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Curved Paths

Curved Paths. ballistics and circles. §3.3–3.4. Poll Question. Predict: Which ball will land sooner?. The ball launched horizontally. The ball dropped vertically. Both will land at the same time. It depends on the launch speed. Ballistic Trajectories.

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Curved Paths

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  1. Curved Paths ballistics and circles §3.3–3.4

  2. Poll Question Predict: Which ball will land sooner? The ball launched horizontally. The ball dropped vertically. Both will land at the same time. It depends on the launch speed.

  3. Ballistic Trajectories • Acceleration a = g = 9.8 m/s2 downward • |avertical| = 9.8 m/s2 • |ahorizontal| = 0 • Vertical and horizontal motion are independent and can be treated separately

  4. v vy a vx Ballistic Trajectories • Flight time tis determined by Dy and v0y • Dy = v0y t – 1/2gt2(for up = +y) • Horizontal range is vxt • Components of velocity vx and vy • For a = angle above horizontal of velocity v • vx = vcos(a); vy = v sin(a)

  5. Uniform Circular Motion Speed is constant, direction isn’t

  6. Poll Question The direction of the acceleration of an object moving at constant speed in a circular path is in the direction of its motion. opposite the direction of its motion. toward the center of its circular path. away from the center of its circular path. a zero vector has no direction.

  7. A B Poll Question Two balls with the same speed contact different semicircular guides. Which accelerates the most in the curve? A.Ball A. B.Ball B. C.It’s a tie. D.Need more information.

  8. Poll Question A and B stand the on edge of identical carousels. B has a greater tangential speed. Which accelerates the most? A.A. B.B. C.It’s a tie. D.Need more information. A B B’s greater velocity reverses more often.

  9. A B Poll Question Points A and B are different distances from the center of a rotating disk. Which accelerates the most? A.A. B.B. C.It’s a tie. D.Need more information. A has a greater velocity change in the same time.

  10. Uniform Circular Motion • Constant speed in a circular path • a|| = 0; a = a • What is the actual vector a?

  11. Uniform Circular Motion • Define the system r

  12. dr dq r0 rdt Circling Velocity and Acceleration How far does it move in time dt?

  13. vdt v0 dq r0 rdt Circling Velocity and Acceleration v r always

  14. dv vdt dr dq r0 rdt Circling Velocity and Acceleration Similar triangles dq v0 dv dr v r =

  15. Circling Velocity and Acceleration dv dv 1 dr 1 dr =a = =v v r dt dt dt dt a v = v r dv dr v2 a = v r = r

  16. dv dq v0 vt Direction of acceleration = direction of velocity + 90° = direction of position+ 180° = opposite direction of r = into the center of the circle! Circling Velocity and Acceleration Acceleration =a = v2/r

  17. Poll Question Which of the following controls are used to accelerate a car? Enter the sum of the correct choices. 32 Steering wheel 16 Power windows 8 Brake pedal 4 Gas pedal 2 Defroster 1 Windshield wipers

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