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Exploring 2D & 3D Motion: Beyond Straight Line Motion

Learn about vector descriptions, instantaneous velocity, acceleration, and projectile motion through interactive physics simulations. Discover the concepts of parallel and perpendicular components of acceleration, as well as uniform and non-uniform circular motion.

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Exploring 2D & 3D Motion: Beyond Straight Line Motion

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  1. 2 & 3-D Motion • Beyond straight line motion • vector descriptions

  2. 2-D v vy y a vx x The instantaneous velocity is in the direction of motion

  3. Dv v2 y v1 x Acceleration: changing velocity Interactive Physics a_v_plr simulation: how controlling a controls motion.

  4. Dv v1 v2 v1 Dv v2 Dv|| Dv v1 Dv v2 • Parallel and perpendicular components of acceleration • If a is parallel || to v • change in velocity is along the direction of velocity • effect is solely a change in speed • If a is perpendicular  to v • change in velocity is perpendicular to the direction of velocity • effect is solely a change in direction • The parallel component of a results in a change of speed, while the perpendicular component of a results in a change of direction of v.

  5. Projectile Motion: prototype for 2+D constant acceleration • Motion in the vertical plane: a simple illustration • natural choice of coordinate axes • horizontal motion: no acceleration • vertical motion: acceleration of gravity (downwards) • motion is resolved into horizontal and vertical components • Dropped ball vs. ball rolled off of a horizontal table B A + ballistic cart demo: another combination of two motions

  6. Projectile Motion: • Initial Velocity from initial speed and direction: • a0 is the initial angle of the velocity wrt the positive x axis

  7. Other relations for projectile motion:

  8. Example 3-6: A motorcycle stunt rider rides off the edge of a cliff at a speed of 9 m/s. Determine the rider’s position, distance (both relative to the edge of the cliff) and velocity after .50 s. • Example 3-7: A batter hits a baseball so that it leaves the bat with an initial speed of 37.0 m/s at an angle of 53.1°. • Find the position and velocity of the ball after 2.00 s. • Find the time it takes the ball to reach its maximum height, and the maximum height. • Find the horizontal range of the ball (distance when it hits the ground again)

  9. Example 3-8: Zoo keeper and the monkey a0 d Example 3-9: Range-Height equations

  10. Example 3-10: A water balloon is tossed out a window 8.00 m above the ground at a speed of 10.0 m/s and an angle of 20.0 ° above the horizon. How far from the window does the balloon hit the ground?

  11. Uniform Circular Motion • motion in a circle at constant speed v1 v1 Df Ds Dv R v2 v2 Df

  12. Example 3-11: An automobile is capable of a lateral acceleration of “.87g” which is the maximum centripetal acceleration the car can undergo without skidding. What is the minimum turning radius of the car at speed of 40.0m/s? What is the minimum turning radius of the car at speed of 20.0m/s? Example 3-12: Passengers in a carnival ride travel at a constant speed around a 5.00 m radius circle. They make one circuit every 4.00s. What is their centripetal acceleration?

  13. v atan a arad • Non-Uniform Circular Motion • two components of acceleration • radial (centripetal) • tangential (how fast speed is changing)

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