2. 1 Physics 7B - AB Lecture 9 May 29 Detailed Relation of Force to Motion Recap Newtonian Model, Circular Motion Simple Harmonic Motion

3. 2 Quiz 3 Re-evaluation Request Due TODAY Quiz 4 Due June 5 (next Thursday) Quiz 5 & 6 Due June 9 at the time of Final Quiz 5 Rubrics on the website TODAY Quiz 6 (Last Quiz!!!)

4. 3 11 days till…

5. 4 7B Final June 9 Mon 1- 3pm Practice Final as well as Quiz problems from Fri lecture sections are on the course website (solutions will be posted on Tuesday, June 3) Next Week, June 5 is Last lecture will focus on Final Review = Practice Final Problems Come prepared! Review session schedule (June 5 - 8) will be on the course web site next week.

6. 5 Final format 6 ~ 8 questions (most likely…) Quantitative and qualitative questions Questions are on any material throughout the quarter. Chapter 5 Fluids, Circuits, Transport, Capacitor/Exponential Chapter 6 Vectors/Force (Galilean Space-Time Model) Chapter 7 Momentum/Force, Angular Momentum/Torque Chapter 8 Newtonian Model, SHM To do science, one must practise! But make sure your practice is useful...... available resources : Quiz problems from this quarter, Quiz problems from lecture section C/D, Practice Final Problems.

7. 6 Which takes longer to hit the ground: a bullet shot horizontally or a bullet dropped from the same height? Recap Detailed Relation of Force to Motion A) The dropped bullet hits the ground first B) The fired bullet hits the ground first C) It depends on the mass of the bullet D) They both hit the ground at the same time

8. 7 Some relevant questions to ask: What is the vertical component of the initial velocity in two cases? Are they different? How is the force diagram look like in two cases? What is the vertical component of acceleration (while the bullet is moving toward the ground)? A) The dropped bullet hits the ground first B) The fired bullet hits the ground first C) It depends on the mass of the bullet D) They both hit the ground at the same time Recap Detailed Relation of Force to Motion

9. 8 Some relevant questions to ask: What is the vertical component of the initial velocity in two cases? Are they different? How is the force diagram look like in two cases? What is the vertical component of acceleration (while the bullet is moving toward the ground)? A) The dropped bullet hits the ground first B) The fired bullet hits the ground first C) It depends on the mass of the bullet D) They both hit the ground at the same time Recap Detailed Relation of Force to Motion

10. 9 A rider in a “barrel of fun” is shown to the right. The rider finds herself stuck with her back to the wall. Which diagram below correctly shows the forces acting on her? Recap Detailed Relation of Force to Motion Rotating at constant speed

11. 10 A rider in a “barrel of fun” is shown to the right. The rider finds herself stuck with her back to the wall. Which diagram below correctly shows the forces acting on her? Recap Detailed Relation of Force to Motion Rotating at constant speed

12. 11 Consider two carts of masses M and 2M, at rest on a frictionless track. If you push one cart for 3s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is: A)Four times B)Twice C)Equal to D)One-half E)One quarter The momentum of the heavy cart M 2M Recap Detailed Relation of Force to Motion

13. 12 Consider two carts of masses M and 2M, at rest on a frictionless track. If you push one cart for 3s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is: A)Four times B)Twice C)Equal to D)One-half E)One quarter The momentum of the heavy cart M 2M Recap Detailed Relation of Force to Motion Impulse ext = ∆ p =  F ave.ext x ∆ t

14. 13 Consider two carts of masses M and 2M, at rest on a frictionless track. If you push one cart for 3s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is: A)Four times B)Twice C)Equal to D)One-half E)One quarter The momentum of the heavy cart M 2M Recap Detailed Relation of Force to Motion Impulse ext = ∆ p =  F ave.ext x ∆ t

15. 14 A person spins a tennis ball on a string in a horizontal circle. At the point indicated in the figure, the ball is given a sharp blow in the forward direction. This causes a change in the angular momentum L in the A)x direction B)y direction C)z direction Recap Detailed Relation of Force to Motion

16. 15 A person spins a tennis ball on a string in a horizontal circle. At the point indicated in the figure, the ball is given a sharp blow in the forward direction. This causes a change in the angular momentum L in the A)x direction B)y direction C)z direction  (torque exerted by the blow) ∆L Net Angular Impulse ext = ∆ L =  ave.ext x ∆ t Recap Detailed Relation of Force to Motion

17. 16 A person spins a tennis ball on a string in a horizontal circle. At the point indicated in the figure, the ball is given a sharp blow in the forward direction. This causes a change in the angular momentum L in the A)x direction B)y direction C)z direction  (torque exerted by the blow) ∆L Net Angular Impulse ext = ∆ L =  ave.ext x ∆ t Recap Detailed Relation of Force to Motion

18. 17 An asteroid is traveling to the right through deep space at a constant velocity. The path of the asteroid is shown to the right. Suddenly, it is hit fairly hard by a comet that comes flying in from above and then bounces off. So the asteroid feels a Recap Detailed Relation of Force to Motion downward force, which acts only for a very short time. Which path in the picture is the most reasonable for the asteroid to follow after the impact?

