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Chapter 4

Chapter 4

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PHYS 183
Tracy Webb

PHYS 183 – The Milky Way Inside and Out – Tracy Webb Winter 2013 4: Making Sense of the Universe 4.1 Describing Motion: Examples from Daily Life  speed: tells us how fair something will go in a certain amount of time  100 km/hour  velocity: tells us speed and direction  100 km/hour N  acceleration: velocity is changing in any way (speed, direction or both)  going faster or slower  slowing down means acceleration is negative, so velocity decreases  turning changes velocity since you change direction, so turning is a form of acceleration even if your speed remains constant  gravity accelerates all objects by the same amount regardless of mass  air resistance causes differences in acceleration of objects falling  acceleration gravity: acceleration of a falling object; g = 9.8 m/s ) o on earth, it is 9.8 metres/second o happens each second so after 2 seconds it is 20 m/s  momentum: product of the mass of an object and it’s velocity; momentum = mass x velocity  force: anything that can cause a change in an object’s momentum  if a 2 ton truck and a fly have the same velocity towards your car, the truck will do more damage o truck has greater mass  more momentum o truck passes more momentum onto the care than the bug  more force o truck imparts enough momentum to change car’s momentum fast  presence of force doesn’t always change momentum  air resistance and friction doesn’t affect car if you maintain a constant velocity and therefore a constant momentum  some forces always present  gravity, electromagnetic forces  net force: overall force representing combined effect of all individual forces put together o no net force of car when driving at constant velocity  force generated by engine to turn wheels offsets forces of air resistance & friction  change in momentum occurs when net force is not zero  when an object accelerates, a none-zero amount of net force must be causing the acceleration  planets are always acceleration as they orbit the sun because their direction of travel constantly changes as they go around their orbits  some force is causing the acceleration  angular momentum: total momentum when spinning or moving along a curved path o earth has angular momentum since it is rotating  rotational angular momentum o earth has angular momentum since it is orbiting  orbital angular momentum  angular momentum can only change when special type of force is applied to it  torque: the type of force that can change an object’s angular momentum  twisting force o ie/ if you push on the hinges of a swinging door, nothing will happen; if you push on part of door farthest from hinges it will swing o amount of torque depends on how much force is applied & where it is applied  mass: the amount of matter in your body  weight: the force a scale measures when you stand on it  depends on mass & forces acting on mass  weight changes in an elevator when it accelerates o increases when elevator accelerates positively  working against gravity PHYS 183 – The Milky Way Inside and Out – Tracy Webb Winter 2013 o decreases when elevator accelerates negatively  working with gravity  free fall: falling without any resistance to slow you down  makes you weightless o happens when there’s nothing to prevent you from falling o you are weightless when you jump until you hit the ground  space station & orbiting objects stay in orbit because they are constantly falling around the earth  constant state of free fall makes them weightless 4.2 Newton’s Laws of Motion  Isaac Newton saw an apple fall from a tree  realized gravity making the apple fall was the same force holding the moon in orbit  at this time, Copernican Revolution displaced earth from central position  first time in history, earth & heavens brought together as one universe  birth of astrophysics  quantified laws of motion & gravity, conducted experiments with light, built first reflecting telescopes, invented mathematics of calculus  Newton’s laws of motion: laws that govern the motion of everything  Newton’s first law: an object moves at constant velocity if there is no net force acting upon it o objects with no velocity remain at rest, objects with velocity remain in motion o you don’t feel motion on an airplane because the plane is traveling at a constant velocity so there is no net force acting on it  Newton’s second law: force = mass x acceleration (F = ma) o having a net force change’s an objects momentum & accelerates it in the direction of the force o you can throw a baseball farther than a shot-put because the mass of a shot-put is greater so there is a smaller acceleration making it leave with less speed & therefore a shorter distance o explains why larger planets have greater effects on asteroids/comets  exerts stronger gravitational force so sends them scattering with greater acceleration o explains acceleration around curves  force pulls ball inward since acceleration must be the same direction as the force o gravity is the force that keeps an orbiting planet always accelerating toward the sun  Newton’s third law: for any force, there is always an equal and opposite reaction force o when you stand on the ground you are not falling because there is an equal force acting o objects always attract each other through gravity o when you jump you fall to the earth because you exert more acceleration since mass smaller 4.3 Conservation Laws in Astronomy  conservation of momentum: total momentum of interacting objects cannot change as long as no external force is acting on them o momentum of rocket shooting forward is equal to the momentum of the gases shooting back o when no net force acts on an object, there is no way for the object to transfer any momentum to & from another object o when you jump up your legs give you force to go up and you are pushing the earth in the opposite direction  can’t tell since earth has much greater mass  conservation of angular momentum: as long as there is no external torque, the total angular momentum of a set of interacting objects can’t change PHYS 183 – The Milky Way Inside and Out – Tracy Webb Winter 2013 o individual object can change angular momentum only by transferring angular momentum to/from another object o orbital angular momentum  angular momentum = (m)(v)(r) where m = mass, v = velocity r = radius of orbit/distance from sun  no objects around to give/take angular momentum from earth so it always stays the same  earth needs no fuel/push to keep orbiting  will orbit unless something comes to take angular momentum away  earth’s orbital speed must be faster when it is closer to the sun  radius/distance to the sun is smaller o rotational angular momentum  as long as not transferring angular momentum of rotation to another object, keeps rotating at same rate  earth is gradually transferring RAM to moon, so it’s slowing  conservat
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