© 2005 Pearson Education Inc., publishing as Addison-Wesley Chapter 4 Making Sense of the Universe:...

© 2005 Pearson Education Inc., publishing as Addison-Wesley

Chapter 4 Making Sense of the Universe:

Understanding Motion, Energy, and Gravity

“If I have seen farther than others, it is because I have stood on the shoulders of giants.”

Sir Isaac Newton (1642 – 1727)


The history of Universe is essentially a story about the interplay between matter and energy.

We can understand what happens in Universe using physics laws we can test on the Earth (even though the sizes involved are on much bigger scale).

In this Chapter we will discuss laws which govern motion and energy in the Universe;• first we will learn how to describe motion;• we will see what is mass (and what is weight); and then • Newton’s laws of motion, • conservation laws of momentum and energy• and gravity law.


4.1 Describing Motion

• Our goals for learning:

• How do we describe motion?

• How is mass different from weight?


How do we describe motion?Precise definitions to describe motion:

• speed: rate at which object moves

speed = distancetime

units of ms

example: speed of 10 m/s

• velocity: speed and direction example: 10 m/s, due east

• acceleration: any change in velocity units of speed/time (m/s2)

• momentum: product of mass and velocity.


Acceleration:

Speeding up

turning

Slowing down


The Acceleration of Gravity

• All falling objects accelerate at the same rate (not counting friction of air resistance).

• On Earth, acceleration of gravity is g ≈ 10 m/s2: speed increases 10 m/s with each second of falling (the unit is therefore m/s/s)

Question: if you drop a feather and a rock at the same time, which one will fall first? Why? What will happen if you repeat this on the Moon?


The Acceleration of Gravity (g)

It was Galileo who showed that g is the same for all falling objects, regardless of their mass. He devised experiments (on the leaning

tower of Pisa, the legend says) which proved this to be true (contrary to the experience).

Apollo 15 demonstrationReview: what experiment about the motion done by Galileo do you remember from the last class? (hint: he proved Aristotle was wrong)


Momentum and Force

• Momentum = mass velocity• Only a net (overall) force can change momentum. It changes

momentum by changing velocity or equally by causing acceleration. • Force actually equals to the rate of momentum change, or the

acceleration caused (times the mass).

• Question: What will happen if a bug, moving with speed of 30km/hr hits your car? What will happen if 2 tone truck, moving at a same speed hits it? Explain why. (hint: which has bigger momentum?)


Thought Question:Is there a net force? Y/N

1. A car coming to a stop.

2. A bus speeding up.

3. An elevator moving up at constant speed.

4. A bicycle going around a curve.

5. A moon orbiting Jupiter.


Is there a net force? Y/N

1. A car coming to a stop. Y

2. A bus speeding up. Y

3. An elevator moving at constant speed. N

4. A bicycle going around a curve. Y

5. A moon orbiting Jupiter. Y

Question: If elevator is moving at a constant speed, does that mean there is no force acting on it?


Summary:

Whenever there is a change of speed or a direction of motion (whenever there is an acceleration) there is a net (overall) force acting on a body. That force actually equals to the mass of the body times the acceleration caused (which is also a momentum change).

Change of momentum = m change of velocity = = m acceleration (= F)


How is mass different from weight?

• mass – the amount of matter in an object; it never changes!• weight – the gravitational force that acts upon an object; it

changes depending were you are, or how do you move (weather you accelerate or not). W=m g.

You are weightless in free-fall!


Summary:

• Mass never changes, no matter where you are, or how are you moving.

• Weight is actually a gravitational force exerted on you, which you in turn exert on the floor. It depends on:

• Where you are (bigger planets will exert bigger gravity pool on you)• And weather you are accelerating or not (acceleration equals force, so if you are accelerating that is like that something is applying additional force on you).

• Free-fall: if there is nothing to stop you from moving under the attraction of gravity (no floor) you would be weightless, while free-falling.


Questions:

1. Why is your weight the same while elevator moves with a constant speed? (hint: what is the acceleration of elevator? What does it tell us about the force?)

2. Why your weight changes if the elevator accelerates?3. Would your mass change if the elevator would go with a

constant speed, on the Moon? Why?


