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Mastering Physics of 2D Motion: Equations and Relative Motion Demystified

Dive into the physics of 2D motion with this lecture discussing key concepts, kinematic equations, and relative motion. Explore scenarios like running vs. walking in rain, river problems, and more. Learn to solve problems with constant acceleration and separate motion into x and y components for a deeper understanding of projectile motion.

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Mastering Physics of 2D Motion: Equations and Relative Motion Demystified

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

  2. Agenda • Administration • Key Concepts – Physics 2D motion • Relative Motion

  3. Administration • 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

  4. Review Questions • Let’s 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 ?

  5. 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

  6. Review Questions • v=at+v0 , what does x=? • x=(1/2)at2+v0t+x0

  7. Review Questions • When you throw a ball up, at max height, acceleration in y is? (-9.8 m/s2) • 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 car’s acceleration? (8 m/s2)

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

  9. 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

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

  11. 2D Motion

  12. 2D Motion • 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?

  13. Kinematic Equations X Y

  14. Relative Motion

  15. Relative Motion – Math • Relative motion – motion of a frame that an object is moving in • Motion of object in frame is just equal to object’s motion • Motion of object out of frame is equal to object’s motion + frame motion

  16. 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 can’t 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

  17. 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

  18. 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

  19. 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? Wind at 2 m/s Original rain 5 m/s 5 m/s Scenario #2 Scenario #1

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

  21. 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

  22. 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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