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Physics 7B - ABLecture 9

May 29

Detailed Relation of Force to Motion

Recap Newtonian Model, Circular Motion

Simple Harmonic Motion

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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…

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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?

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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

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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

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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

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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

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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)

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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

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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

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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?

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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