93803 - Physics 2211 Matter and Interactions Dr Ed Greco...

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The position update formula Combining the definition of the average velocity and the change in position: r f − r i =  v avg dt r f = r i   v avg t f t i Given information about the average velocity we can determine an new position Physics allows us to predict the future! How good the prediction is will depend on the accuracy of the average velocity calculation Physics 2211: Matter and Interactions Dr. Ed Greco
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Example: Parabolic Motion (throwing something) The direction of instantaneous velocity is tangent to the path of the objects motion Smaller time intervals yield more accurate estimates Physics 2211: Matter and Interactions Dr. Ed Greco v avg =  r t v = d r dt v B
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PRS: A yellow jacket flies in a straight line at constant speed. At 15 s after 9 AM, the yellow jacket's position is <2, 4, 0> m. At 15.5 s after 9 AM, the yellow jacket's position is <3, 3.5, 0> m. What is the average velocity of the yellow jacket? (1) <6, 7, 0> m/s (2) <0.193, 0.225, 0> m/s (3) 2.236 m/s (4) <0.50, -0.25, 0> m/s (5) <2, -1, 0> m/s Physics 2211: Matter and Interactions Dr. Ed Greco
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When we observe a change in an objects velocity we say that it has interacted with something Aristotle (384 BC – 322 BC) held that it was an objects natural tendency to be at rest Heavy objects on the ground, light objects in the air! Physics 2211: Matter and Interactions Dr. Ed Greco
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Galileo (1564 AD – 1642 AD) claimed that an objects natural tendency was to travel in a straight line at a constant speed unless it was interacting with something Newton (1643 AD – 1727 AD) codified this in his first (of three) laws of motion: “An object moves in a straight line and at a constant speed except to the extent that it interacts with other objects” Physics 2211: Matter and Interactions Dr. Ed Greco
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Physics 2211: Matter and Interactions Dr. Ed Greco Examples of Newtons First Law Walking with a cup of very hot coffee Riding your bicycle into a stopped car Designing a good seatbelt Standing up too fast Playing Super Mario World Riding a rocket sled
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Physics 2211: Matter and Interactions Dr. Ed Greco PRS: A car is navigating a circular turn when it suddenly encounters a large patch of ice at point P . On the ice, the car's tires are frictionless. Which path would the car most likely follow after hitting the ice? P 1 2 3 4 5
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We need a way to mathematically relate the changes in velocity with interactions What makes it hard to change somethings velocity? Baseball vs. Linebacker Baseball vs. Bullet An objects velocity and mass determine how strong of an interaction is required to change its velocity Newton defined momentum as the product of mass and velocity Physics 2211: Matter and Interactions Dr. Ed Greco p = m v
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Momentum Einstein (1879 AD – 1955 AD) gave us the relativistic correction to Newtons definition of momentum “c” is the speed of light Physics 2211: Matter and Interactions Dr. Ed Greco p = m v = 1 1 v c 2 c = 3 × 10 8 m / s
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