Fall 2005 Astronomy 110 1

Lecture 9 + 10

Fall 2005 Astronomy 110 2

Isaac Newton and the birth of Physics

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

Nature and Nature's laws lay hid in night;God said, Let Newton be! And all was light.Alexander Pope (1688 -1744)(Newton’s epitaph)

Fall 2005 Astronomy 110 3

• Realized the same physical laws that operate on Earth also operate in the heavens⇒ one universe

• Discovered laws of motion• Discovered gravity• Co-invented Calculus• First reflecting telescope• Many experiments with

light and color.Sir Isaac Newton(1642-1727)

Fall 2005 Astronomy 110 4

Position is a description of the location of an objectVelocity is the rate of change of position.It is made up of two pieces of information:

speed: rate of motion •

example: speed of 10 m/sand Direction

example: 10 m/s, due eastAcceleration: any change in velocity

units of speed/time (m/s2)

How did Newton describe the motion of a particle?

speed = distancetime units of ms

⎛

⎝ ⎜

⎞

⎠ ⎟

Fall 2005 Astronomy 110 5

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

When your car hits a wall - you go through the windshield.Isaac says: “Wear your seatbelt!”

Fall 2005 Astronomy 110 6

Newton’s second law of motion: Force = mass × acceleration

• Defines Mass

• Defines the effect of forces

• Includes first law (Force = 0)

Hitting the wall causes a large deceleration hence a large force on the car.

Isaac says: “Drive carefully”

Fall 2005 Astronomy 110 7

Newton’s third law of motion:For every force, there is an equal and opposite reaction force.

Putting a large force on the car results in a large reactive force on the wall –the wall breaks.

Isaac says: “Fix my wall!”

Fall 2005 Astronomy 110 8

Momentum and Force

Momentum = mass × velocity• Has direction and magnitude• A force is a change in momentum. It can be:

– an acceleration (change in velocity)• Change in speed • Change in direction

– or a change in mass (rocket)

Fall 2005 Astronomy 110 9

Newton’s Law of Universal Gravitation1. 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..

Fall 2005 Astronomy 110 10

The Acceleration of Gravity

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

• On Earth, g ≈ 10 m/s2: speed increases 10 m/s with each second of falling.

Fall 2005 Astronomy 110 11

The Acceleration of Gravity (g)

• Galileo showed that gis the same for all falling objects, regardless of their mass.

Fall 2005 Astronomy 110 12

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.

Fall 2005 Astronomy 110 13

Is there a net force? Y/N

1. A car coming to a stop. Y2. A bus speeding up. Y3. An elevator moving at constant speed. N4. A bicycle going around a curve. Y5. A moon orbiting Jupiter. Y

Fall 2005 Astronomy 110 14

What is the force between You and the Earth?

2( )You Earth

YEYou Earth

EarthYE You

Earth

YE You

Mass MassF GD

G MassF MassRadius

F g Mass

→

=

⎛ ⎞×= ×⎜ ⎟

⎝ ⎠= ×

Fall 2005 Astronomy 110 15

How is mass different from weight?• mass – an intrinsic property of an object –its resistance to

being accelerated.• weight – the force caused by gravity acting on an object. Weight is an extrinsic property! It depends on where you are.

You are weightless in free-fall!

Fall 2005 Astronomy 110 16

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.

Fall 2005 Astronomy 110 17

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.

Fall 2005 Astronomy 110 18

Why are astronauts weightless in space?

• There IS gravity in space…• weightlessness is due to a constant state of free-fall:

Fall 2005 Astronomy 110 19

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.

Fall 2005 Astronomy 110 20

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

Fall 2005 Astronomy 110 21

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.

Fall 2005 Astronomy 110 22

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.

Fall 2005 Astronomy 110 23

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

Fall 2005 Astronomy 110 24

Where do objects get their energy?

Energy is either associated with motion (Kinetic energy, heat etc)

OrThe ability to do work. (chemical potential energy, gravitational potential

energy)Energy is conserved, but it can:

– Transfer from one object to another– Change in form

Fall 2005 Astronomy 110 25

Gravitational Potential Energy

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

potentially fall

Fall 2005 Astronomy 110 26

Gravitational Potential Energy

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

⇒A contracting cloud converts grav. potential energy to thermal energy.

Fall 2005 Astronomy 110 27

Newton’s law of gravity derives Kepler’s laws.

• Ellipses are not the only orbital paths. Orbits can be:– bound (ellipses)– unbound

• Parabola• hyperbola

• Kepler’s first two laws apply to all orbiting objects, not just planets

Fall 2005 Astronomy 110 28

• Newton generalized Kepler’s Third Law:Planet orbits balance Gravity with Centripetal acceleration

2

2

2 32

2

4

p

p p

pp

p

p p

VGMR R

RV

P

GM P R

π

π

=

=

⎛ ⎞ =⎜ ⎟⎝ ⎠

Fall 2005 Astronomy 110 29

• 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)

Fall 2005 Astronomy 110 30

How does gravity cause tides?

Fall 2005 Astronomy 110 31

Tides vary with the phase of the Moon:

Fall 2005 Astronomy 110 32

Tidal friction…

• Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth).

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

Fall 2005 Astronomy 110 33

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)