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Two Dimensional Dynamics

This lecture covers the topic of two-dimensional dynamics in physics, including velocity and acceleration in two dimensions, projectile motion, and the concepts of position, velocity, and acceleration vectors. The lecture also includes demonstrations and examples to further illustrate the concepts.

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Two Dimensional Dynamics

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  1. Two Dimensional Dynamics Physics 101: Lecture 06 • Today’s lecture will coverTextbook Chapter 4

  2. ACT – from lecture 5 • The speed of an object in free fall (Neglect Air Resistance) • Always increases. • is constant. • Always decreases. • May increase or decrease or be constant. • May increase or decrease but is never constant. s=|v| v t t

  3. Brief Review Thus Far • Newton’s Laws of motion: SF=ma • Kinematics: • Dynamics • Today we work in 2 Dimensions! x = x0 + v0t + ½ a t2 v = v0 + a t v2 = v02 + 2 a (x-x0)

  4. y x 2-Dimensions • X and Y are INDEPENDENT! • Break 2-D problem into two 1-D problems

  5. Position, Velocity and Acceleration • Position, Velocity and Acceleration are Vectors! • x and y directions are INDEPENDENT!

  6. y x Velocity in Two Dimensions A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 25 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s.What is the magnitude of the change in velocity? A) 0 m/s B) 2 m/s C) 2.6 m/s D) 3 m/s E) 5 m/s 3 m/s 5 m/s 25°

  7. y x Acceleration in Two Dimensions A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 25 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s.What is the average acceleration? 3 m/s 5 m/s

  8. Kinematics in Two Dimensions • x = x0 + v0xt + 1/2 axt2 • vx = v0x +axt • vx2 = v0x2 + 2axx • y = y0 + v0yt + 1/2 ayt2 • vy = v0y +ayt • vy2 = v0y2 + 2ayy x andymotions areindependent! They share a common time t

  9. Train Demo Act A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land? A. Forward of the center of the car B. At the center of the car C. Backward of the center of the car

  10. y x ACT A flatbed railroad car is accelerating down a track due to gravity. The ball is shot perpendicular to the track. Where will it land? A. Forward of the center of the car B. At the center of the car C. Backward of the center of the car

  11. Projectile Motion ACT One marble is given an initial horizontal velocity, the other simply dropped. Which marble hits the ground first? A) dropped B) pushed C) They both hit the ground at the same time

  12. Monkey Pre-Flight You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting? 1 Right at the monkey 2 Below the monkey 3 Above the monkey Demo - monkey

  13. See text: 4-3 Shooting the Monkey... x= v0 t y= -1/2 g t2 x = x0 y= -1/2 g t2

  14. Dart hits the monkey! Shooting the Monkey... y= y0 - 1/2 g t2 • Still works even if you shoot upwards! y= v0yt - 1/2 g t2

  15. Projectile Motionax = 0 ay = -g • y = y0 + v0y t - ½ gt2 • vy = v0y–g t • vy2 = v0y2 – 2 g y • x = x0 + v0x t • vx = v0x • Choose direction where you “know” information • Solve kinematics in that direction. • Use t from that direction as t in other direction

  16. Summary of Concepts • X and Y directions are Independent! • Position, velocity and acceleration are vectors • “Share” t • F = m a applies in both x and y direction • Projective Motion • ax = 0 in horizontal direction • ay = g in vertical direction

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