Physics 7B - AB Lecture 8 May 22 Summary of Newtonian Model (Chapter 8)

1. Physics 7B - ABLecture 8May 22Summary of Newtonian Model (Chapter 8)

2. Quiz 2 Re-evaluation Request Due TODAY Quiz 3 Due May 29 (next Thursday) Quiz 4 Rubrics on the website Next week Quiz 6 (Last Quiz!!!)Will cover Lecture 7 & 8DL activities and FNTs from DLM13, 14, and activities from DLM15. FNTs from DLM15 will not be covered.

3. Due to Memorial day holiday, One DLM will be cancelledToday Normal DLM scheduleFri May 23 No DL meetingsMon May 26 No DL meetingsTues May 27 No DLM for Section 2- 4 DLM16 Section 5, 6Wed May 28 DLM 16 Section 7 -11

4. 18 days till…

5. 18 days till… 7B Final June 9 Mon 1- 3pm • June 5 Last lecture Final Review • Each DL instructor will hold 1.5 hour review session (June 5,6) • Practice Final will be on the course website (answer keys will be posted next week, after Quiz 6)

6. Which one of the below parameters are NOT vectors? L (Angular Momentum) P (Pressure)  (Torque) I (Rotational Inertia) p (Linear Momentum)  (Density) m (mass) F (Force) a (Acceleration) v (Velocity) Energy  (Angular Velocity)  (Angular Acceleration) Speed g (Acceleration of an object in free fall.)

7. NOT vector = Scalar quantity, i.e., it’s a number. P (Pressure) I (Rotational Inertia)  (Density) m (mass) Energy Speed

8. Capitalized quantity = Vector quantity i.e., it’s got direction as well as magnitude! Non- capitalized quantity = Scalar quantity L (Angular Momentum) P (Pressure) (Torque) I (Rotational Inertia) p (Linear Momentum)  (Density) m (mass) F (Force) a (Acceleration) v (Velocity) Energy  (Angular Velocity)  (Angular Acceleration) Speed g (Acceleration of an object in free fall.)

9. Who is right? Aristotle Force is always necessary to keep an object moving (even at constant velocity)! Gallileo I disagree!! No change in velocity (constant velocity), No force!

10. Who is right? Aristotle Force is always necessary to keep an object moving (even at constant velocity)! Gallileo I disagree!! No change in velocity (constant velocity), No force!

11. Newton’s first law: If the momentum changes, there is a net force on the system. If the momentum is not changing, there is no net force on the system. Newtonian ModelNewton’s Laws of Motion ∆ p = ∑ Fave.extx ∆ t Ex. Quiz 5 (Alice and Bob on a stationary sled on frictionless icy surface, each throws a snowball) There is no net external force on the system (Alice&Bob + Sled + Snowballs), therefore there is no change in the linear momentum of the system after the throw.

12. Newtonian ModelNewton’s Laws of Motion Newton’s second law: ∑ Fext = d p /dt = m dv/dt = ma An net force (∑ Fext 0) causes acceleration (acceleration = time rate change of velocity = change in motion of an object) Dan Chris Ex. The bobsled accelerates because the team exerts a non zero net force

13. Newtonian ModelNewton’s Laws of Motion Force diagram of the bobsled (focus on the forces exerted on the bobsled! ) F Team on Bobsled F  Ice on Bobsled Dan F Earth on Bobsled Chris Assume icy surface is frictionless. ∑ Fext = FTeam on Bobsled = mbobsledabobsled Bobsled accelerates, i.e., its velocity vector changes, and the rate of change is given by its acceleration (abobsled = d vbobsled/dt )

14. Wall Ice surface Newtonian ModelNewton’s Laws of Motion F A on B = – F B on A Newton’s third law: You cannot push without being pushed yourself! Ex. When an ice skater pushes against the wall, the wall pushes back. FSkater on Wall = – FWall on Skater

15. Wall Ice surface (Assume frictionless) Force diagram of the skater (focus on the forces exerted on the skater! ) F Wall on Skater F  Ice on Skater F Earth on Skater According to Newton’s 2nd Law, this force causes her to accelerate away from the wall ∑ Fext = FWall on Skater= mSkateraSkater

16. Position vs Velocity vs Acceleration 1. The velocity of an object is shown on the board as a function of time. Draw a graph that describes its acceleration as a function of time (a(t)) and its position as a function of time (x(t)).

17. Position vs Velocity vs Acceleration Train A 2. The graph on the right shows the position as a function of time for two trains running on parallel tracks. Which statement is true? Train B At time, tB, both trains have the same velocity Both trains speed up all the time Both trains have the same velocity at some time before None of the above is true!

18. Position vs Velocity vs Acceleration Train A 2. The graph on the right shows the position as a function of time for two trains running on parallel tracks. Which statement is true? Train B At time, tB, both trains have the same velocity Both trains speed up all the time Both trains have the same velocity at some time before None of the above is true!

