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Chapter 4

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John Lester

Astronomy Textbook Notes Chapter 4 Making Sense of the Universe Speed – tells us how fast an object will go in a certain amount of time. Velocity – tells us both the speed and the direction. Acceleration – an object has acceleration if its velocity is changing in anyway, whether its speed or direction.  In science, accelerating is used when you are slowing down or turning, not just motion.  Slowing down occurs when acceleration is in a direct opposite to the motion  acceleration = negative, causing velocity to decrease.  Turning changes your velocity because it changes the direction which you are moving  even if your speed is constant.  You don’t feel effects when moving at a constant speed. Acceleration of Gravity: - Galileo demonstrated that gravity accelerates all objects by the same amount, regardless of their mass.  Air resistance causes a difference of acceleration. o If you dropped an object on the moon, where there is no air, they would both fall at exactly the same rate. - Acceleration of a falling object is called the acceleration of gravity (G).  Earth causes the acceleration of gravity to fall faster by 9.8 m/s or 10 m/s each passing second. o Suppose you drop a rock from a tall building, the moment you let it go, its sped is about 10 m/s. After 1 second, the rock will be falling at about 10 m/s and after 2 seconds, it will fall at 20 m/s. o Absence of air resistance will cause speed to increase by about 10 m/s each second until it hits the floor. o Therefore the acceleration of gravity is 10 meters per second, per second (10m/s^2) Momentum – the product of its mass and its velocity = mass X velocity. - The only way to change an objects momentum is to apply force to it.  two concepts that show relationship between interaction of objects.  Example: Truck and bug move at 30 km/hr. If bug slams into you at that speed, bug will squish and cause little damage because it did not exert that much speed. However, if a truck slams into you at 20 km/hr, it will cause more damage. This is due to the fact that it imparted enough of its momentum to cause dramatic and sudden change in your car’s momentum. You feel this sudden change in momentum as a force.  Mere presence of a force doesn’t always cause a change in momentum. o Ex. Car is always affected by air resistance and friction. Forces will slow your car if you take your foot of the gas pedal. You an maintain a constant a constant velocity, constant momentum if Astronomy Textbook Notes Chapter 4 Making Sense of the Universe you apply enough force to overcome these slow effects of these forces.  Forces are always present such as force of gravity or electromagnetic forces acting between atoms.  Net Force (overall force) – acting on an object represents the combined effect of all the individual forces put together. o There is no net force on your car, because force from engine to move wheels, offsets forces of air resistance and road friction. o A change of momentum occurs when the net force is not zero.  A net force that is not zero causes an object to accelerate.  An object must accelerate whenever a net force acts on it. o Planets accelerating as they orbit the sun beause travel constantly changes as they go around their orbits… Some force must be acting this acceleration. Mass vs. Weight: - Bathroom scale = measures your weight NOT mass… doesn’t matter when we are talking about objects on earth. In Astronomy however:  Your mass is the amount of matter in your body.  Weight/Apparent Weight is the force that a scale measures when you stand on it. Depends on your mass and the forces acting on your mass (including gravity). o Example: elevator with scale. When moving upward = greater force. Downward = lower weight. Shows different weight when elevator is accelerating, not going up/down at a constant speed.  Your mass is the same no matter where you are, but your weight can vary. o Example: Moon = your mass is the same as on Earth, but your weight is less, because the forces of gravity is weaker. Free-fall – falling without resistance to slow you down.  Free-fall makes you weightless. o Jumping off a chair or of a diving board/trampoline. We experience it many times in our lives. - Astronauts are in free-fall, reason to why they are weightless.  They are in constant state of free-fall.  Imagine jumping off a tower, the faster you run from it, the farther you go from falling from it.  If you go fast enough (28,000 km/hr) you would move far enough, that you’d not be going down at all.. you’d be high above earth as you were before = you would be orbiting Earth.  The Space Shuttle, Space Station and all other objects orbiting stay in orbit because they are constantly “falling around” Earth. Their constant state of free-fall makes these spacecraft and everything in them weightless. Astronomy Textbook Notes Chapter 4 Making Sense of the Universe Newton’s Law of Motion: - Born in Lincolnshire, England on Christmas Day 1642 - Had inspiration in 1666 when he saw an apple fall to the ground, realizing that the gravity that made it fall was the gravity held the moon in orbit around the Earth.  Shattered the remaining vestiges of the Aristotelian view of the world, for which centuries has been accepted. o Belief in an Earth-centered cosmo. Believed that heavens were completely distinct from Earth and Earth did not apply to heavenly motion.  When he saw the apple fall, the Copernican revolution had displaced earth from a central position and Galileo’s experiments had shown that the laws of physics were not what Aristotle believed. - Showed that the same physical laws that operate on Earth as well as in the heavens.  