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Transcript of 1 Physics 7B - AB Lecture 9 May 29 Detailed Relation of Force to Motion Recap Newtonian Model,...
1
Physics 7B - ABLecture 9
May 29
Detailed Relation of Force to Motion
Recap Newtonian Model, Circular Motion
Simple Harmonic Motion
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!!!)
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11 days till…
4
11 days till…
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.
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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.
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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 firstB) The fired bullet hits the ground firstC) It depends on the mass of the bulletD) They both hit the ground at the same time
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 firstB) The fired bullet hits the ground firstC) It depends on the mass of the bulletD) They both hit the ground at the same time
Recap Detailed Relation of Force to Motion
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 firstB) The fired bullet hits the ground firstC) It depends on the mass of the bulletD) They both hit the ground at the same time
Recap Detailed Relation of Force to Motion
9
18. 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?
A) C) D) B) E)
other
Rotation direction
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
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18. 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?
A) C) D) B) E)
other
Rotation direction
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
19. 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 time s. B) twice C) equal to D) one-half E) one-quarter the momentum of the heavy cart.
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
12
19. 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 time s. B) twice C) equal to D) one-half E) one-quarter the momentum of the heavy cart.
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
Impulseext = ∆ p = F ave.ext x ∆ t
13
19. 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 time s. B) twice C) equal to D) one-half E) one-quarter the momentum of the heavy cart.
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
Impulseext = ∆ p = F ave.ext x ∆ t
14
20. A person spins a tennis ball on a string in a horizontal circle (so that the axis of rotation is vertical). 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
x
y z
v F
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
15
20. A person spins a tennis ball on a string in a horizontal circle (so that the axis of rotation is vertical). 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
x
y z
v F
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 Impulseext = ∆ L = ave.ext x ∆ t
Recap Detailed Relation of Force to Motion
16
20. A person spins a tennis ball on a string in a horizontal circle (so that the axis of rotation is vertical). 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
x
y z
v F
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 Impulseext = ∆ L = ave.ext x ∆ t
Recap Detailed Relation of Force to Motion
17
23. 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 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?
Asteroid is hit here.
A
B
C E D
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?
18
23. 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 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?
Asteroid is hit here.
A
B
C E D
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
19
25. An asteroid is traveling to the right through deep space at a constant velocity as shown. Suddenly a giant rocket engine that 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 starts here.
A
B
C E D
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
20
25. An asteroid is traveling to the right through deep space at a constant velocity as shown. Suddenly a giant rocket engine that 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 starts here.
A
B
C E D
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
21
33. The moon does not crash into the earth because: A) it is not accelerating B) it is not accelerating too much C) it is not accelerating toward the earth D) it is accelerating away from the earth E) more than one of the above
moon
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
22
33. The moon does not crash into the earth because: A) it is not accelerating B) it is not accelerating too much C) it is not accelerating toward the earth D) it is accelerating away from the earth E) more than one of the above
moon
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
23Tuning fork
Detailed Relation of Force to Motion
Atoms in Liquids and Solids
A lot of things oscillate (periodically)
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
equilibrium
“Stable” means the net force pushes back to equilibrium
∑F = – k x
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 pointtipping point
The environmentThe stock market
etc.SHM applicable for small oscillations
near (stable) equilibrium.
new equilibrium
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 d2x/dt2
This means, a(t) = d2x(t)/dt2 = – (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?
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 d2x/dt2
This means, a(t) = d2x(t)/dt2 = – (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.
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 constantresponsible for the offset at t = 0
xx(t)(t)
timetime
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
29
Explaining the parameters in SHM:
A is the amplitude
is the phase constantresponsible for the offset at t = 0
T: is the period
k: spring constant
m: mass
f : frequencySet by what you do
to the system
Set by what the systemis made of. A may change, but T must remain the same.
The same setup with a different starting push always have the same periods
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 periodsB) They have different amplitudesC) They have different phase constantsD) Only two of the aboveE) a, b and c correct
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 periodsB) They have different amplitudesC) They have different phase constantsD) Only two of the aboveE) a, b and c correct
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 periodsB) They have different amplitudesC) They have different phase constantsD) Only two of the aboveE) a, b and c correct
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 periodsB) They have different amplitudesC) They have different phase constantsD) Only two of the aboveE) a, b and c correct
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 periodsB) They have different amplitudesC) They have different phase constantsD) Only two of the aboveE) a, b and c correct
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 periodsB) They have different amplitudesC) They have different phase constantsD) Only two of the aboveE) a, b and c correct
36
Be sure to write your name, ID number & DL section!!!!!1 MR 10:30-12:50 Dan Phillips
2 TR 2:10-4:30 Abby Shockley
3 TR 4:40-7:00 John Mahoney
4 TR 7:10-9:30 Ryan James
5 TF 8:00-10:20 Ryan James
6 TF 10:30-12:50 John Mahoney
7 W 10:30-12:50 Brandon Bozek
7 F 2:10-4:30 Brandon Bozek
8 MW 8:00-10:20 Brandon Bozek
9 MW 2:10-4:30 Chris Miller
10 MW 4:40-7:00 Marshall Van Zijll
11 MW 7:10-9:30 Marshall Van Zijll