Thought QuestionOn the Moon:

A. My weight is the same, my mass is less.

B. My weight is less, my mass is the same.

C. My weight is more, my mass is the same.

D. My weight is more, my mass is less.


On the Moon…

A. My weight is the same, my mass is less.

B. My weight is less, my mass is the same.

C. My weight is more, my mass is the same.

D. My weight is more, my mass is less.


Why are astronauts weightless in space? (make a guess…)



• Question: is it true that there is no gravity in the space?



• Question: is it true that there is no gravity in the space?• weightlessness is due to a constant state of free-fall:

Let’s imagine you could fall through the Earth. Question: If you would run on the tower and then jump of off it, what would your path be? Now imagine your speed when jumping off the tower is so huge, you actually miss the Earth…


What have we learned?

•How do we describe motion?•Speed = distance/time •Speed + direction => velocity (v)•Change in velocity => acceleration (a)•Momentum = mass velocity•Force causes a change in momentum, which means acceleration.


What have we learned?

• How is mass different from weight?• Mass = quantity of matter• Weight = force acting on mass• Objects are weightless when in

free-fall


4.2 Newton’s Laws of Motion

Our goals for learning:

• How did Newton change our view of the universe?

• What are Newton’s three laws of motion?


• Realized the same physical laws that operate on Earth also operate in the heavens one universeQuestion: how does this compare with

Aristotle’s understanding of nature (remember Aristotle’s teaching were “near gospel truth” at that time)?

• Discovered laws of motion and gravity

• Much more: experiments with light; first reflecting telescope, calculus…

How did Newton change our view of the Universe?

Sir Isaac Newton (1642-1727)


What are Newton’s three laws of motion?

Question: who was the first to discover the basics of this law in his careful experiments? (hint: it helped him as an argument against Earth-centered system)

Published in 1687, under the title “Philosophiae Naturalis Principia Mathematica”

Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.


Newton’s second law of motion:

Force = mass accelerationWhat happens when the force is present…

Question: if you throw away a ball made of plastic and the rock of about the same size, which one would fly further? Why? (hint: what is the force in this example? What is the acceleration?)


Newton’s third law of motion:

For every force, there is always an equal reaction force in opposite direction.

Question: when we are pulled down by Earth’s gravity, are we also pulling up the Earth? Why doesn’t the Earth move?

Example: measuring weight on a balance.

A rocket is propelled upward by a force equal and opposite to the force with which gas is expelled out its

back.


Thought Question:A compact car and a Mack truck have a head-on

collision. Are the following true or false?

1. The force of the car on the truck is equal and opposite to the force of the truck on the car.

2. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck.

3. The change of velocity of the car is the same as the change of velocity of the truck.


Thought Question:A compact car and a Mack truck have a head-on

collision. Are the following true or false?

1. The force of the car on the truck is equal and opposite to the force of the truck on the car. T

2. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. T

3. The change of velocity of the car is the same as the change of velocity of the truck. F


What have we learned?• How did Newton change our view of the universe?

• He discovered laws of motion & gravitation.• He realized these same laws of physics were identical in the

universe and on Earth.

• What are Newton’s Three Laws of Motion?1) Object moves at constant velocity if no net force is acting.2) Force = mass acceleration 3) For every force there is an equal and opposite reaction force.


4.3 Conservation Laws in Astronomy:


• What keeps a planet rotating and orbiting the Sun?

• Where do objects get their energy?


Newton used force to describe interactions. We will se now a different approach.

There are three important conservation laws:

• Conservation of momentum• Conservation of angular momentum• Conservation of energy

These laws are embodied in Newton’s laws, but offer a different and sometimes more powerful way to consider motion.

The conservation laws actually show why Newton’s laws are true, by reflecting deeper aspects of nature – conservation of certain quantities.Example: According to Newton’s second law can we actually change

momentum? (hint: how do you change momentum of an object)


What keeps a planet rotating and orbiting the Sun?Conservation of Angular Momentum

As long as Earth doesn’t transfer angular momentum to other objects, its rotation and orbit cannot change.

Question: we have seen this law during the last class already? Do you remember who discovered it? Remember, then it was only an empirical law, here it is explained based on laws of nature.