Were brought together as one universe for the first time in history. - Heralded the birth of the modern science of astrophysics (applies physical laws discovered on Earth to phenomena throughout the cosmos). - He quantified the laws of motion and gravity, conducted crucial experiments regarding the nature of the light, build first reflecting telescope, and invented the mathematics of calculus. - Published the laws of motion and gravity in “Mathematical Principle of Natural Philosophy” (principia). Laws: 1) Newton’s First Law: An object moves at constant velocity of there is no net force acting upon it.  Example: If a car were in space, moving at a constant speed (no friction or air resistance), then it would keep on moving forever. o This is why spaceships needs no fuel to keep going after they are launched into space (or other objects in space).  Explains why you don’t feel sensation of motion on an airplane because it is moving at a constant velocity (no net force is acting upon it). You can walk around, sit, sleep as though as you were on the ground. 2) Newton’s Second Law: Force = mass X acceleration (F=ma)  Tells us what happens when a force is present.  The amount of acceleration depends on the objects mass and strength of the net force. o Example: When you can throw a baseball farther than you can throw a shot in the shot put. A baseball accelerates as the pitcher applies a force from the pitchers arm ceases and the ball’s path changes only because the forces of gravity and air resistance. o Explains why large planets such as Jupiter have a greater effect on asteroids and comets than small planets such as Earth. Jupiter is much more massive than Earth, it exerts stronger gravitational Astronomy Textbook Notes Chapter 4 Making Sense of the Universe force on passing asteroids and therefore sends them scattering with greater acceleration. 3) Newton’s Third Law: For any force, there is always an equal and opposite reaction force.  Example: when you are standing on the ground, you are extering a downward force because of your weight. The fact that you are not falling means there is no net force acting on you, meaning that the ground is extering an upward force, offsetting the downward force.  Tells us objects always are attracting each other through gravity. o Example: Earth and Us. Your body exerts a gravitational force on earth (vice versa). The same force means that a much greater acceleration for you than Earth which is why we fall towards Earth when we jump, rather than Earth falls towards us.  Explains Rockets: propelled upward by a force equal and opposite to the force with which gas is expelled out its back. - Conservation of momentum: the law that tells us that the total momentum of all interacting objects always stays the same.  An object can lose and gain momentum when a force causes it to exchange momentum with another object. Angular Momentum: Momentum attributable to rotation or revolution. The angular momentum of an object moving in a circle of radius r is the product m X v X r.  Angular rises because a circle turns through an angle of 360 degrees. Conservation of Angular Momentum: an objects angular momentum cannot change unless it transfers angular momentum to or from another object.  m X v X r o M= Earth’s mass, V=speed(velocity) around the orbit, R=radius of the orbit (Earth’s distance from the Sun).  Because there is no objects around to take angular momentum from Earth as it orbits the sun, Earth’s orbital angular momentum remains always the same. Two key facts about the Earth’s orbit: 1) Earth needs no fuel or push of any kind to keep orbiting the Sun—it 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)  Kepler’s law is proved to be TRUE. Astronomy Textbook Notes Chapter 4 Making Sense of the Universe - As long as Earth isn’t transferring any of its angular momentum of its rotation to another object, it keeps rotating the same.  However, it is transferring (GRADUALLY) to the moon, which is slowing its rotation. - Also tells us why we see spinning disks in the universe, such as disk galaxies, like the milky way and disks of materials orbiting young stars.  Figure Skater – when arms are extended she decreases her radius, meaning her velocity of rotation must increase.  Like spinning skaters, large clouds that made our galaxy must spin faster as gravity makes them shrink in size. Laws of conservation energy: energy can be transferred from one object to another or transformed from one type to another, but the total amount of energy is usually conserved. - Like momentum and angular momentum, energy cannot appear of nowhere and disappear into nothingness. Objects can gain or lose energy with other objects. Basic Types of Energy: - Kinetic Energy (kinetic = motion; Greek) – energy of motion.  Falling rocks, orbiting planets, and the molecules moving in the air. Thermal Energy: represents collective kinetic energy of the many individual particles (atoms and molecules) moving randomly within a substance. o Ex. Rock or the air or the gas within a distant star. o Related to temperature, but not the same thing. Thermal energy measures the total kinetic energy of all the randomly moving particles in a substance. Temperature = measures the average kinetic energy of the particles.  For a particular object, a higher temperature means that the particles o average have more kinetic energy and hence are moving faster.  Measured by Kelvin  measured at absolute zero (K) coldest possible temperature, no random motions, no negative temperatures. o Thermal energy relies on temperature because a higher o average kinetic energy for the particles in a substance must also lead to a higher total energy. o Depends on the density and number of particles.  Example: Pot of boiling water, air in a hot oven… reason is density. If air or water is hotter than your body, molecules striking your skin transfer thermal energy to molecules in your arm. T
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