on modern values. There appears to be no evidence of based on modern values. There appears to be no evidence of any more large planets nearby.any more large planets nearby.

Smaller bodies (Pluto size and smaller), now called “dwarf Smaller bodies (Pluto size and smaller), now called “dwarf planets”, continue to be discovered.planets”, continue to be discovered.

Escape VelocityEscape Velocity Throw an object upwards: it goes up, stops, falls Throw an object upwards: it goes up, stops, falls

back down.back down. Throw the object up with a faster speed and it Throw the object up with a faster speed and it

will go higher before falling back.will go higher before falling back. Throw an object fast enough (called the Throw an object fast enough (called the escape escape

velocityvelocity) and Earth’s gravity is not enough to ) and Earth’s gravity is not enough to stop it and bring it back. It escapes into space.stop it and bring it back. It escapes into space.

Escape velocity for earth is 11,200 m/s or 11 Escape velocity for earth is 11,200 m/s or 11 m/s or m/s or 25,805 mph25,805 mph. sq rt. (G x m/r). sq rt. (G x m/r)

Speed of light is 670,616,629 miles per hour Speed of sound is 768 mph

The Earth, a Pencil, and The Earth, a Pencil, and GravityGravity

The Earth exerts a force of gravity on a pencil The Earth exerts a force of gravity on a pencil causing it to fall (accelerate) to the floor, but causing it to fall (accelerate) to the floor, but clearly the pencil does not exert an equal clearly the pencil does not exert an equal force on the Earth! Right?force on the Earth! Right?

The pencil moves but the Earth just sits there.The pencil moves but the Earth just sits there. The forces The forces areare equal! That does not mean the equal! That does not mean the

accelerations are equal.accelerations are equal. a = F/ma = F/m The Earth has a mass 10The Earth has a mass 102727 times more than times more than

the pencil, so for the same force it has 10the pencil, so for the same force it has 102727 times less acceleration, immeasurably small.times less acceleration, immeasurably small.