1 Physics 7B - AB Lecture 8 May 22 Summary 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 & 8 DL 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 cancelled Today Normal DLM schedule Fri May 23No DL meetings Mon May 26No DL meetings Tues May 27No DLM for Section 2- 4 DLM16 Section 5, 6 Wed May 28DLM 16 Section 7 -11

4 18 days till…

5 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 ? I (Rotational Inertia) L (Angular Momentum) p (Linear Momentum) F (Force) a (Acceleration) v (Velocity)  (Angular Velocity) m (mass)  (Torque)  (Angular Acceleration) g (Acceleration of an object in free fall.)  (Density) P (Pressure) Energy Speed

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

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

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

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

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

13 Newtonian Model Newton’s Laws of Motion Assume icy surface is frictionless. ∑ F ext = F Team on Bobsled = m bobsled a bobsled Chri s Dan F Team on Bobsled Force diagram of the bobsled (focus on the forces exerted on the bobsled! ) F  Ice on Bobsled F Earth on Bobsled Bobsled accelerates, i.e., its velocity vector changes, and the rate of change is given by its acceleration (a bobsled = d v bobsled /dt )

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

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

16 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)). Position vs Velocity vs Acceleration

17 Position vs Velocity vs Acceleration A)At time, t B, both trains have the same velocity B)Both trains speed up all the time C)Both trains have the same velocity at some time before D)None of the above is true! 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 A Train B

18 Position vs Velocity vs Acceleration A)At time, t B, both trains have the same velocity B)Both trains speed up all the time C)Both trains have the same velocity at some time before D)None of the above is true! 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 A Train B

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 ? A)It will stop suddenly and begin speeding up in the other direction. B)Its acceleration will instantly switch directions and then remain constant C)Its acceleration will deacrease at a steady rate D)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 ? F1F1 Initial StateFinal State F1F1 F2F2 A)It will stop suddenly and begin speeding up in the other direction. B)Its acceleration will instantly switch directions and then remain constant C)Its acceleration will decrease at a steady rate D)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 ? F1F1 Initial StateFinal State F1F1 F2F2 A)It will stop suddenly and begin speeding up in the other direction. B)Its acceleration will instantly switch directions and then remain constant C)Its acceleration will decrease at a steady rate D)It depends upon how much stronger the new force is compared to the original force a initial = F 1 /ma final = (F 1 + F 2 ) /m

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? A)Yes, it is correct! B)No, it includes force(s) that don’t belong. C)No, there are force(s) missing. D)Both B) & C) are correct F  Table on B F Earth on B F B on A F A on B

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? A)Yes, it is correct! B)No, it includes force(s) that don’t belong. C)No, there are force(s) missing. D)Both B) & C) are correct F  Table on B F Earth on B F B on A F A on B

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? A)Yes, it is correct! B)No, it includes force(s) that don’t belong. C)No, there are force(s) missing. D)Both B) & C) are correct F  Table on B F Earth on B F //Table on B (friction) F A on B

25 Who is right? Aristotle Gallileo 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! 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 (search for Galileo on the Moon)

27 Who is right? Aristotle Gallileo 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! 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 Gallileo All objects have the same acceleration toward the Moon,i.e., all objects’velocities increase at the same rate toward the Moon. For a hammer, ∑ F ext = F Moon on hammer = M hammer a hammer F Moon on hammer = M hammer g Moon, therefore a hammer = g Moon For a feather, ∑ F ext = F Moon on feather = m feather a feather F Moon on feather = m feather g Moon, therefore a feather = g Moon

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

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

31 For a hammer, ∑ F ext = F Earth on hammer + F Air on hammer = M hammer a hammer F Earth on hammer = M hammer g Earth, therefore a hammer = g Earth + F Air on hammer /M hammer For a feather, ∑ F ext = F Earth on feather + F Air on feather = m hammer a hammer F Earth on feather = m feather g Earth, therefore a feather = g Earth + F Air on feather /m feather So then why a hammer and a feather will NOT reach the ground at the same time when dropped on Earth?

32 For a hammer, ∑ F ext = F Earth on hammer + F Air on hammer = M hammer a hammer F Earth on hammer = M hammer g Earth, therefore a hammer = g Earth + F Air on hammer /M hammer For a feather, ∑ F ext = F Earth on feather + F Air on feather = m hammer a hammer F Earth on feather = m feather g Earth, therefore a feather = g Earth + F Air on feather /m feather So then why a hammer and a feather will NOT reach the ground at the same time when dropped on Earth?

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

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