Gravitational Potential Energy and Escape Velocity
3
Blast-off: Forces at work during rocket launches
3
Circular Motion
3
Satellites and Newton’s Law of Universal Gravitation
4
Deep-Space Probes
4
Communication Between Earth and Satellites
4
Re-entry Into the Earth’s Atmosphere
5
Limitations of Current Space Travel
5
Galolean-Newtonian Theory
5
The Ether
5
The Michelson-Morley Experiment
5
Einstein’s Relativity
5
Simultaneity
6
Time Dilation and the Twin Paradox
6
Length Contraction
6
Four-Dimensional Space-Time
6
Mass Increase
6
Mass and Energy
6
Future Space Travel
7
Electric Motors and Generators
8
Introduction
8
Electric Charges in Magnetic Fields
8
Conductors Carrying a Current in a Magnetic Field
8
Two Parallel Wires Carrying Current
8
Designing Electric Motors
9
Moving a Conductor in a Magnetic Field
9
What Happens in the External Circuit?
10
Electromagnetic Induction Using a Coil and a Magnet
10
Designing Generators
10
Transmitting Electricity From the Generator to the Consumer
11
AC or DC Generators?
11
Transformers
11
Motors That Operate on AC
12
1
Space
Gravitational Acceleration
• All objects accelerate towards the Earth at the same rate
• The weight of an object is equal to its mass multiplied by the acceleration due to gravity.
Projectile Motion and Galileo’s Analysis
• Galileo stated that any projectile motion near or on the Earth’s surface could be determined by using the formula.
for the horizontal distance travelled, and
for vertical distance travelled.
• Half-flight projectile motion:
• Full-flight projectile motion:
2
Escape Velocity
• The slowest speed at which a projectile can travel into space is called the escape velocity.
Gravitational Potential Energy and Escape Velocity
• The formula for gravitational energy of an object at a distance r from the centre of the Earth is:
• The escape velocity, ve can be found by determining the kinetic energy that a body of mass m must use to escape from the gravitational potential of a planet of mass M and radius r:
Blast-off: Forces at work during rocket launches
• Space rockets burn liquid fuel with their own supply of oxygen. Gaseous products of combustion shoot out of the rocket with tremendous force. Reaction to the force propels the rocket forwards. • The velocity at the conclusion of powered flight is called vacuum burnout velocity (vvb):
• Lift-off, re-entry, and landing impose considerable stress on the human body. Launch accelerations of 5g to 7g are, however, easily tolerated by astronauts because of the support given by the carefully designed launch-and-operations couch.
Circular Motion
• Angular velocity:
• Tangential, linear, or orbital velocity:
• Centripetal acceleration:
3
• Centripetal force:
Satellites and Newton’s Law of Universal Gravitation
• Newton’s Law of Universal Gravitation can explain the motion of satellites around the Earth and the motion of planets around the sun.
• The force of gravity (FG) provides the centripetal force Fc for a satellite to orbit the Earth:
• Relationships between the period (T) of the satellite, the mass of the Earth (ME) and the distance from the centre of the Earth to the satellite (r) are expressed by:
• A satellite 35 680 km above the Earth’s surface takes 24 hours to complete one orbit of the
Earth. Such a satellite is said to be geosynchronous.
• A geostationary satellite is a geosynchronous satellite whose orbit is in the same plane as the
Earth’s equator.
Deep-Space Probes
• The simplest way to travel between the planets is to let the sun’s gravity do the work and take
