Physics 8 Wednesday, September 25, 2013

Transcription

1 Physics 8 Wednesday, September 25, 2013 HW4 due Friday. Only 11 problems! Covers chapters 6+7. Problem 1 is somewhat ambiguous: we ll do it in class today. short (10 min.) quiz on a modified HW2 problem today. Today: key ideas from ch7 (interactions), start ch8 (forces) After ch9, the pace of reading will slow down to 1ch/wk! HW help sessions: Wed 7pm DRL 2N36, Thu 7pm DRL 3W2. My summary of key equations ( equation sheet ): positron.hep.upenn.edu/wja/phys008_2013/equations.pdf

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3 The book s original wording for HW4 problem 1 is ambiguous. One possible interpretation makes no sense, as you would never make it down the up escalator. Let s work two versions of the problem. (Doing either version is good for full credit.) Riding up an escalator while staying on the same step for the whole ride takes 30 s. Walking up the same escalator (when it s not moving) takes 20 s. How long does it take to walk down the up escalator? Suppose the elevator s length is 30 m. How fast do you walk (v w ) and how fast does the escalator move (v e )? (a) v w = 0.67 m/s (b) v w = 0.67 m/s (c) v w = 1.0 m/s (d) v w = 1.0 m/s (e) v w = 1.5 m/s (f) v w = 1.5 m/s v e = 1.0 m/s v e = 1.5 m/s v e = 1.0 m/s v e = 1.5 m/s v e = 1.0 m/s v e = 1.5 m/s

4 The book s original wording for HW4 problem 1 is ambiguous. One possible interpretation makes no sense, as you would never make it down the up escalator. Let s work two versions of the problem. (Doing either version is good for full credit.) Riding up an escalator while staying on the same step for the whole ride takes 30 s. Walking up the same escalator (when it s not moving) takes 20 s. How long does it take to walk down the up escalator? (a) 10 s (b) 15 s (c) 20 s (d) 30 s (e) 45 s (f) 60 s (g) 90 s

5 second version of HW4 problem 1 If you assumed (moving) instead of (when it s not moving), then the book s original value (20 s) makes no sense, so let s change it to 10 s and work it out together. Riding up an escalator while staying on the same step for the whole ride takes 30 s. Walking up the same (moving) escalator takes 10 s. How long does it take to walk down the up escalator? If the escalator length is 30 m, then what are The speed v e at which the escalator moves? The speed v up,up at which I am moving upward? My walking speed v w? The speed v down at which I will move downward? The time it will take me to walk down the up escalator?

6 We worked through two examples on Monday of collisions analyzed from the zero momentum frame the reference frame in which the center of mass is not moving. You ll work out a similar (but easier) problem on HW4, to practice using the ZM frame. The ZM frame is something you re unlikely to use routinely, but it can be handy at times, because collisions look so much simpler when viewed from the ZM frame. If you don t like it, you don t need to use it after this week! Why bother moving to the ZM frame? was a good question on Monday! The recipe: Subtract v ZM. Then each v f add back v ZM. is just e v i. Then As you saw in last night s reading about forces, it is sometimes helpful to separate the internal from the external forces. The motion of the CoM is affected only by the external forces. The ZM frame focuses only on the internal.

7 A golf club of mass M is moving at speed V i when it strikes (elastically) a stationary golf ball of mass m. Let s study this collision from the zero momentum frame. How fast (v f ) does the golf ball move after the collision? (We worked this out Monday on the board. Result next page.)

8 Moving object of mass M, velocity V i strikes stationary object of mass m. For the (initially stationary) ball, final velocity v f was ( ) M v f = +2V i M + m and for the (initially moving) club, final velocity V f was ( ) M m V f = V i M + m Let s just stare at the answer and see if it seems to make sense, for M m, M = m, and M m.

9 We also worked out on Monday the case of a baseball bat of mass M and swing speed V s elastically hitting an incoming baseball of mass m moving with pitch speed v p. The baseball s final velocity v xf was ( ) v xf = vxf + v MVs mv p ZM = v p + 2 M + m In extreme case M m, this approaches the limit v xf v p + 2V s It s easier to hit a home run off of a fastball! Also look at this equation in three extreme cases: fastball + full swing; fastball + bunt (V S = 0); little kids tee-ball (v p = 0).

10 We used the v ball,f = v p + 2V s result to conclude answer (c) for this on Monday. A tennis ball is put on top of a basketball, and the combination is dropped from a certain height. Compared to the speed that the tennis ball has just before the basketball hits the ground, the speed with which the tennis ball rebounds is (a) the same (b) twice as large (c) three times as large (d) four times as large (e) nine times as large (f) none of the above Hint: imagine that the basketball lands first, turns around, and hits the down-going tennis ball, in the M m case.

11 Now think about gravitational potential energy If the tennis ball rebounds at 3 the speed of the basketball, how should the maximum height (after rebounding) of the tennis ball compare with the maximum height (after rebounding) of the basketball? (a) the same (b) twice as large (c) three times as large (d) four times as large (e) nine times as large (f) none of the above

12 Chapter 7 ( interactions ) key ideas Hugely important: when two objects interact only with one another: p 1x = p 2x v 1x / v 2x = m 2 /m 1 a 1x a 2x = m 2 m 1 When the medicine ball and I push apart from one another, we both accelerate: in opposite directions, and in inverse proportion to our masses. Lifting an object up a height x in Earth s gravity changes its gravitational potential energy by U G = mg x I usually remember U = mgh where h is height (Q2) Basketball: back & forth between 1 2 mv 2 and mgh until mechanical energy is dissipated into thermal energy

13 Chapter 7 reading Q #2 Can you think of an example from everyday life of an interaction that is reversible and an interaction that is irreversible? It s very difficult in ordinary life to find examples that are perfectly reversible (except e.g. celestial motion), but this comes pretty close: Newtons_cradle_animation_book_2.gif

14 Dissipative / incoherent / irreversible A simple ball / spring model of the atoms in a solid. This is sometimes a useful picture to keep in your head.

15 Dissipative / incoherent / irreversible 2D version for simplicity illustrate reversible and irreversible deformation with e.g. marbles and egg crate

16 Dissipative / incoherent / irreversible I made a low-tech animation of two objects in a totally inelastic collision. Collision converts coherent motion (kinetic energy) into incoherent jiggling (thermal energy)

17 HW4 due Friday. Only 11 problems! Covers chapters 6+7. Problem 1 was ambiguous: oops. See today s slides. HW help sessions: Wed 7pm DRL 2N36, Thu 7pm DRL 3W2. Friday: continue discussing forces, free-body diagrams, etc. I ll put today s slides up on Canvas this afternoon. Quiz on HW #2 (handing out now) 10 minutes. Work alone. Closed book, 1 page of handwritten notes OK. Calculator OK. Relax: 5% weight, 80% 100%. (a) With what minimum speed must a ball be thrown straight up in order to reach a height of 5.0 m (five meters) above the launch position? Show your work. If you don t have a calculator, feel free to pretend that g = 10.0 m/s 2. (b) How many seconds does the ball take to reach this height? Show your work. If you don t have a calculator, feel free to pretend that g = 10.0 m/s 2.