AST101 - Chapter 4.docx

4 Pages
Unlock Document

University of Toronto St. George
Astronomy & Astrophysics
Michael Reid

4.1 Describing motion examples from daily life How do we describe motion?  Speed: how far it in a certain amount of time  Velocity: both speed and direction  Acceleration: when velocity is changing in any way (examples: speeding up, turning, slowing down) The Acceleration of Gravity -Galileo demonstrated that gravity accelerates all objects by the same amount, regardless of their mass. However, while a feather floats gently to the ground, while a rock plummets, air resistance causes this difference in acceleration. If you dropped a feather and a rock on the Moon, where there is no air, both would fall at exactly the same time  Acceleration of gravity: the acceleration of a falling object is called the, abbreviated g  Acceleration of gravity on Earth: about 10 m/s^2, which means an unsupported object’s downward velocity increases by 10m/s with each passing second (neglecting air resistance) Momentum and Force Momentum - is the product of its mass and velocity (momentum = mass x velocity) - only way to change an object’s momentum is to apply a force to it - a change in momentum occurs only when the net force (overall force) is not zero, which causes an object to accelerate - changing an object’s momentum means changing its velocity, as long as its mass remains constant - an object with greater mass has more momentum - planets are always accelerating as they orbit the Sun, because their direction of travel constantly changes as they go around their orbits Force - always present o Ex. on Earth we always feel the force of gravity and there are always electromagnetic forces acting between atoms - mere presence of a force does not always cause a change in momentum - there is no net force on your car when you are driving at constant velocity, because the force generated by the engine to turn the wheels precisely offsets the forces of air resistance and road friction Mass - is amount of matter in your body Weight - is the force that a scale measures when you stand on it, that is, weight depends both on your mass and on the forces (including gravity) acting on the mass Free-fall - falling without any resistance to slow you down - the floor drops away at the same rate that you fall, allowing you to float freely above it, and the scale reads zero because you are no longer held to it o In other words, your free-fall has made you weightless - you are in free-fall whenever there’s nothing to prevent you from falling - astronauts are weightless when they orbit Earth because they are in a constant state of free-fall 4.2 Newton’s Laws of motion - your body always exerts a gravitational force on Earth identical to the force that Earth exerts on you, except that it act in the opposite direction - the same force means a much greater acceleration for you than for Earth (because your mass is so much smaller than Earth’s), which is why you fall toward Earth when you jump off a chair, rather than Earth falling to you - Newton realized that gravity operated in the heavens as well as on Earth, eliminating Aristotle’s distinction between the two realms. For the first time in history, the heavens and Earth were brought together as one universe Newton’s three laws of motion  Newton’s First Law: an object moves at constant velocity if there is no net force acting upon it (objects will remain in motion unless a force acts to stop them)  Newton’s Second Law: force = max x acceleration (or F = ma) (the amount of acceleration depends on the object’s mass and the strength of the net force)  Newton’s Third Law: for any force, there is an equal and opposite reaction force (objects always attract each other through gravity, a departing rocket) 4.3 Conservation Laws in Astronomy  Law of conservation of momentum: the total momentum of interacting objects cannot change as long as no external force is acting on them. An individual object can gain or lose momentum only if some other object’s momentum changes by a precisely opposite amount  Law of conservation of angular momentum: as long as there is no external torque (twisting force), the total angular momentum of a set of interacting objects cannot change. An individual object can change its angular momentum only by transferring some angular momentum to or from another object. Angular momentum = (mass) x (velocity) x (radius)  Law of conservation energy: like momentum and angular momentum, energy cannot appear out of nowhere or disappear into nothingness. Objects can gain or lose energy only by exchanging energy with other objects. Two key facts about Earth’s orbit: 1) Needs no fuel or push to keep orbiting the Sun (will keep orbiting as long as nothing comes along to take angular momentum away) 2) Because Earth’s angular momentum at any point in its orbit depends on the product of its speed and orbital radius (distance from the Sun), Earth’s orbital speed must be faster when it is nearer to the Sun (and the radius is smaller) and slower when it is farther from the Sun (and the radius is larger) -If distance (r) is greater, velocity (v) is smaller and vice versa Where do objects get their energy? - Energy is what makes matter move - Regardless of which type of energy we are dealing with, we can measure the amount of energy with the same standard units (joule-the standard unit of energy) - Energy can be converted from one form to another, but it can never be created or destroyed Basic Types of Energy  Kinetic energy (energy of motion): Falling rocks, orbiting planets, and the molecules moving in the air are all examples of objects with kinetic energy. Quantitatively, the kinetic energy of a moving object is 1/2 mv^2, where m is the object’s mass and v is its speed  Radiative energy (energy carried by light): All light carries energy, which is why light can cause changes in matter. For example, light warms the surface of a planet  Stored energy (potential energy): Which might later be converted into kinetic or radiative energy. For example, a rock perched on a ledge has gravitational potential energy because it will fall if it slips off the edge, and gasoline contains chemical potential energy that can be converted into the kinetic energy of a moving car Thermal Energy – The Kinetic Energy of Many particles Thermal energy (subcategory of kinetic energy): measures the total (collective)kinetic energy of all the randomly moving particles in a substance, while temperature measures the average kinetic energy of the particles. Kelvin temperature scale: often used in science, this scale never uses negative temperatures, because it starts from the coldest possible temperature, known as absolute zero (0 k) Potential Energy in Astronomy Gravitational potential energy - depends on an object’s mass and how far it can fall as a result of gravity - has more gravitational potential energy when it is higher For an object near Earth’s surface, its gravitational potential energy is mgh, where m is its mass, g is the acceleration of gravity, and h is its height above the ground) -if you throw a ball up into the air, it has more potential energy when it is near the ground. Because energy must be conserved during the ball’s flight, the ball’s kinetic energy increases when its gravitational potential energy decreases, and vice versa. -the higher it is, the more gravitational potential energy it has and the slower the ball travels (less kinetic energy) -the second particularly important form of potential energy in astronomy is the energy con
More Less

Related notes for AST101H1

Log In


Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.