General Physics I: Day 2 Kinematics Quantities. First Warm-Up… 47+ people were able to do the Warm-Up! Remember: Warm-Ups due Monday are available Saturday.

General Physics I: Day 2Kinematics Quantities

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First Warm-Up…

47+ people were able to do the Warm-Up!

Remember:

• Warm-Ups due Monday are available Saturday

• Warm-Ups due Wednesday are available Tuesday

Deadline for Warm-Ups is 10:00 PM sharp.Graded on thoughtful effort. 10% of your grade

I also got 37+ image submissions!

Questions?

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Image Submission

Please read the intro pages!

Submit an image of the Self-Explanation Prompts. They say “Image Submission”

Difficulties/Interests

One WarmUp question is always:

What part of the material in the reading did you find the most confusing? If none of the material was confusing to you, what part did you find the most interesting and why?

This question is worth points just like others and is your chance to reflect on what you have read.

Ignore the last part on the page where it has space for comments. Totally optional, I may not read it.

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Converting Between Representations

Take a vector that is |A| = 15 units long, which is at angle θ = 25° relative to the x-axis, and convert it into component form.

Take these components and convert them back into magnitude-direction form.

Will the x-component always be associated with the cosine function?

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No! It depends…

Is it possible for the result of subtracting two vectors to have a larger magnitude than the result of adding them?

A) Yes, and I can give an example

B) I think so, but can’t give an example

C) I don’t think so, but I can’t say why

D) No

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Adding Vectors

Be careful! Adding the magnitudes of and will almost never give you something useful.

does NOT mean

You must always be clear on whether a given quantity is a vector or a scalar!

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Adding Vectors: Geometric MethodHead-to-tail method:

1. Draw first vector

2. Draw the second vector from the head of the first

3. Draw a vector from the tail of the first vector to the head of the second vector. That is their sum.

4. Measure the length and angle of vector sum.

Pros: Intuitive and easy to see.

Cons: Doesn’t give numbers directly, introduces human error into the process.

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Consider the vectors in the diagram. If we combine these vectors in the following way, into which quadrant will the resultant point?

A) Quadrant I

B) Quadrant II

C) Quadrant III

D) Quadrant IV

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?A B C

IV

III

III

Adding Vectors: Component Method

1. Calculate components all vectors being added2. Components of the vector sum are just the sum

of the components of the vectors being added: and

3. Recombine components of vector sum to get magnitude and direction.

Pros: No measurement error, no drawing toolsCons: Less intuitive, not as easy to check visuallySo… do both! Draw the vectors and calculate their sum using components

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Multiplication With Vectors

Three cases:

1. Multiply a vector and a scalar

–Easy, this only changes the magnitude

2. Scalar product of two vectors (a.k.a. Dot product)

3. Vector product of two vectors (a.k.a. Cross product)

–We will need these later… but not yet.

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Warm-Up: Motion Diagrams

Assume the times marked are in seconds and that the big tick marks are cm (that is, there are 6 cm shown). Only consider what you can see…

a) Which one is ahead to start with?

~95% → The grey ball is ahead to start

~5% → The blue ball is ahead to start

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b) Does one ball ever pass the other? If so, roughly when? If not, how can you tell.

~5% → Blue passes at 2 seconds~35% → Blue passes between 2 and 3 seconds~20% → Blue passes at 3 seconds~10% → Blue passes at 4 seconds~15% → Gave a location (not a time)

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“A. The grey one is ahead to start with. B. The grey ball passes over the blue ball at 2 seconds and 1.2 cm.”

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“a. The grey ball is ahead at the start, its position is .40cm b. The blue ball does pass the grey ball, somewhere between 2 and 3 seconds. I can tell because at 3 seconds, the blue ball is further along than the grey ball at the same amount of time.”

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“Grey is ahead at the start. Blue surpasses grey at the 2 second mark. I can tell because at the 2 second mark, blue and grey are equal and at the 3 second mark, blue is ahead. This means that just after the 2 second mark, blue took the lead.”

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1D Vectors

For 1 dimensional vectors, (+) or (-) gives direction

That is the only thing the sign tells you…

Most common: Set up a set of axes so that (+) is to the right and (-) is to the left.

(this is a totally arbitrary choice!)

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Position & Average Velocity

Position . Vector quantity!• Different than distance ( d ) which is a scalar.• Or as displacement, ,which is also a vector)

(Note that is one quantity)

Average Velocity . Vector quantity!• Displacement divided by time• speed ≠ velocity

x

avg.

xv

t

distance traveled

time intervalspeed

avg.v

x

x

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Instantaneous Velocity

What about the velocity at a given moment?

Velocity is the rate of change of position with respect to time.

Given , the instantaneous velocity at time is the slope of the tangent line at time .

inst0

. limt

xv

t

inst.or dx

vdt

21Worked-Example: Shuttle TakeoffQualitative description of motion:

~50% → Goes up

~0% → Starts at rest

~70% → Speeds up (some said steady/constant)

~30% → Had some wrong information or answered a different question.



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Difficult/Interesting

“I found phrasing and vocabulary confusing in the homework problems.”

25Worked-Example: Shuttle Takeoff after 1 min compared to at 1 min?

~70% → is larger than

~0% → is smaller than

~5% → is the same as (or close to)

~10% → Didn’t answer the question

26Worked-Example: Shuttle Takeoff after 1 min compared to at 1 min?

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Warm-Up: Choose the Plot

A person initially at point P in the illustration stays there a moment and then moves along the axis to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to P.

~75% → Plot 2

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A train car moves along a long straight track. The graph shows the position as a function of time for this train. The graph shows that the train:

A) speeds up all the time

B) slows down all the time

C) moves at a constant velocity

D) speeds up at first and the slows down later.

(x)

(t)

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Acceleration

We go through the same evolution for acceleration:

Acceleration is the rate of change of velocity with respect to time.

Careful!In daily life we often interchange velocity and acceleration… can’t do that here!

Be very careful with "deceleration"… bad term!

insa t.vg. v dv

a at dt

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The graph shows position as a function of time for two trains running on parallel tracks. Which is true:

A) At time tB, 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 tB.

D) Somewhere on the graph, both trains have the same acceleration.

(x)

(t)

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Coming up…Tuesday (8/26) → 2.4 – 2.6

Background Assessment link is on the homepage, Due by Tuesday at 9:30 AM

Next WarmUp is due Monday by 10:00 p.m.

MasteringPhysics:Intro. to MasteringPhysics due Sat. by 11:59 PM.Homework #1 due Tuesday by 11:59 PM.

General Physics I: Day 2 Kinematics Quantities. First Warm-Up… 47+ people were able to do the Warm-Up! Remember: Warm-Ups due Monday are available Saturday.

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