19. 18 An asteroid is traveling to the right through deep space at a constant velocity. The path of the asteroid is shown to the right. Suddenly, it is hit fairly hard by a comet that comes flying in from above and then bounces off. So the asteroid feels a Recap Detailed Relation of Force to Motion downward force, which acts only for a very short time. Which path in the picture is the most reasonable for the asteroid to follow after the impact? C

20. 19 Recap Detailed Relation of Force to Motion An asteroid is traveling to the right through deep space at a constant velocity. Suddenly, a giant rocket engine which is attached to the asteroid is fired upward so that there is a constant downward force on the asteroid. Which path in the picture is the most reasonable for the asteroid to follow after the impact? Rocket engine starts here

21. 20 Recap Detailed Relation of Force to Motion An asteroid is traveling to the right through deep space at a constant velocity. Suddenly, a giant rocket engine which is attached to the asteroid is fired upward so that there is a constant downward force on the asteroid. Which path in the picture is the most reasonable for the asteroid to follow after the impact? Rocket engine starts here B

22. 21 Earth The moon does not crash into the Earth because: Recap Detailed Relation of Force to Motion A)It is not accelerating too much B)It is not accelerating toward the Earth C)It is accelerating away from the Earth D)More than one of the above

23. 22 Earth The moon does not crash into the Earth because: Recap Detailed Relation of Force to Motion A)It is not accelerating too much B)It is not accelerating toward the Earth C)It is accelerating away from the Earth D)More than one of the above

24. 23 Tuning fork Detailed Relation of Force to Motion Atoms in Liquids and Solids A lot of things oscillate (periodically)

25. 24 Simple harmonic motion: is simply a type of motion which follows a repetitive pattern caused by a restoring force Force is zero at equilibrium. For many systems, the net force takes this form near equilibrium, provided equilibrium is stable equilibrium Particle in a bowl equilibrium “Stable” means the net force pushes back to equilibrium ∑F = – k x

26. 25 Not all systems are “stable” equilibrium We don’t find many unstable systems, as any small “bump” has already disrupted them SHM not applicable Most realistic systems have SHM like behaviour close to equilibrium, but behave in very different ways if they get a large push. equilibrium tipping point The environment The stock market etc. SHM applicable for small oscillations near (stable) equilibrium. new equilibrium

27. 26 Simple harmonic motion: SHM means that: The nice thing about SHM is we can solve it! ∑F = – k x From Newton’s Second Law, ∑F = – k x = ma From the definition of a, ∑F = – k x = ma = m d 2 x/dt 2 This means, a(t) = d 2 x(t)/dt 2 = – (k/m) x(t) Math Question What kind of function x(t) is a function whose second derivcative is proportional to the negative of the original function?

28. 27 Simple harmonic motion: SHM means that: The nice thing about SHM is we can solve it! ∑F = – k x From Newton’s Second Law, ∑F = – k x = ma From the definition of a, ∑F = – k x = ma = m d 2 x/dt 2 This means, a(t) = d 2 x(t)/dt 2 = – (k/m) x(t) = – (constant) x(t) Math Question What kind of function x(t) is a function whose second derivcative is proportional to the negative of the original function? Answer: Sine function! Where T = 2  √m/k, A and  depend on the initial condition,e.g. how far you pull the spring before letting it go.

29. 28 Simple harmonic motion: A is the amplitude Position of the object with above restoring force exerted on it is SHM, i.e. is the phase constant responsible for the offset at t = 0 x(t) time T A A T is the period: time it takes for one cycle (crest to crest, or trough to trough) The motion is identical one period later at any point. ∑F = – k x T

30. 29 Explaining the parameters in SHM: A is the amplitude is the phase constant responsible for the offset at t = 0 T: is the period k: spring constant m: mass f : frequency Set by what you do to the system Set by what the system is made of.  A may change, but T must remain the same.  The same setup with a different starting push always have the same periods

31. 30 Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

32. 31 Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

33. 32 Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

34. 33 Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

35. 34 Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

36. 35 Shown to the right are two systems undergoing SHM. The vertical position represents displacement and the horizontal axis represents time. How are the two systems different? A) They have different periods B) They have different amplitudes C) They have different phase constants D) Only two of the above E) a, b and c correct

37. 36 Be sure to write your name, ID number & DL section!!!!! 1MR 10:30-12:50 Dan Phillips 2TR 2:10-4:30Abby Shockley 3TR 4:40-7:00John Mahoney 4TR 7:10-9:30Ryan James 5TF 8:00-10:20Ryan James 6TF 10:30-12:50John Mahoney 7W 10:30-12:50Brandon Bozek 7F 2:10-4:30Brandon Bozek 8MW 8:00-10:20Brandon Bozek 9MW 2:10-4:30Chris Miller 10MW 4:40-7:00Marshall Van Zijll 11MW 7:10-9:30Marshall Van Zijll