Physics 8 Friday, September 6, 2013

Transcription

1 Physics 8 Friday, September 6, 2013 HW1 took most people about 2 hours; if HW1 took you 3-4 hours, you should find a couple of classmates with whom you can discuss the HW. Also come by on Wed/Thu evenings. I will put HW2 online later today. Printed copies Monday. Read Ch3 (acceleration) for Monday & send online response. I read all responses before class (helps me focus on key topics), and try to respond individually to about 1/3 of them. Bill hosts HW study/help sessions on Thursdays at 7pm in DRL 3W2 (started this week). Zoey hosts HW study/help sessions on Wednesdays at 7pm in DRL 2N36 (starting next week). Free physics tutoring (by physics majors) for intro physics courses, M Th 3 7pm in Room 253 of Education Commons in Weiss Pavillion. I marked up Weds. slides with answers & corrections in red.

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3 Is anything unclear from the material covered so far (Chapters 1 & 2)? On HW1, people singled out problem 7 (husband & wife meet for lunch), problem 6 (equations for projectile), problem 1 (mass of glass curtain wall), and maybe also problem 5 (walk to restaurant & back).

4 An object goes from one point in space to another. After it arrives at its destination, the magnitude of its displacement is: (a) either greater than or equal to (b) always greater than (c) always equal to (d) either smaller than or equal to (e) always smaller than (f) either smaller or larger than the total distance traveled by the object.

5 Slope of the x(t) curve The slope (also known as derivative, dt ) of the curve in a position (x) vs. time (t) graph for an object s motion gives (A) the magnitude of the object s acceleration (B) the x component of the object s acceleration (C) the magnitude of the object s average velocity (D) the x component of the object s average velocity (E) the magnitude of the object s instantaneous velocity (F) the x component of the object s instantaneous velocity (G) the magnitude of the object s displacement (H) the x component of the object s displacement (I) the object s speed dx

6 Representing motion as x vs. t A person initially at point P in the illustration stays there a moment and then moves along the axis to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to P. Which of the position vs. time graphs below correctly represents this motion? 2/B

7 Below I graphed an object s position (x) vs. time (t). Is the value of v x (the x component of the object s velocity) at t = 25 s (a) smaller than b) the same as (c) larger than d) (not enough information given) the value of v x at t = 10 s?

8 Below I graphed an object s position (x) vs. time (t). Is the value of v x (the x component of the object s velocity) at t = 25 s (a) smaller than b) the same as (c) larger than d) (not enough information given) the value of v x at t = 10 s?

9 Below I graphed an object s position (x) vs. time (t). Is the object s speed at t = 25 s (a) smaller than b) the same as (c) larger than d) (not enough information given) the object s speed at t = 10 s?

10 Similar to #6 and #5 combined. A mouse runs along a baseboard in your house. The mouse s position x as a function of time t is given by x(t) = qt pt 2 with q = 2.0 m/s and p = 0.50 m/s 2. At what time (or times) does the mouse s position equal 1.0 m? Technically, x is the x component of the mouse s position vector, but it can be tedious to speak so precisely.

11 Solving quadratic equation gives two solutions: t = s, t = 3.41 s.

12 What is the mouse s distance traveled from t = 0 to t = 4.0 s?

13 What is the mouse s average speed from t = 0 to t = 4.0 s?

14 What is mouse s average velocity v x,av from t = 0 to t = 4.0 s?

15 A mouse runs along a baseboard in your house. The mouse s position x as a function of time t is given by x(t) = qt pt 2 with q = 2.0 m/s and p = 0.50 m/s 2. Calculate and graph (the x component of) the mouse s velocity v x from t = 0 to t = 4.0 s.

16 x(t) = qt pt 2 with q = 2.0 m/s and p = 0.50 m/s 2. Calculate and graph (the x component of) the mouse s velocity v x from t = 0 to t = 4.0 s. v x = dx dt = q 2pt = (2.0 m/s) (1.0 m/s 2 )t

17 Modified version of #7. A husband and wife work in buildings ten blocks apart and plan to meet for lunch. The husband strolls at 1.0 m/s, while the wife walks briskly at 1.5 m/s. Knowing this, the wife picks a restaurant between the two buildings at which she and her husband will arrive at the same instant, if the two leave their respective buildings at the same instant. In blocks, how far from the wife s building is the restaurant?

18 (If we re ahead of schedule) Two runners in a 100 meter race start from the same place. Runner A starts as soon as the starting gun is fired and runs at a constant speed of 8.00 m/s. Runner B starts 2.00 s later and runs at a constant speed of 9.30 m/s. (a) Who wins the race? (b) At the instant she crosses the finish line, how far is the winner ahead of the other runner?

19 Chapter 3 reading (for Monday): acceleration. Working in 1 dim. (I ll write x components instead of vectors), position: displacement: (instantaneous) velocity: average velocity: (instantaneous) acceleration: average acceleration: x x f x i v x = dx dt v x,av = x f x i t f t i a x = dvx dt = d2 x dt 2 a x,av = v x,f v x,i t f t i Velocity is the rate of change of position. Acceleration is the rate of change of velocity. Both are vector quantities.

20 Objects moving in free fall in Earth s gravity move with a constant downward acceleration, of magnitude g = 9.8 m/s 2. ( Down means toward Earth s center.)

21 Objects moving in free fall in Earth s gravity move with a constant downward acceleration, of magnitude g = 9.8 m/s 2. Down means toward Earth s center. If we define the x axis to point upward, then a x = g For the (very useful) special case of motion under constant acceleration, we can integrate the above equation to get (R.H.S. is for the case of free-fall motion) v x (t) = v x,i + a x t = v xi gt Then we can integrate again to get (R.H.S. = free fall) x(t) = x i + v x,i t a xt 2 = x i + v x,i t 1 2 gt2 One more useful consequence of a x = constant is v 2 x,f = v 2 x,i + 2a x (x f x i )

22 A low-friction cart traveling down an inclined plane that makes an angle θ with respect to the horizontal moves with a constant downhill acceleration, of magnitude g sin θ. If we define the x axis to point downhill, then we have (note plus sign) a x = +g sin θ with g = 9.8 m/s 2.

23 Physics 8 Friday, September 6, 2013 HW1 took most people about 2 hours; if HW1 took you 3-4 hours, you should find a couple of classmates with whom you can discuss the HW. Also come by on Wed/Thu evenings. I will put HW2 online later today. Printed copies Monday. Read Ch3 (acceleration) for Monday & send online response. I read all responses before class (helps me focus on key topics), and try to respond individually to about 1/3 of them. Bill hosts HW study/help sessions on Thursdays at 7pm in DRL 3W2 (started this week). Zoey hosts HW study/help sessions on Wednesdays at 7pm in DRL 2N36 (starting next week). Free physics tutoring (by physics majors) for intro physics courses, M Th 3 7pm in Room 253 of Education Commons in Weiss Pavillion. I ll put today s slides up on Canvas this afternoon.