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Physics 203 College Physics I Fall 2012

Physics 203 College Physics I Fall 2012. S. A. Yost. Chapter 2. Motion in 1 Dimension – Part 2. Today’s Topics & Announcements. Continuously Changing Velocity - Graphical Acceleration - Graphical Constant Acceleration Motion and Falling

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Physics 203 College Physics I Fall 2012

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  1. Physics 203College Physics IFall 2012 S. A. Yost Chapter 2 Motion in 1 Dimension – Part 2

  2. Today’s Topics & Announcements • Continuously Changing Velocity - Graphical • Acceleration - Graphical • Constant Acceleration Motion and Falling • We will work a couple of problems similar to what you will do in the homework, and discuss problem solving approaches.

  3. Thursday’s Assignment • Read Ch. 3, sec. 1 – 4. The topic is vectors. • Problem Set HW2 is open and due Thursday. It is mostly on Chapter 2, but includes some trigonometry practice for Chapter 3. • We will review some trigonometry next time. • A problem set on HW3 on Ch. 3 will be due the following Thursday. You may start it as soon as it is posted. • A reading quiz is a possibility for any lecture. Always come prepared.

  4. Non-Constant Velocity • Estimate the velocity at t = 10 s. • v = Δx/Δt = 5 m / 17.5 s = 0.29 m/s

  5. Non-Constant Velocity • At what time is v = 0? • v = 0 at the turning point, t = 37.5 s

  6. Non-Constant Velocity • Estimate the velocity at t = 30 s. v = Δx/Δt = 25 m / (37.5 – 16) s = 1.1 m/s

  7. Velocity Graph • Average acceleration is the change in velocity over a time interval. • What is the average acceleration for the first 50 s? • a = Δv/ Δt = (38 – 14) m/s = 0.48 m/s2 50 s

  8. Velocity Graph • What is the average acceleration from 50 s to 100 s? • a = Δv/ Δt = (0 – 38) m/s = – 0.76 m/s2 50 s

  9. Train x • A train car moves along a straight track. The graph shows that it • Speeds up all the time • Slows down all the time • Speeds up some of the time and slows down some of the time. • Has constant velocity. t

  10. Acceleration and Speed • Can an object at rest have nonzero acceleration? • A. Yes B. No • Otherwise it would remain at rest. • If an object has positive acceleration, does that mean its speed is increasing? • A. Yes B. No • If its velocity is negative, its speed is increasing.

  11. Example • If a car initially in reverse comes to rest, its acceleration is positive, but its speed is decreasing. v t 0 v0

  12. Constant Acceleration x (m) • When the acceleration is constant, the position vs time graph forms a parabola. • The velocity vs time graph is linear. • The velocity is zero at the turning point of the motion. t (s) v (m/s) t (s)

  13. Constant Acceleration • Galileo dropped balls from the Tower of Pisa to show that the time to fall did not depend on the weight. • The gravitational acceleration is g = 9.80 m/s2at the Earth’s surface. • The motion forms a parabola, with the distance traveled given by y = ½ g t2.

  14. Dropping vs Throwing • If you drop an object, and can neglect air resistance, it accelerates downward at 9.80 m/s2. If you throw it downward, after you let go, it • accelerates at less than 9.8 m/s2 • accelerates at 9.8 m/s2 • accelerates at more than 9.8 m/s2

  15. Constant Acceleration Equations • x = x0 + v0 t + ½ a t2(quadratic equation) • v = v0 + a t (linear equation) • v2 = v02 + 2a Δx (Δ x = x – x0) • v = ½ (v0+vf) (average velocity is in the middle)

  16. Ball Thrown Upward • When you throw a ball straight up, which are true at the highest point? (A) The velocity and acceleration are both zero. (B) The velocity is nonzero and the acceleration is zero. (C) The acceleration is nonzero and the velocity is zero. (D) The velocity and acceleration are both nonzero.

  17. Ball Thrown Upward • If a ball is thrown upward at 4.9 m/s at point A, how long does it take to return to be caught at point C? • Let y = 0 at A or C. • A → B: v = v0 – gt = 0 • t = v0/g = 4.9/9.8 s = 0.5 s. • The time to fall is the same, so the ball takes 1.0 s to be caught.

  18. Ball Thrown Upward • How high is the ball at point B, its high point? • y = v0 t – ½ gt2 • v0 = 4.9 m/s, t = 0.5 s. • y = (4.9 m/s)(0.5 s) • + ½ (9.8 m/s2)(0.5 s)2 • = 3.7 m.

  19. Ball Thrown from Cliff • A ball is thrown vertically upward at 5.0 m/s and lands at the base of the cliff 20 m below. • (a) How fast is it falling just before it lands? • (b) How long is it in the air?

  20. Up vs Down • A man on a cliff at the edge of a crater on the moon throws one ball straight up and another straight down at the same initial speed. Which hits the bottom of the crater at the higher speed? • The one thrown up hits faster. • The one thrown down hits faster. • They hit at the same speed.

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