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PHYS16 – Lecture 6 Physics of 2D Motion September 20, 2010 To run or walk???

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Administration Key Concepts – Physics 2D motion Relative Motion Agenda

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Homework Assignments – Due Tuesday, Online lab homework – Due Sunday, Written homework, & Ch. 4 Online homework Help Sessions – T/TH 8-9pm View Jupiter – Tonight 9 pm, Merrill Beach Administration

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Review Questions Lets say you have a velocity vector that is 6 mph at 55 degrees relative to the x axis. What is the component of the vector along x? – A) 6cos(55 degrees) – B) 6sin(55 degrees) – C) 6/sin(55 degrees) – D) 6tan(55 degrees) 6 mph ?

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Review Questions If you add vector 1 (5 at 37 degrees) to vector 2 (2 at 0 degrees), what do you get for the component in the x direction? – A) 5 – B) 4 – C) 6 – D) 7

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Review Questions v=at+v 0, what does x=? – x=(1/2)at 2 +v 0 t+x 0

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Review Questions When you throw a ball up, at max height, acceleration in y is? (-9.8 m/s 2 ) When you throw a ball up, at max height, velocity in y is?(0 m/s) A car goes from 0 to 4 m/s in 0.5 s. What is the cars acceleration?(8 m/s 2 )

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Usain Bolt vs. a Fly Except between time 0 s to 1.89 s, Usain has a constant velocity of ~10 m/s Usains acceleration = 0 m/s^2 Usains Position vs. time

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Usain Bolt vs. Fly Position vs. time for two flies Each dot is a position at 20 Hz Velocity vs. time and acceleration vs. time is more complicated than Usain Bolt

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Key Concepts: Physics 2D Motion 2D Motion – Independent in x and y – Constant acceleration Relative Motion Projectile Motion

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2D Motion

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Motion in x and motion in y is independent – Separate into motion in x and motion in y – Use the equations of motion for 2D to solve for unknowns – Separate and Solve Most problems will assume constant acceleration – Equations of motion?

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Kinematic Equations XY

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Relative Motion

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Relative Motion – Math Relative motion – motion of a frame that an object is moving in Motion of object in frame is just equal to objects motion Motion of object out of frame is equal to objects motion + frame motion

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Relative Motion – Walkway at Airport I am running at 2 m/s in the airport and the moving walkway is at 3 m/s. If I take the walkway what is my speed? – 5 m/s Do I take the walkway or run if there is a family on walkway so that I cant run on it? – take walkway If I just run the 10 m to the gate instead of taking the walkway will I still beat my brother who is going 3 m/s and is 11 m behind me? – yes

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Relative Motion – River Problem A river has a current of 3 m/s. A boat pointed straight across the river with a speed of 4 m/s appears from the shore to have a velocity of what value? 4 m/s 3 m/s

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Relative Motion – River Problem A river has a current of 3 m/s. A boat pointed straight across the river with a speed of 4 m/s appears from the shore to have a velocity of what value? – 5 m/s at an angle of 40 degrees from the shore

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Relative Motion – Bucket Problem A bucket is left out in the rain. The rain is coming down at 5 m/s. If a crosswind starts to blow at 2 m/s, will the bucket fill faster or slower? 5 m/s Original rain 5 m/s Wind at 2 m/s Scenario #1 Scenario #2

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Relative Motion – Run or Walk in Rain? Is it better to run or walk in the rain?

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Relative Motion – Run or Walk in Rain? Is it better to run or walk in the rain? – Assume rain is coming straight down at 1 m/s – If you run at 2 m/s, what does the rain look like in your frame? looks like coming at you instead of straight down – If you just look at surface area of body getting wet, does walking or running hit less surface area? Walking – If you look at how many rain drops hit you, does walking or running have less total rain drops? Running because you reach your destination sooner

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Summary Separate 2D motion into x and y and then solve Use Kinematic equations of Motion to solve for problems with constant acceleration Relative Motion – make sure to add velocity of frame to velocity of object to get relative velocity

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