Gravity & Motion Chapter 10 Section 2

Gravity Force that pulls objects towards each other Force that pulls objects towards each other Galileo Galilee and Isaac Newton Galileo Galilee and Isaac Newton Law of Universal Gravitation Law of Universal Gravitation -Gravity acts between all objects in the universe

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

If I push a chair across the floor… Aristotle says it continues a little while due to inertia but then slows to its natural state of rest. Aristotle says it continues a little while due to inertia but then slows to its natural state of rest. Galileo says the chair wants to continue moving (inertia) but is being slowed down by a force, (sliding friction with the floor). Galileo says the chair wants to continue moving (inertia) but is being slowed down by a force, (sliding friction with the floor). On ice, the chair would have the same inertia but the friction force would be less, hence it will slide further. On ice, the chair would have the same inertia but the friction force would be less, hence it will slide further. On ice, Aristotle’s ideas do not explain why it takes longer for the chair to eventually stop. On ice, Aristotle’s ideas do not explain why it takes longer for the chair to eventually stop.

Galileo: same rule applies in space In space (the ‘heavens’), Aristotle says things are made out of a special fifth element (quintessence) which does not naturally slow down. In space (the ‘heavens’), Aristotle says things are made out of a special fifth element (quintessence) which does not naturally slow down. In space, Galileo says there must be little or no resisting forces (no air or fluid friction) which allows the object to keep up its natural motion - the same rules that apply on Earth. In space, Galileo says there must be little or no resisting forces (no air or fluid friction) which allows the object to keep up its natural motion - the same rules that apply on Earth. Planets can move around the Sun without slowing down because nothing is making them slow down. Planets can move around the Sun without slowing down because nothing is making them slow down.

Galileo’s Experiment Aristotle had claimed that heavier objects fell faster than lighter ones. Twice the weight would fall twice as fast he said. Aristotle had claimed that heavier objects fell faster than lighter ones. Twice the weight would fall twice as fast he said. Galileo did experiments that easily proved this was not true (although that he did the experiments at the Leaning Tower of Pisa may be a myth). Galileo did experiments that easily proved this was not true (although that he did the experiments at the Leaning Tower of Pisa may be a myth).

Falling Objects If we include the force due to air-resistance, we would find that - all other things being equal - heavier objects do fall faster. Anything with more surface area will also fall slower, due to more fluid friction. If we include the force due to air-resistance, we would find that - all other things being equal - heavier objects do fall faster. Anything with more surface area will also fall slower, due to more fluid friction. But when air resistance is minimal, all objects fall on the Earth at 9.81 m/s 2 or 32.2 ft/s 2 or (22 mph)/s. But when air resistance is minimal, all objects fall on the Earth at 9.81 m/s 2 or 32.2 ft/s 2 or (22 mph)/s.

Notes about acceleration If either the speed or direction of an object changes, we say that it is accelerating. If either the speed or direction of an object changes, we say that it is accelerating. Speeding up, slowing down, or turning a corner are all accelerations. Speeding up, slowing down, or turning a corner are all accelerations. Any change in velocity (magnitude or direction) is an acceleration. Any change in velocity (magnitude or direction) is an acceleration.

1) Mass & Distance: Force of gravity between objects… Increases with greater mass Decreases with less mass Increases with closer distance. Decreases with greater distance.