Angular momentum conservation also explains why objectsrotate faster as they shrink in radius:

Also explains why everything in the universe is rotating…


Conservation of Energy Where do objects get their energy? What is energy?

• Energy makes matter move.Basic Types of Energy• Kinetic (motion): all objects which move have this energy. E=mv2/2.

• Radiative (light): all radiation carries this type of energy, that is why sun-light warms up our planet.

• Stored or potential: energy which can be converted to other two types, I.e., rock on a hill has gravitational potential energy, because if it slips it will start to fall, converting its energy to kinetic energy of his new motion.


Energy can change type but cannot be destroyed.

•Energy is conserved, but it can:

–Transfer from one object to another

–Change in form


Scientific unit of energy is Joule, (1 calorie = 4,184 J).There is the same unit for all three forms of energy.


Subcategory: thermal energy - the collective kinetic energy of many particles

It is easier to talk about thermal energy than kinetic energy of each of the billions of molecules in a glass of water, for example.

Thermal energy is related to temperature but it is NOT the same.

Temperature is parameter which measures the average kinetic energy of the many particles in a substance.

Subcategories of energy important in Astronomy:


Temperature Scales

Kelvin (K) is the unit used in scientific computations.


Thermal energy is a measure of the total kinetic energy of allthe particles in a substance. It therefore depends both ontemperature AND densityExample:


Subcategory: gravitational potential energy

• On Earth, depends on:– object’s mass (m)– strength of gravity (g)– distance object could

potentially fall (height, h)

Question: where does the ball travel faster, when it is higher or closer to the ground?


•Question: In space, does a gas cloud has more gravitational energy when it is spread over a large area or when it closer to the center of gravity? (hint: farther the particles are from the center, is their gravitational potential energy bigger or smaller?)


A contracting cloud converts gravitational potential energy to thermal energy.


Subcategory: energy contained in mass itself – “mass-energy”

• Mass itself is a form of potential energy

E = mcE = mc22

• A small amount of mass can release a great deal of energy• Concentrated energy can spontaneously turn into particles (for example, in particle accelerators or in the early Universe)

1 mega tone H bomb converts only about 100 grams (3 ounces) of mass into energy. Enough to destroy a major city.


Conservation of Energy

• Energy can be neither created nor destroyed.

• It can change form or be exchanged between objects.

• The total energy content of the Universe was determined in the Big Bang and remains the same today.

Question: where do objects get their energy?


Question: why do we say that the history of Universe is based on the interplay between mater and energy?


What have we learned?• What keeps a planet rotating and

orbiting the Sun?• The law of conservation of angular

momentum

• Where do objects get their energy?– Conservation of energy: energy

cannot be created or destroyed; it can only be transformed from one type to another.

– Energy comes in 3 basic types: kinetic, potential, radiative. Some subtypes important in astronomy: thermal energy, grav. Potential energy, mass-energy (E = mc2).


4.4 The Force of Gravitythe most important force in astronomy


•What determines the strength of gravity?

•How does Newton’s law of gravity extend Kepler’s laws?

•How do gravity and energy together allow us to understand orbits?

•How does gravity cause tides?


What determines the strength of gravity? The Universal Law of Gravitation (Newton)1. Every mass attracts every other mass.2. Attraction is directly proportional to the product of

their masses.3. Attraction is inversely proportional to the square of

the distance between their centers..

G- gravitational constant.


Question: how does the gravitational force between two objects change if the distance between them triples? If the mass of one object doubles?


How does Newton’s law of gravity extend Kepler’s laws?

• Newton published Principia in 1687. By that time Kepler’s laws have been well tested (for 70 years) and there was no doubt they were correct. But they were empirical laws (based on observation and it was not clear why they are true.

•Newton used mathematical expression of his law of gravity and derived all three of Kepler laws, showing they are consequence of more fundamental laws. In doing so, he also found that Kepler’s laws are only part of a story of how objects move under the influence of gravity.


Newton found that:

• Kepler’s first two laws apply to all orbiting objects, not just planets (for example, satellites around Earth, two stars in a binary system…)

• Ellipses are not the only stable orbital paths. Orbits can be:

– bound (ellipses)

– Unbound (objects close only once)

• Parabola

• hyperbola


• Newton also generalized Kepler’s Third Law:

Question: What is Kepler’s third law stating?


