Sept. 30 – Formative Quiz

Here's the formative quiz we did today:

• Formative Quiz

The following is to help you prepare for the test this week...

Test Topics

1. Significant Digits, Units, Scientific Notation (throughout the test).
2. Vectors (adding vectors, vector diagrams, vector components).
3. Definitions (distance, displacement, speed, velocity, acceleration, etc.)
4. Graphing (DT, VT, AT)
5. Kinematic Equations
6. Projectile Motion

Knowledge/Understanding: Multiple choice, some full solutions required.

Application: Problem solving, full solutions required.

Communication: Explanations and diagrams.

Thinking: Challenge Question.

Reminders

• Lab Due Wednesday for P1, Thursday for P5
• Test Thursday
• Thinking Question Friday

Now's the time to buckle down and prepare for the test.  Good luck!

Sept. 26 – Projectile Motion Problems

Announcements

Here's the plan for next week:

• Monday: Work Period
• Tuesday: Formative Quiz
• Wednesday: Review day, Lab Due (period 2)
• Thursday: Test day, Lab Due (Period 5)
• Friday: Thinking Question

Today I worked out some full solutions to projectile motion problems.  Look at this one involving Milos Raonic serving a ball from the top of the CN tower:

The second question involved this golfer:

The video tells us that the ball went 279 yards (we'll make it meters!).  We timed it to find that ∆t = 6.6 s.  We were then able to calculate the initial speed and angle of the hit.  See the full solution above.

In period 5, I also showed the full solution to number 3 of this problem set:

• Advanced Kinematics Problems 1

Homework

• Work on your lab write up.
• Work on day 11 homework from the Unit Outline.

Sept. 25 – Lab Day

Announcements!

Here is a new schedule for the rest of the unit:

• Formative Quiz Tuesday Sept. 30
• Lab due Wednesday Oct. 1 (for Period 2), Thursday Oct. 2 (for Period 5)
• Test on Thursday/Friday Oct. 2, 3

Today the Period 5 class collected data for their lab.  Period 2 class had a lesson on projectile motion.  Please see the notes from yesterday's post.

Homework for Period 2 Class

• Do homework from day 10 in the unit outline.

Homework for Period 5 Class

• Work on your lab writeup.

Sept. 24 – Projectile Motion

Today the Period 2 Class collected data for their lab.

Period 5 had a normal lesson.  Here are the notes from Period 5.
I took up problem 2 from yesterday's handout:

At this point you need the quadratic formula!  Don't remember it?  Listen to this song...

Next we discussed projectile motions.  Here are the notes:

Here are some examples of projectile motions:

I also showed you evidence that X and Y components of velocity behave independently.  Here's how the Mythbusters confirmed that a bullet dropped and fired all fall at the same rate:

Tomorrow, we switch and Period 5 class will collect data while Period 2 class will have the lesson.

Homework for Period 5 Class

• Do homework from day 10 in the unit outline.

Homework for Period 2 Class

• Work on your lab writeup.

Sept. 23 – Advanced Kinematic Equations and Lab Introduced

Welcome back from your long weekend!  I hope you used the opportunity to catch up on all your homework.

I started today by reviewing one of the homework problems:

Then I provided you with some more advanced kinematic problems as well as the lab for tomorrow.  Please have a look at the lab handout and come prepared to collect data tomorrow.

Handouts

• Advanced Kinematics Problems 1
• Advanced Kinematics Problems 2
• Gravity Lab 
• Gravity Lab Marking Scheme

Homework

• Complete any previous homework.
• Work on Advanced Kinematics Problems.
• Read the Lab handout.

Sept. 19 – Kinematic Equations

On Friday I showed you where the 5 kinematic equations come from.

Here is your long awaited formula sheet!

• Formula Sheet

Here are the notes:

This chart is on page 54 in your textbook.  It shows the relations between these 5 equations and the 5 variables.

Example: A light bulb drops from a 3 m ceiling and falls to the floor.  How long does this take?  (Acceleration due to gravity is 9.81 m/s²).

Given: ∆d = 3m [down]        vi = 0 m/s [down]      a = 9.81m/s² [down]

Required: ∆t

Analysis: The third equation contains all these variables.

∆d = vi ∆t + 1/2 a (∆t)²

Solve: ∆t = 0.78 s

Statement: The light bulb takes 0.78 s to fall to the ground.

We then tested it by dropping stuff from the ceiling and got surprisingly accurate results!

Homework

You can now do the homework from day 7 and 8 of the Unit Outline.

Sept. 18 – Tonnes of Graphing!

Announcement: Tryouts for the McMaster Engineering and Science Olympics will be next week!  Put together your team and sign up outside the Science Office, 143.

Today in class I got the document camera working!  Yay!