2) Gravity & Weight -Weight = Gravitational force exerted on a person towards earth. on a person towards earth. -Objects with greater mass have greater weight Weight = Mass x Acceleration due to Gravity Acceleration due to Gravity = 9.81 m/s 2 What is the SI Unit for Mass? Kg

Math Practice Leroy has a mass of 60 kg and is hanging out on earth. What is Leroy’s weight? First write the equation: Weight = Mass X Acceleration due to gravity Weight = 60 kg x 9.8 m/s 2 Leroy’s Weight = 588 Newtons

Gravity & Motion 1) Free Fall: When Gravity is the ONLY force acting on object. Object accelerates (speeds up) downward Acceleration due to Gravity = 9.81 m/s 2 Same for ALL objects…regardless of Mass! What does that mean? Velocity increases 9.8 m/s each second it falls. After 1 second, velocity has increased to 9.8 m/s After 2 seconds, velocity has increased to 19.6 m/s ( )

2) Air Resistance: Fluid Friction (air) acts in OPPOSITE direction to motion. Upward force exerted on falling objects Which object will experience greater air resistance? An object with a large surface area or a small surface area? What is an example? Greater Surface Area = Greater Air Resistance

Are the sky divers going to fall at the same rate of acceleration? Are they in true Free Fall?

Terminal Velocity The terminal velocity of a falling object is the velocity of the object when the sum of the drag force (F d ) and buoyancy equals the downward force of gravity(F G ) 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 The record was set due to the high altitude where the lesser density of the atmosphere decreased drag.

3) Projectile Motion An object that is thrown is a projectile If the only force acting on two objects is Gravity…and one object is dropped and another is thrown horizontally…which will hit the ground first? Gravity continues to act on both objects at the same rate. They will hit the ground at the same time. DESPITE MASS!!

Enter Isaac Newton, Orbital Motion and Gravity Newton extended the study of motion begun by Galileo. Newton extended the study of motion begun by Galileo. Newton summarized his work on motion in three laws. Newton summarized his work on motion in three laws. A force is any kind of push or pull exerted by one object on another. A force is any kind of push or pull exerted by one object on another. Besides contact, friction, electric, magnetic, elastic, pressure, etc. forces, Newton said that objects also exert a gravitational force on each other. Besides contact, friction, electric, magnetic, elastic, pressure, etc. forces, Newton said that objects also exert a gravitational force on each other. The force of gravity causes all bodies to attract all other bodies. The force of gravity causes all bodies to attract all other bodies. Gravity, coupled with laws of motion, enabled Newton to explain exactly how orbits work. Gravity, coupled with laws of motion, enabled Newton to explain exactly how orbits work.

The Moon and the Earth the Earth will exert a gravitational forces on the Moon pulling the Moon towards the Earth. the Earth will exert a gravitational forces on the Moon pulling the Moon towards the Earth. So, what holds the Moon up? So, what holds the Moon up? Why doesn’t it fall down like if you drop a rock? Why doesn’t it fall down like if you drop a rock? Moon Earth

The Moon and the Earth If the Moon was just sitting up there, it would fall straight down onto the Earth. If the Moon was just sitting up there, it would fall straight down onto the Earth. But the Moon is moving, “sideways” at a pretty high speed. But the Moon is moving, “sideways” at a pretty high speed. The Moon does fall down, but it is moving sideways at the same time. The Moon does fall down, but it is moving sideways at the same time. Just like if I throw a baseball, it moves across the room while falling downwards Just like if I throw a baseball, it moves across the room while falling downwards g earth Moon Moon’s velocity

The Moon and the Earth Without gravity, the Moon would move in a straight line, flying away from the Earth. Without gravity, the Moon would move in a straight line, flying away from the Earth. The orbit is a balance between the natural straight-line motion and the attractive pull towards the Earth. The orbit is a balance between the natural straight-line motion and the attractive pull towards the Earth. The Moon is always falling towards the Earth but it is also always shooting away from the Earth The Moon is always falling towards the Earth but it is also always shooting away from the Earth g g earth earth Moon Moon’s velocity Path followed by the Moon

The Sun and Planets Orbits of planets around the Sun work just like the Moon’s orbit around the Earth. Orbits of planets around the Sun work just like the Moon’s orbit around the Earth. If the gravitational force and orbital speed are exactly balanced, a planet will orbit in a perfect circle. If the gravitational force and orbital speed are exactly balanced, a planet will orbit in a perfect circle. If the planet’s speed is a little faster or slower, a non-circular orbit results. If the planet’s speed is a little faster or slower, a non-circular orbit results. If the planet’s speed is much too fast or slow it may escape the Sun altogether or fall into the Sun. If the planet’s speed is much too fast or slow it may escape the Sun altogether or fall into the Sun.

