# Chapter 4 Making Sense of the Universe Understanding Motion, Energy, and Gravity.

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Chapter 4 Making Sense of the Universe Understanding Motion, Energy, and Gravity

4.1 Describing Motion: Everyday Life Examples  How do we describe motion?  How is mass different from weight?

How do we describe motion? Speed: Rate at which object moves speed of 10 meters/second = 10 m/s speed of 22 miles/hour = 22 mph Velocity: Speed and direction 10 m/s, due east 22 mph down Hesperian Blvd.

How do we describe motion? Velocity: Speed and direction example : 10 m/s, due east Acceleration: Any change in velocity; either in direction, magnitude, or both

The Acceleration of Gravity  As objects fall, they move faster & faster.  They accelerate.

The Acceleration of Gravity  Acceleration near Earth’s surface from gravity means falling speed increases by 10 meters/second each second

The Acceleration of Gravity  Falling from rest…  after 1 second, moving 10 m/s (about 22 mph)  after 2 seconds, moving 20 m/s (about 44 mph)

The Acceleration of Gravity  Higher you drop a ball, greater its velocity will be at impact…  …unless other forces act!

The Acceleration of Gravity (g)  Galileo demonstrated that g is the same for all objects, regardless of their mass!  Heavier objects (with more mass) must be pulled more to accelerate at the same rate. And Gravity indeed pulls more on heavier objects!

The Acceleration of Gravity (g)  Confirmed by Apollo astronauts on the Moon, where there is no air resistance.

How is mass different from weight?  Mass—the amount of matter in an object (protons, neutrons, electrons)  Weight—the force from graivty that acts upon an object from other mass

There is no gravity in space. The force of gravity is much less. The moon is pulling astronauts in the other direction. The Earth’s magnetic field holds them up. They are massless. Why are astronauts weightless in space?

There is no gravity in space. The force of gravity is much less. The moon is pulling astronauts in the other direction. The Earth’s magnetic field holds them up. They are massless. Why are astronauts weightless in space?

There is no gravity in space. The force of gravity is much less. The moon is pulling astronauts in the other direction. The Earth’s magnetic field holds them up. They are massless. Why are astronauts weightless in space? Gravity IS pulling them towards Earth. They ARE falling!

There is gravity in space. Weightlessness is due to a constant state of free-fall. Why are astronauts weightless in space?

How can they ORBIT?

As spacecraft fall, they also move sideways fast At 300 miles above Earth: Falling towards Earth continuously, but… Moving at 17,000 miles per hour SIDEWAYS Orbits are continuous falling “around” Earth! How can they ORBIT?

Sir Isaac Newton  Invented the reflecting telescope  Invented calculus  Connected gravity and planetary forces Philosophiae naturalis principia mathematica

Universal Laws of Motion “ If I have seen farther than others, it is because I have stood on the shoulders of giants.” Sir Isaac Newton (1642 – 1727) Physicist

Newton’s Laws of Motion 1 A body at rest or in motion at a constant speed along a straight line remains in that state of rest or motion unless acted upon by an outside force.

Newton’s 1 st Law  Planets orbit stars stay in motion, but are continually being pulled in their orbit by the star.  Rockets heading to the moon or Mars, once launched, can coast along a straight line.

Newton’s Laws of Motion 2

Newton’s 2 nd Law The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it, but is inversely proportional to the body’s mass. F = m a  Launch a rocket – as fuel is used up, mass decreases, and rocket accelerates even faster!  “Staging” rockets is even smarter!

Thought Question A car coming to a stop. A bus speeding up. An elevator moving up at constant speed. A bicycle going around a curve. A moon orbiting Jupiter. Is there a net force for each of the following?

Thought Question A car coming to a stop. Yes A bus speeding up. Yes An elevator moving up at constant speed. No A bicycle going around a curve. Yes A moon orbiting Jupiter. Yes Is there a net force for each of the following?

Newton’s Laws of Motion 3

Newton’s 3 rd Law For every applied force, a force of equal size but opposite direction arises.  As rocket exhaust pushes backwards, the rocket itself moves forwards  As Earth pulls on the Moon, the Moon pulls on Earth

Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

Law of Gravity Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects. Gravity is ONLY attractive! There is no “anti-gravity”

Gravity Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects. What kind of Mass? It doesn’t matter ! What shape, size, temperature, state? It doesn’t matter!!

Illustrating Gravity with Tides Why are there two high tides each day? Why are tides on Earth caused primarily by the Moon rather than by the Sun? Why is Earth’s rotation gradually slowing down? Why does the Moon always show the same face to Earth?

Tides  Gravitational force decreases with (distance) 2,

Tides  Since gravitational force decreases with (distance) 2, the Moon’s pull on Earth is strongest on the side closer to the Moon, and weakest on the opposite side.

Tides  Since gravitational force decreases with (distance) 2, the Moon’s pull on Earth is strongest on the side closer to the Moon, and weakest on the opposite side.

Tides  The Earth gets stretched along the Earth-Moon line.  The oceans rise relative to land at these points.

Tides - Observations  Every place on Earth passes through these points, called high tides, twice per day as the Earth rotates.  SF Bay Tide Tables SF Bay Tide Tables

Tides - Observations  High tides occur every 12 hours… plus!  Average difference between high tides = 12 hours and 25 minutes  remember, the Moon moves!

Tides - Observations  Tides are tied to the phases of the moon

Tides - Observations  High tides occur every 12 hours 25minutes  remember, the Moon moves!  The Sun’s tidal effect on Earth is not as strong.  About ½ as large as the Moon  But when BOTH stretch in the same direction, even larger tides!

Tides - Observations  Tides are tied to the phases of the moon

Tides  When Sun & Moon pull in the same direction (new & full phases)  high tide is HIGHER than usual

Tides When Sun & Moon pull at right angles (first & last quarter phases)  high tide is LOWER than usual

Tidal Friction  Reaction between Moon’s pull & Earth’s rotation.  Earth’s rotation slows down (1 sec every 50,000 yrs.)  Moon moves farther away from Earth.

Where’s the PROOF? Stromatolites!  Earth’s rotation slows down

Synchronous Rotation  When rotation period of a moon, planet, or star equals its orbital period about another object.  Tidal friction on the Moon (caused by Earth) has slowed its rotation down to 1 month.  The Moon now rotates synchronously.  We always see the same side of the Moon.

Orbital Paths  Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths.  possible orbital paths  ellipse (bound)  parabola (unbound)  hyperbola (unbound)

Newton’s Version of Kepler’s Third Law Using calculus, Newton was able to derive Kepler’s Third Law from his own Law of Gravity. In its most general form: P 2 = 4  2 a 3 / G (m 1 + m 2 ) If you can measure the orbital period of two objects (P) and the distance between them (a), then you can calculate the sum of the masses of both objects (m 1 + m 2 ).

Changing Orbits orbital energy = kinetic energy + gravitational potential energy conservation of energy implies orbits can’t change spontaneously An object can’t crash into a planet unless its orbit takes it there.

Changing Orbits An orbit can only change if it gains/loses energy from another object, such as a gravitational encounter If an object gains enough energy so that its new orbit is “unbound” it has reached escape velocity.

Changing Orbits We can use the gravitational pull of planets to “slingshot” spacecraft to other parts of the solar system! “Gravitational Assist” cuts travel time to outer solar system by years!

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