Ch4: making Sense of the Universe: Understanding Motion, Energy, and Gravity part1
Making Sense of the Universe: Understanding PHYSICS
1) Motion
a. Position, Speed, Velocity, Acceleration
b. Momentum and Force
c. Types of Motion (Straight, Curved)
d. Mass and Weight
2) Newton’s 3 Laws
3) Momentum’s 3 Laws
4) Gravity
How do we describe motion? ~Position & Distance~
Motion = Change in Position → Distance is generated.
Position = Location of Object (A point on coordinate measured from Origin)
Distance = Amount of Change in Position (A range over coordinate)
How do we describe motion? ~Speed & Velocity~
Speed: Rate of Distance over Time
~Acceleration~
Acceleration: Rate of change in VELOCITY unit of speed/time [m/s²]
The Acceleration of Gravity
All falling objects accelerate at the same rate (not counting friction of air resistance).
On Earth, g=10 m/s with each second of falling
The Gravitational Acceleration (g)
Galileo showed that g is the same for all falling objects, regardless of their mass
Momentum and Force
→ Means how “powerfully” an object is moving.
A net force changes momentum, which generally means an acceleration (change in velocity). → Newton’s 2^nd law
Rotational momentum of a spinning or orbiting object is known as angular momentum.
→ Means how “powerfully” an object is spinning.
How is mass different from weight?
Mass : a measure of the amount of matter in an object
Weight : the force that a scale exerts upon an object due to gravity
Thought Question
On the moon:
→ My weight is less, my mass is the same
Why are astronauts weightless in space ?
There is gravity in space.
Weightlessness is due to a constant state of free-fall.
Moving in Circles
Angular momentum describes objects that are spinning or moving in circles.
A special force, a torque, is needed to change an object’s angular momentum.
What have we learned?
How do we describe motion?
Speed = distance / time
Speed and direction => velocity
Change in velocity => acceleration
Momentum = mass x velocity
Angular Momentum = mass x radius x velocity
Force causes change in momentum, producing acceleration
How is mass different from weight?
Mass = quantity of matter
Weight = force acting on mass
Objects are weightless in free-fall
Thought Question
For each of the following is there a net force on the object described? Y/N
A car coming to a stop → Y
A bus speeding up → Y
An elevator moving at constant speed → N
A bicycle going around a curve → Y
A moon orbiting Jupiter → Y
Newton’s Laws of Motion
How did Newton change our view of the universe?
Realized the same physical laws that operate on Earth also operate on Earth also operate in the heavens
“one universe”
Discovered laws of motion and gravity
Much more: experiments with light, first reflecting telescope, calculus….
What are Newton’s three laws of motion?
Newton’s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.
👇🏻
Inertia
Newton’s Second Law of Motion
Two equivalent expressions
Newton’s third law of motion:
For every force, there is always an equal and opposite reaction force.
“Action & Reaction pair!
Thought Question
How does the force the Earth exerts on you compare with the force you exert on it?
→ Earth and you exert equal and opposite forces on each other.
What have we learned?
How did Newton change our view of the universe?
He discovered laws of motion and gravitation
He realized these same laws of physics were identical in the universe on Earth.
What are Newton’s three laws of motion?
Object moves at constant velocity if no net force is acting.
Force = mass x acceleration
For every force there is an equal and opposite reaction force.
Conservational Laws in Astronomy
Why do objects move at constant velocity if no force acts on them?
Objects continue at constant velocity because of 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.
Thought Question
A compact car and a Mack truck have a head-on collision. Are the following true or false?
The force of the car on the truck is equal and opposite to the force of the truck on the car. → T
The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck → T
The change of velocity of the car is the same as the change of velocity of the truck. → F
What keeps a planet rotating and orbiting the Sun?
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.
Angular momentum conservation also explains why objects rotate faster as they shrink in radius.
Where do objects get their energy?
Energy makes matter move.
Energy is conserved, but it can:
Transfer from one object to another
change in form
Basic Types of Energy
Kinetic (motion)
Radiative (light)
Potential (stored)
Energy can change type, but cannot be created or destroyed
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 is a substance.
Temperature Scales
Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends on both temperature AND density
Example:
Gravitational Potential Energy
On Earth, depends on:
object’s mass (m)
strength of gravity (g)
distance object could potentially fall
In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.
A contracting cloud converts gravitational potential energy to thermal energy.
Mass-Energy
Mass itself is a form of potential energy:
E = mc²
A small amount of mass can release a great deal of energy (for example, an H-bomb).
Concentrated energy can spontaneously turn into particles (for example, in particle accelerators).
Conservation of Energy
Energy can be neither created nor destroyed.
It can change form or be exchanged between objects.
The total energy content in an isolated system is always the same.
What have we learned?
Why do objects move at constant velocity if no force acts on them?
Conservation of momentum
What keeps a planet rotating and orbiting the Sun?
Conservation of angular momentum
Where do objects get their energy?
Conservation of energy: energy cannot be created or destroyed but only transformed from one type to another.
Energy comes in three basic types: kinetic, potential, radiative
The Universal Law of Gravitation
What determines the strength of gravity?
The universal law of gravitation:
Every mass attracts every other mass.
Attraction is directly proportional to the product of their masses.
Attraction is inversely proportional to the square of the distance between their centers.
How does Newton’s law of gravity extend Kepler’s laws?
Kepler’s laws apply to all orbiting objects, not just planets.
Eclipses are not the only orbital paths.
Orbits can be:
bound (eclipses)
unbound
parabola
hyperbola (Swing-by method to accelerate interplanetary satellite)
Center of Mass
Because of momentum conservation, orbiting objects orbit around their center of mass.
Newton and Kepler’s Third Law
Newton’s laws of gravity and motion showed that the relationship between the orbital period and average orbital distance of a system tells us the total mass of the system.
Examples:
Earth’s orbital period (1 year) and average distance (1AU) tells us the Sun’s mass.
Orbital period and distance of a satellite from Earth tell us Earth’s mass
Orbital period and distance of a moon of Jupiter tell us Jupiter’s mass
Newton’s Version of Kepler’s Third Law
p = orbital period
a = average orbital distance (between centers)
(M1 + M2) = sum of object masses
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
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
Can be used to measure mass of orbiting systems
Orbits, Tides, and the Acceleration of Gravity
How do gravity and energy together allow us to understand orbits?
Total orbital energy (gravitational + kinetic) stays constant it there is no external force
Orbits cannot change spontaneously.
Changing an orbit
So what can make an object gain or lose orbital energy?
Friction or atmospheric drag
A gravitational encounter
Escape Velocity
If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit).
Escape velocity from Earth = 11km/s from sea level (about 40,000 km/hr)
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
The Sun also has a small tidal effect on Earth. (Less than half of the Moon’s)
Size of tides thus depends on phase of Moon.
Tidal Friction
Tidal friction gradually slows Earth’s rotation (and makes the Moon get farther from Earth).
The Moon once orbited faster (or slower); tidal friction caused it to “lock” in synchronous rotation.
Why do all objects fall at the same rate?
The gravitational acceleration of an object like a rock does not depend on its mass because M rock in the equation for acceleration cancels M rock in the equation for gravitational force.
This “coincidence” was not understood until Einstein’s general theory of relativity.
What have we learned?
How do gravity and energy together allow us to understand orbits?
Change in total energy is needed to change orbit
Add enough energy (escape velocity) and object leaves
How does gravity cause tides?
The Moon’s gravity stretches Earth and its oceans.
Why do all objects fall at the same rate?
Mass of object in Newton’s second law exactly cancels mass in law of gravitation.