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Physics 1A, Section 2

Physics 1A, Section 2. November 29, 2010. schedule for end of Section 2. Tuesday, Nov. 30 – last scheduled office hour, 3:30 – 5:00 PM, Cahill 312 Wednesday, Dec. 1 – last homework due, final exam handed out

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Physics 1A, Section 2

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  1. Physics 1A, Section 2 November 29, 2010

  2. schedule for end of Section 2 • Tuesday, Nov. 30 – last scheduled office hour, 3:30 – 5:00 PM, Cahill 312 • Wednesday, Dec. 1 – last homework due, final exam handed out • The final exam score required in order to pass the course is available by email request (cdd@astro.caltech.edu).

  3. Quiz 4, Problem 1

  4. Quiz 4, Problem 1 • Answer: • Ktrans = Mgh[2r2/(2r2+R2)] • Krot = Mgh[R2/(2r2+R2)] • b) v0 = 2r[gh/(2r2+R2)]1/2 • c) v/v0 = (R+2r)/3r

  5. Final Exam • History suggests that the final will contain: • one problem on orbits • Frautschi et al., chapters 16-18 • Homework #9 (due Dec. 1) • Nov. 22 recitation section • one problem on fluid dynamics • Homework #8 (due Nov. 24) • Nov. 18 recitation section • 2–4 problems drawn from the rest of the course • Recitation section notes: • http://www.submm.caltech.edu/~cdd/PHYS1A_2010

  6. Quiz 4, Problem 2

  7. Quiz 4, Problem 2 • Answer: • d2q/dt2 + [2C/(MR2)]q = 0 • w0 = [2C/(MR2)]1/2 • b) W0/w0 (zero to peak) • c) U = [CW02/(2w02] sin2w0t • d) wnew = [2C/(MR2 + 2mr2)]1/2 • e) W0MR2/[2C(MR2 + 2mr2)]1/2

  8. QP40

  9. QP40 • Answer: • D+2l • b) 2p(2l/g)1/2 • c) 2(2)1/2l peak-to-peak • d) (3p/4)(2l/g)1/2

  10. The Physics of Billiards • Question: At what height should a billiard ball (of radius R) be struck so that it rolls without slipping? (Assume coefficient of friction from the table is very small.) F h

  11. The Physics of Billiards • Question: At what height should a billiard ball (of radius R) be struck so that it rolls without slipping? (Assume coefficient of friction from the table is very small.) F h • Answer: • h = 7/5 R

  12. Conservation Laws – Wrap-Up • Internal forces within a system of objects “cancel” due to Newton’s third law: • Internal forces do not change total linear momentum. • Internal forces do not change total angular momentum. • Therefore, if no forces act from outside the system, linear momentum is conserved. • And, if no torques act from outside the system, angular momentum is conserved. • If internal collisions are elastic, internal forces are conservative (gravity, springs), and outside forces are conservative and accounted with a potential, then mechanical energy (K + U) is conserved. • Static friction does not violate conservation of mechanical energy.

  13. Final Problem 8

  14. Final Problem 8 • lin. momentum: not conserved during collision, not conserved afterward • ang. momentum: conserved • mech. energy: not conserved during collision, conserved afterward

  15. Quiz Problem 41

  16. Quiz Problem 41 • (lin. momentum: not relevant) • ang. momentum: conserved • mech. energy: not conserved

  17. Quiz Problem 24

  18. Quiz Problem 24 • lin. momentum: conserved • ang. momentum: conserved • mech. energy: not conserved

  19. Final Problem 19

  20. Final Problem 19 • lin. momentum: conserved during collision, but not conserved afterward • (ang. momentum: not relevant) • mech. energy: not conserved during collision, but conserved afterward

  21. Quiz Problem 38

  22. Quiz Problem 38 • lin. momentum: conserved during ball-ball collision, not during ball-ground collision • (ang. momentum: irrelevant) • mech. energy: conserved

  23. Quiz Problem 32

  24. Quiz Problem 32 • (lin. momentum: not relevant) • ang. momentum: conserved during collision • mech. energy: conserved before and after collision, but not during

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