Chapter 4 Making Sense of the Universe

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

Sir Isaac Newton• Much of what we learned

from Newton was published in a text he wrote which is known today as “Principia”.

• Newton’s picture will indicate one of his contributions presented in this lecture that was first published in the Principia

Before we go into what Newton taught us. How do we 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

• ForceAn influence on motione.g. pushing, pulling, friction, gravity, etc.

Newton’s first law of motion: Law of Inertia

• An object moves at constant velocity unless a net force acts to change its speed or direction.

or• “A body remains at rest or moves in a straight line at a

constant speed unless acted upon by a force.”

More definitions• Acceleration

– Change in Velocity• What are three examples of acceleration?

– Speeding up– Slowing Down– Turning

• Mass- the amount of matter in an object. Also a measure of the resistance of an object to undergo an acceleration

Or as Newton first defined it• The quantity of matter is that which arises conjointly from its density and

magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass.

Newton’s Second Law

• Net Force = mass • acceleration• F = m a

• “The amount of acceleration that a force produces depends on the mass of the object being accelerated.”

• If more than one force is acting on an object the sum of the forces is called the net force…. Examples

Forces

• We earlier gave examples of forces as– pushing, pulling, friction, gravity, etc

• Newton was the first to identify and mathematically define the force of gravity.

• End of Aristotle’s separation of Heaven and Earth

Newton’s The Law of Gravity

• Every mass exerts a force of attraction on every other mass.

• The math…

• G = 6.67 10-11 N·m2/kg2

2rGMmF

Gravity Questions

• If the distance between two objects in space is doubled, then what happens to the gravitational force between them?

• What if the distance is tripled?• …quadrupled?

If we drop a rock

• The only force acting on the falling object is gravity. Thus the net force is the force of gravity.

• Write F=ma and solve for a

arock Fg

M rock

Fg G MEarth M rock

REarth2

22Earth

Earth

rock2Earth

rockEarthrock /81.9 sm

RMG

MRMMGa

Acceleration due to gravity

• The acceleration due to gravity on the earths surface is g=9.81m/s2 and always points towards the center of the earth for all objects regardless of their mass.

• This was first demonstratedby Galileo dropping objectsfrom the leaning tower of Pisa

Apollo 15 demonstration

Mass of the Earth

• Since we can experimentally measure the acceleration due to gravity we could use Newton’s Universal Gravitation to calculate the mass of the earth.

• Density

Weight

• Weight is the force of gravity acting on an object.

• Weight = (mass • acceleration due to gravity)• W=mg

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.

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.

How does gravity cause tides?

• Moon’s gravity pulls harder on near side of Earth than on far side

• Difference in Moon’s gravitational pull stretches Earth

Tides and Phases

Size of tides depends on phase of Moon

Newton’s Third Law Action-Reaction

• Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body.”

Thought Question:When you jump out of a plane, is the force the Earth exerts on you larger,

smaller, or the same as the force you exert on it?

A. Earth exerts a larger force on you. B. I exert a larger force on Earth.C. Earth and I exert equal and opposite forces on

each other.

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

Apparent Weight

• What a scale would read.

• You appear weightless in free-fall

Weightless

• To have a weight equal to zero you would have to be an infinite distance from all mass.

• Weightless instead implies your apparent weight would be zero.

• This is the case in the elevator accelerating down with a=g

• This is the case for astronauts in orbit

• There is gravity in space

• Weightlessness is due to a constant state of free-fall

Why are astronauts weightless in space?

Kepler’s laws revisited

• Newton was able to show that Kepler’s laws hold for all gravitationally bound orbits, not just planets around the sun.– Moon orbiting earth, comets, etc.

• Newton also showed orbits can be any conic section not just ellipses. – Parabolic and hyperbolic orbits are “unbound”

meaning they do not close on themselves

Kepler’s 3rd law revisited

• Newton was also able to generalize Kepler’s 3rd law.

• G is the G from Universal gravitation, M1 and M2 are the masses of the system

• With this we can calculate the mass of each member of the solar system.– We know the mass of the earth– Use earth to get the sun…

p2 42G(M1M2)a3 OR M1M2

42

Ga3

p2

Geosynchronous orbitsAll are at an altitude of 3.58 x 107 m or ~ 22,300 miles above the Earth. The period is one day

Conservation Laws in Physics

• It can be shown (by magic, hand waving, or miracle) that certain quantities in physics are constant under certain circumstances. Thus we say these quantities are conserved.

• Conserved quantities– Momentum– Angular momentum– Energy

Conservation of Momentum

• The total momentum of interacting objects cannot change unless an external force is acting on them

• Interacting objects exchange momentum through equal and opposite forces

Conservation of Angular Momentum

• The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it

• Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely

• This is the reason for precession of the earths axis

angular momentum = mass x velocity x radius

Conservation of angular momentum is hat keeps a planet

rotating and orbiting the Sun?

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

Energy

• Energy is the mover of matter, it cannot be created or destroyed, only changed from one type to another

• Types of energyKinetic PotentialRadiative (Radiation/light) ThermalMass-energy And others...

Kinetic Energy• Kinetic Energy is the energy of motion.

• Kinetic Energy = ½ mass speed2

2mv21KE

Braking ExampleA car traveling 60 mph will skid 4 times

farther than a car traveling 30 mph.

Cosmic ConnectionsIn 1994 a comet collided with Jupiter.

The more massive fragments imparted more energy into the atmosphere of Jupiter.

150 ft. meteor impact in Arizona. 1 mi in diameter

June 30, 1908, 7:17 a.m. local time, Tungus natives and Russian settlers in the hills observed a column of bluish light, nearly as bright as the Sun, moving across the sky. About 10 minutes later, there was a flash and a sound similar to artillery fire. The sounds were accompanied by a shock wave that knocked people off their feet and broke windows hundreds of miles away. The majority of eyewitnesses reported only the sounds and the tremors, and not the sighting of the explosion. The explosion registered on seismic stations.Kulik's party reached the site in 1927.

Tunguska Event

• ~ 100 m (330 ft.) meteor exploded above ground.

Thermal Energy: the collective kinetic energy of many particles

(for example, in a rock, in air, in water)

Thermal energy is related to temperature but it is NOT the same.Temperature is the average kinetic energy of the many particles in a substance.

Thermal Energy

Cool Hot

Temperature Scales

Mass-Energy• Mass itself is a form of potential energy

E = mc2

• A small amount of mass can release a great deal of energy

• Concentrated energy can spontaneously turn into particles (for example, in particle accelerators)

Potential Energy• The energy that is stored is called

potential energy.

• Examples: – Rubber bands– Springs– Bows– Batteries– Gravity– Chemical

Gravitational Potential Energy

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

potentially fall

Gravitational Potential Energy

• In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.

Þ A contracting cloud converts gravitational potential energy to thermal energy.

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

• Total orbital energy (gravitational + kinetic) stays constant if there is no external force

• Orbits cannot change spontaneously.

More gravitational energy;Less kinetic energy

Less gravitational energy;More kinetic energy

Total orbital energy stays constant

Þ So what can make an object gain or lose orbital energy?

• Friction or atmospheric drag

• A gravitational encounter.

Changing an Orbit

Orbital velocity

• It can be shown the speed of an object in orbit at a given radius R is given by

• Note it is only dependent on the mass of the object being orbited.

RGMV =

• 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)

Escape Velocity

RGM2Ve =

Escape Velocity