Curved Paths ballistics and circles §3.3–3.4

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

Ballistic Trajectories Acceleration a = g = 9.8 m/s 2 downward –|a vertical | = 9.8 m/s 2 –|a horizontal | = 0 Vertical and horizontal motion are independent and can be treated separately

Ballistic Trajectories Flight time t is determined by  y and v 0y   y = v 0y t – 1/2 gt 2 (for up = +y) Horizontal range is v x t Components of velocity v x and v y  For  = angle above horizontal of velocity v  v x = v cos(  ); v y = v sin(  ) vyvy vxvx v 

Uniform Circular Motion Speed is constant, direction isn’t

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

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. A B

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

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

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

Uniform Circular Motion Define the system r

Circling Velocity and Acceleration How far does it move in time dt? dr r0r0 rdtrdt dd

Circling Velocity and Acceleration v  r always dd r0r0 rdtrdt vdtvdt v0v0

Circling Velocity and Acceleration Similar triangles v0v0 vdtvdt dd dv dr r0r0 rdtrdt dd dv v dr r =

Circling Velocity and Acceleration dv v dr r = dv dt = a= a dr dt = v= v dv dt dr dt = 1 v 1 r = a v v r a = v2v2 r

Circling Velocity and Acceleration Acceleration = a = v 2 /r v0v0 vtvt dd dvdv Direction of acceleration = direction of velocity + 90° = direction of position+ 180° = opposite direction of r = into the center of the circle!

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