Discovery of planets Uranus was discovered in the 1700’s but never followed exactly the expected orbit. Uranus was discovered in the 1700’s but never followed exactly the expected orbit. Some astronomers guessed that the pull of gravity from an 8 th planet could be causing the deviation Some astronomers guessed that the pull of gravity from an 8 th planet could be causing the deviation A French astronomer in 1846, calculated where the 8th planet could be to explain Uranus’s motion and sent his calculations to a German astronomer friend. A French astronomer in 1846, calculated where the 8th planet could be to explain Uranus’s motion and sent his calculations to a German astronomer friend.

Discovery of Neptune Minutes after starting his search at the given coordinates, the astronomer found Neptune. Minutes after starting his search at the given coordinates, the astronomer found Neptune. Neptune is sometimes referred to as the “first planet discovered by mathematics”. Neptune is sometimes referred to as the “first planet discovered by mathematics”. The most impressive thing a theory can do is correctly predict something totally unknown before. The most impressive thing a theory can do is correctly predict something totally unknown before. Newton’s Laws did that here and have continued to do so for centuries. Newton’s Laws did that here and have continued to do so for centuries.

Discovery of Pluto Now let’s just watch Neptune and if it goes off course we’ll do a ‘little’ math and find a new planet. Now let’s just watch Neptune and if it goes off course we’ll do a ‘little’ math and find a new planet. Neptune went of course, calculations were made, no planet was discovered. Neptune went of course, calculations were made, no planet was discovered. Pluto eventually discovered in 1930 but far too small for the measured perturbations. Pluto eventually discovered in 1930 but far too small for the measured perturbations. Pluto was a lucky accident. Pluto was a lucky accident. Neptune had not gone off course, we had incorrect masses for some planets which made the calculated path incorrect. Neptune had not gone off course, we had incorrect masses for some planets which made the calculated path incorrect. Planets currently show zero deviation from the expected paths based on modern values. There appears to be no evidence of any more large planets nearby. Planets currently show zero deviation from the expected paths based on modern values. There appears to be no evidence of any more large planets nearby. Smaller bodies (Pluto size and smaller), now called “dwarf planets”, continue to be discovered. Smaller bodies (Pluto size and smaller), now called “dwarf planets”, continue to be discovered.

Escape Velocity Throw an object upwards: it goes up, stops, falls back down. Throw an object upwards: it goes up, stops, falls back down. Throw the object up with a faster speed and it will go higher before falling back. Throw the object up with a faster speed and it will go higher before falling back. Throw an object fast enough (called the escape velocity) and Earth’s gravity is not enough to stop it and bring it back. It escapes into space. Throw an object fast enough (called the escape velocity) and Earth’s gravity is not enough to stop it and bring it back. It escapes into space. Escape velocity for earth is 11,200 m/s or 11 m/s or 25,805 mph. sq rt. (G x m/r) Escape velocity for earth is 11,200 m/s or 11 m/s or 25,805 mph. 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 Gravity The Earth exerts a force of gravity on a pencil causing it to fall (accelerate) to the floor, but clearly the pencil does not exert an equal force on the Earth! Right? The Earth exerts a force of gravity on a pencil causing it to fall (accelerate) to the floor, but clearly the pencil does not exert an equal 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 are equal! That does not mean the accelerations are equal.a = F/m The forces are equal! That does not mean the accelerations are equal.a = F/m The Earth has a mass times more than the pencil, so for the same force it has times less acceleration, immeasurably small. The Earth has a mass times more than the pencil, so for the same force it has times less acceleration, immeasurably small.