Newton’s version of Kepler’s Third Law

p = orbital period

a=average orbital distance (between centers)

(M1 + M2) = sum of object masses

So, if you measure the period and average distance of a smaller

object orbiting the larger one, you can calculate the mass of larger object!

p2 42G(M

1M

2)a3


Examples:• Calculate mass of Sun from Earth’s orbital period (1 year) and average distance (1 AU).• Calculate mass of Earth from orbital period and distance of a satellite.• Calculate mass of Jupiter from orbital period and distance of one of its moons.

Question: whether the space shuttle and the astronaut outside of it have the same orbital period around the Earth? Why, what determines their periods? Does the astronaut needs to be attached to the shuttle?

p2 42G(M

1M

2)a3


How can orbital paths change?

• Question: Can orbits change spontaneously?


How can orbital paths change?

• Question: Can orbits change spontaneously? • Let’s define an energy of an object in its orbit: total orbital energy = kinetic energy + gravitational potential energy• Total orbital energy stays constant along an orbit.• Question: Does kinetic energy change along orbit? How about potential

energy?


So what can make an object gain or lose orbital energy?1. A gravitational encounter with a third object: for example,

if a comet passes by Jupiter (large planet), comet’s orbit around the Sun can change dramatically.

• Question: where did the energy lost by a comet go (when it went from unbound to the bound orbit)?

Also used by spacecraft to boost orbits. Each of the two Voyagers that visited the outer planets in 1980s was deliberately sent close by Jupiter on a path that caused it to gain orbital energy at Jupiter’s expense.


2. Friction or atmospheric drag:

Examples:• satellites in low-Earth orbit can crash to Earth due to energy loss to friction

with atmosphere

• captured moons like Phobos/Deimos or many moons of Jupiter: they are big and not easy to capture. Capture by Jupiter must have happened when an extended atmosphere or gas cloud allowed enough friction for the asteroid (now moon) to lose significant amount of its energy.


• And other way around: If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit)

•escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr).

Adding some energy to a spacecraft can make a spacecraft move to a higher orbit, or ultimately escape to an unbound orbit.

Example: Hubble telescope.


Escape and orbital velocities don’t depend on the mass of the

cannonball


How does gravity cause tides?

Questions: How many tides there are during a day?

The stretching (tidal) force arises from the difference between the force of gravity on the side of the Earth closer and farther from the Moon.


Tides vary with the phase of the Moon:

The Sun also affects the tides.


Special Topic: Why does the Moon always show the same face to Earth?

Moon rotates in the same amount of time that it orbits… But why?


Tidal friction…

• Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth). Question: Explain this effect using a conservation law? (hint: which quantity describes rotation?)

• Moon once orbited faster; tidal friction caused it to “lock” in synchronous rotation.


• How does Newton’s law of gravity allow us to extend Kepler’s laws?• Applies to other objects, not

just planets.• Includes unbound orbit

shapes: parabola, hyperbola• We can now measure the

mass of other systems.

What have we learned?•What determines the strength of gravity?

•Directly proportional to the product of the masses (M x m)•Inversely proportional to the square of the separation d


What have we learned?• How do gravity and

energy together allow us to understand orbits?• Gravity determines orbits• Orbiting object cannot

change orbit without energy transfer

• Enough energy -> escape velocity -> object leaves.

•How does gravity cause tides?•Gravity stretches Earth along Earth-Moon line because the near side is pulled harder than the far side.


Review:

To describe motion we use: speed, velocity, acceleration, momentum.

Mass is measure of amount of matter in a body. It is different from weight!

Newton’s laws are:If there is no net force the objects move with constant velocityF=maWhenever there is a net force acting on an object, that object is acting with an equal force in the opposite direction on surrounding.

Conservation laws: angular momentum (mvr) and energy are conserved!

Gravitational law: F=GmM/d2

© 2005 Pearson Education Inc., publishing as Addison-Wesley Chapter 4 Making Sense of the Universe:...

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Transcript of © 2005 Pearson Education Inc., publishing as Addison-Wesley Chapter 4 Making Sense of the Universe:...