19. 3. A constant force is pushing an object along, providing a constant acceleration to the object by speeding it up in a straight line. Another force, greater in strength than the first is then introduced so that it opposes the original force (original force is still there).What will happen to the motion of the object ? It will stop suddenly and begin speeding up in the other direction. Its acceleration will instantly switch directions and then remain constant Its acceleration will deacrease at a steady rate It depends upon how much stronger the new force is compared to the original force

20. 3. A constant force is pushing an object along, providing a constant acceleration to the object by speeding it up in a straight line. Another force, greater in strength than the first is then introduced so that it opposes the original force (original force is still there).What will happen to the motion of the object ? Initial State Final State F2 F1 F1 It will stop suddenly and begin speeding up in the other direction. Its acceleration will instantly switch directions and then remain constant Its acceleration will decrease at a steady rate It depends upon how much stronger the new force is compared to the original force

21. 3. A constant force is pushing an object along, providing a constant acceleration to the object by speeding it up in a straight line. Another force, greater in strength than the first is then introduced so that it opposes the original force (original force is still there).What will happen to the motion of the object ? Initial State Final State ainitial = F1/m afinal = (F1 + F2) /m F2 F1 F1 It will stop suddenly and begin speeding up in the other direction. Its acceleration will instantly switch directions and then remain constant Its acceleration will decrease at a steady rate It depends upon how much stronger the new force is compared to the original force

22. 4. In the picture shown to the right, Block A is pushed to the left by a finger. Both blocks are moving at a constant speed to the left. A force diagram for Box B is shown. Is it correct? FTable on B FA on B FB on A FEarth on B Yes, it is correct! No, it includes force(s) that don’t belong. No, there are force(s) missing. Both B) & C) are correct

23. 4. In the picture shown to the right, Block A is pushed to the left by a finger. Both blocks are moving at a constant speed to the left. A force diagram for Box B is shown. Is it correct? FTable on B FA on B FB on A FEarth on B Yes, it is correct! No, it includes force(s) that don’t belong. No, there are force(s) missing. Both B) & C) are correct

24. 4. In the picture shown to the right, Block A is pushed to the left by a finger. Both clocks are moving at a constant speed to the left. A force diagram for Box B is shown. Is it correct? FTable on B FA on B F//Table on B(friction) FEarth on B Yes, it is correct! No, it includes force(s) that don’t belong. No, there are force(s) missing. Both B) & C) are correct

25. Who is right? Aristotle Heavy objects has greater acceleration than light objects. So on the moon, in the absence of air resistance, heavier hammer falls faster than a feather! Gallileo I disagree!! Acceleration is independent of the object’s mass. So on the moon, the time of decent for two objects with different mass (hammer vs feather) will be the same!

26. Astronaut David Scott flies to the Moon on Apollo15 and drops a hammer and a feather simultaneously. You can watch the movie on the www.youtube.com (search for Galileo on the Moon)

27. Who is right? Aristotle Heavy objects has greater acceleration than light objects. So on the moon, in the absence of air resistance, heavier hammer falls faster than a feather! Gallileo I disagree!! Acceleration is independent of the object’s mass. So on the moon, the time of decent for two objects with different mass (hammer vs feather) will be the same!

28. For a hammer, ∑ Fext = FMoon on hammer = Mhammerahammer FMoon on hammer = MhammergMoon, therefore ahammer=gMoon For a feather, ∑ Fext= FMoon on feather = mfeatherafeather FMoon on feather = mfeathergMoon, therefore afeather=gMoon Gallileo All objects have the same acceleration toward the Moon,i.e., all objects’velocities increase at the same rate toward the Moon.

29. So then why a hammer and a feather will NOT reach the ground at the same time when dropped on Earth?

30. So then why a hammer and a feather will NOT reach the ground at the same time when dropped on Earth? Because of the air resistance. The force of air on a falling object is in the opposite direction of the acceleration of the falling object. The larger an object's surface area, the greater the resistant force. The faster the speed of the object, the greater the resistant force.

31. So then why a hammer and a feather will NOT reach the ground at the same time when dropped on Earth? For a hammer, ∑ Fext = FEarth on hammer + FAir on hammer = Mhammerahammer FEarth on hammer = MhammergEarth, therefore ahammer =gEarth+ FAir on hammer /Mhammer For a feather, ∑ Fext = FEarth on feather + FAir on feather = mhammerahammer FEarth on feather = mfeathergEarth, therefore afeather=gEarth+ FAir on feather /mfeather

32. So then why a hammer and a feather will NOT reach the ground at the same time when dropped on Earth? For a hammer, ∑ Fext = FEarth on hammer + FAir on hammer = Mhammerahammer FEarth on hammer = MhammergEarth, therefore ahammer=gEarth+ FAir on hammer /Mhammer For a feather, ∑ Fext= FEarth on feather + FAir on feather = mhammerahammer FEarth on feather = mfeathergEarth, therefore afeather=gEarth+ FAir on feather /mfeather

33. FAir on feather Feather FEarth on feather Let a Feather fall on Earth Air resistance becomes greater as the object’s speed increases t = 0.1 sec. At some point, The magnitude of FAir on feather becomes equal to the magnitude of FEarth on feather FAir on feather Later time FEarth on feather ∑ Fext = FEarth on feather + FAir on feather = 0  mfeatherafeather= 0, afeather= 0 Velocity of the feather will no longer increase. Feather reached its terminal velocity.

34. One way to experience terminal velocity the terminal velocity of a skydiver with a semi-closed parachute is about 120 mph or 55m/s.

35. Next WeekSimple Harmonic Model Quiz 6 (Last Quiz!!!)Will cover Lecture 7 & 8DL activities and FNTs from DLM13, 14, and activities from DLM15. FNTs from DLM15 will not be covered.