Physics 8 Wednesday, September 9, 2015

Transcription

1 Physics 8 Wednesday, September 9, You read Mazur Chapter 5 ( energy ) for today. Handing back HW1. HW2 (from Ch3,4) due Friday. Homework study sessions (optional): Bill will be in DRL 3W2 Thursdays from 6 8:30pm. Camilla will be in DRL 2C4 on Wednesdays from 4 6pm. By the way, we are going pretty quickly through the early chapters of Mazur s book. This is a bit faster than in past years, because I m trying to set aside even more time than usual for the architectural-structures-related topics in October/November. This is my third time teaching this course: I learn a bit more from you each time about what you find most/least interesting, so that I can adapt the course to fit you. Your feedback helps me to make continuous adjustments.

2 Q about chapter 4: extensive quantities A quantity Q describing a system is extensive if when you divide up the system into two parts, Q(part1) + Q(part2) = Q(combined) Typical examples are volume, money, mass, number of moles Some counterexamples (not extensive) are humidity, density, color, temperature. Some (just a few) extensive quantities are conserved, meaning they can be transferred but can never be created or destroyed. Momentum (and next week energy) are examples of conserved quantities in physics. All conserved quantities are extensive, but only a few extensive quantities are conserved.

3 Is number of dots an extensive quantity? (A) Yes. (B) No.

4 Is dot diameter an extensive quantity? (A) No. (B) Yes.

5 Is total area covered by dots an extensive quantity? (A) No. (B) Yes. (C) Yes, as long as the dots can t overlap.

6 This may help you with HW2 #11(d) The velocity-vs-time graph below shows the motion of two different objects moving across a horizontal surface. Could the change in velocity with time be attributed to friction in each case? (a) Yes for the top curve, no for the bottom curve. (b) No for the top curve, yes for the bottom curve. (c) Yes for both curves. (d) No for both curves. (e) I have no idea how friction would affect a velocity-vs-time graph!

7 Work on this together with 1 or 2 nearby people! A box is at the lower end of a frictionless ramp of length L = 10 m that makes a nonzero angle θ = 30 with the horizontal. A worker wants to give the box a shove so that it just reaches the top of the ramp. How fast must the box be going immediately after the shove (assumed to be instantaneous) for it to reach its goal? Remember sin 30 = 1 2 and use g 10 m/s2 to keep the math simple. (A) 1.0 m/s (B) 5.0 m/s (C) 7.0 m/s (D) 10 m/s (E) 20 m/s Put your group s name(s) on the sheet of paper you work this out on, and turn it in at the end for in class credit. Reminder (on board): results derived from a x = constant.

8 Work on this together with 1 or 2 nearby people! A box is at the lower end of a frictionless ramp of length L = 10 m that makes a nonzero angle θ = 30 with the horizontal. A worker wants to give the box a shove so that it just reaches the top of the ramp. (In this case, oddly enough, the math is actually simpler if you use the real value g = 9.8 m/s 2 instead of using the approximate 10 m/s 2. ) What is its speed halfway up the ramp? (A) 1.0 m/s (B) 4.9 m/s (C) 7.0 m/s (D) 9.9 m/s (E) 19.8 m/s Put your group s name(s) on the sheet of paper you work this out on, and turn it in at the end for in class credit.

9 HW2 covers acceleration (Ch 3) and momentum (Ch 4). So let s summarize the key results from Chapter 4 (momentum): Momentum p = m v. Constant for isolated system: no external pushes or pulls (later we ll say forces ). Conservation of momentum in isolated two-body collision implies m 1 v 1x,i + m 2 v 2x,i = m 1 v 1x,f + m 2 v 2x,f which then implies (for isolated system, two-body collision) v 1x v 2x = m 2 m 1 If system is not isolated, then we cannot write p f p i = 0. Instead, we give the momentum imbalance caused by the external influence a name ( impulse ) and a symbol ( J ). Then we can write p f p i = J. You will rarely use J, other than to consider whether or not it is nonzero.

10 Chapter 5: Energy Confusing: Internal energy Closed (or not); isolated (or not) system

11 Kinetic energy K = 1 2 mv 2 is the energy of motion. is conserved in an elastic collision. e.g. 1 2 m 1v1i m 2v2i 2 = 1 2 m 1v1f m 2v2f 2 but it s much easier in practice to write (equivalently) v 12,i = v 12,f i.e. relative speed is the same before and after an elastic collision (v 1x,f v 2x,f ) = (v 1x,i v 2x,i ) [Eqn. 5.4]

12 Types of collisions Elastic collision: objects recoil with same relative speed as before they collided. Kinetic energy K i = K f. (v 1x,f v 2x,f ) = (v 1x,i v 2x,i ) [Eqn. 5.4] Totally inelastic collision: objects stick together. (v 1x,f v 2x,f ) = 0 Inelastic collision: objects recoil, but with a reduction in relative speed (v 1x,f v 2x,f ) = e(v 1x,i v 2x,i ) with 0 < e < 1 Explosive separation: imagine T.I.C. movie played in reverse. (v 1x,i v 2x,i ) = 0 (v 1x,f v 2x,f ) 0 Q (tricky): what value of e describes an explosive separation?!

13 If I play in reverse a movie of an elastic collision, what sort of collision would I appear to see? (a) elastic (b) inelastic (c) totally inelastic (d) explosive separation (e) it depends!

14 When we collide (on a low-friction track) two carts whose masses and initial velocities are known, conservation of momentum allows us to write m 1 v 1x,i + m 2 v 2x,i = m 1 v 1x,f + m 2 v 2x,f We have one equation, but two unknowns. Knowing something about energy gives us a second equation. Relative speed = key. elastic: (v 1x,f v 2x,f ) = (v 1x,i v 2x,i ) totally inelastic: (v 1x,f v 2x,f ) = 0 if e is given: (v 1x,f v 2x,f ) = e(v 1x,i v 2x,i ) if change in internal energy is given: 1 2 m 1v 2 1i m 2v 2 2i = 1 2 m 1v 2 1f m 2v 2 2f + E internal (or equivalently) K 1i + K 2i + E i,internal = K 1f + K 2f + E f,internal (We ll work some HW-like examples on Friday or Monday.)

15 Suppose you find an isolated system in which two objects about to collide have equal and opposite momenta. If the collision is totally inelastic, what can you say about the motion after the collision? (Discuss with your neighbor, and then I ll call on a few people to see what you think. If some of us disagree on the answer, it s not a problem: we will all learn by discussing.)

16 What sort of collision is illustrated by this velocity-vs-time graph? (A) elastic (B) inelastic (C) totally inelastic (D) explosive separation (E) can t tell from given information

17 Physics 8 Wednesday, September 9, You read Mazur Chapter 5 ( energy ) for today. Handing back HW1. HW2 (from Ch3,4) due Friday. Homework study sessions (optional): Bill will be in DRL 3W2 Thursdays from 6 8:30pm. Camilla will be in DRL 2C4 on Wednesdays from 4 6pm. By the way, we are going pretty quickly through the early chapters of Mazur s book. This is a bit faster than in past years, because I m trying to set aside even more time than usual for the architectural-structures-related topics in October/November. This is my third time teaching this course: I learn a bit more from you each time about what you find most/least interesting, so that I can adapt the course to fit you. Your feedback helps me to make continuous adjustments.