We discussed all the different kind of DT graphs that are possible and what the related VT graphs look like.  Here are the notes:

Then I showed you how to convert between DT, VT, and AT graphs.  Here are those notes:

Finally a lot of practice handouts:

• DT, VT, AT graphs 1
• DT, VT, AT graphs 2

You can now do homework from day 5 in the Unit Outline.

Sept. 17 – Acceleration and VT graphs

Announcements

• Projected day of test: Oct. 1
• Lab as been postponed to next week.
• We are looking for teams to compete in the McMaster Engineering and Science Olympics!
  Come to room 121 after school on Thursday if you are interested in competing!  check out the website: http://olympics.mcmaster.ca/

Acceleration

Watch this....

Describe the motion of the cars in the drag race.

  - At the beginning, the speed was slow.

  - At the end, the speed was very fast

  - There was a change in speed

• Uniform motion = constant velocity = no acceleration
  
• Non-Uniform motion = velocity is not constant = acceleration

A change in speed can be written as:

              ∆v = v(final) – v(initial)

This change takes time, ∆t.

We call this rate of change acceleration.

          a = ∆v / ∆t

Example: A Ferrari 458 can go from 0.0 km/h to 100. km/h in 3.4 seconds.  a) What is its acceleration?   b) How long will it take to reach its maximum speed of 325 km/h.

Next we followed up on what we did yesterday, rolling the ball down the hill.  I followed along the instructions on the handout:

• Kinematics Lab 2: Rolling a Ball Down a Hill

Here are my notes based on Period 5 data.

I explained what a tangent line is and how to create a VT graph based on the DT graph.

You can now do homework from Day 4 in the Unit Outline.

Homework

•  Pg. 40 #1-7

Sept. 16 – Vector Components and Formative Lab 2

Hi Everyone,  I was not able to come to class yesterday, so today I reviewed what would have been yesterday's homework.  Page 75 Question #13.  I had perfect attendance in both periods, so everyone should have the full solution to that question.  If you understand that question entirely, you are on a good track!  If not, I will stay after school tomorrow for as long as you need to help you get up to speed.

Please come find me in room 248 after school, Wednesday, for extra help.

For the rest of the period, we did another formative lab.  The second page on this handout:

• Kinematics Lab 1: Rolling a Ball

Here's the data from Period 2:

Rolling a ball down a hill
	Roll 1	Roll2
d (m)	time (s)	time (s)	average (s)
4.0	2.6	1.9	2.3
8.0	4.2	3.4	3.8
12.0	5.3	4.1	4.7
16.0	6.1	4.8	5.5
20.0	7.2	6.0	6.6

The graph from this data is here:

I suggest ignoring the last point when drawing your curve of best fit.

Here's the data from Period 5:

Ball Rolling down a hill
	Roll 1	Roll 2
d (m)	time (s)	time (s)	average (s)
3.0	1.9	1.2	1.6
6.0	3.4	2.1	2.8
9.0	3.4	3.2	3.3
12.0	4.6	3.6	4.1
15.0	5.7	4.4	5.1

The graph of this data is here:

I suggest removing the last two points when drawing your curve of best fit.

Notice the above graphs are not complete!  They have no titles and is not properly labelled.

Homework

• Please complete this graph in your own and continue with the questions on the handout.

Sept. 12 – More on Vectors, 2D Vectors and Adding Vectors

First of all, some of you asked for all the metric prefixes, so here they are:

Next we continued with our Monopoly example:

Example: Write the displacement vector from "Water Works" to "Jail".

Answer: Using some trigonometry we were able to write down the answer in different ways:

Using cardinal directions:   B = 12.8 spaces [W 51.3° S]   or  B = 12.8 spaces [S 38.7° S]

• State one direction first, then how much to turn towards the other direction.

Using bearing:   B = 12.8 spaces [bearing 218.7°]

• North is 0° and all angles go clockwise.

Using the x-y plane:  B = 12.5 spaces [231.3°]

• The x-axis is 0° and all angles go counter-clockwise.

Using vector components: B = 8 spaces [left] + 10 spaces [down]

Vector Components

The final method used above is vector components.  It's a way of breaking up a vector into two directions that are easier to work with.

Example: Montreal is 500 km [E 35° N] relative to Toronto.

What is the x-y component of Montreal if Toronto was at the origin?

Solution: We used trigonometry (SOH CAH TOA) to find,

∆d = 490 km [E] + 287 km [N]

Using components is equivalent to writing down the magnitude and direction.  Both methods contain the same amount of information and you can should be able to convert one form to another.

Adding Vectors

Two vectors can be added together.  The method used is called Head-to-Tail.

For example:

The two black vectors are added together using Head-to-Tail and the result is the red vector.

Example: Cindy walks 3 km [N] to get to school.  Afterschool she walks another 2 km [N 40° E] to get to her soccer practice.  What is her final displacement?

Solution: Using a combination of Cosine Law and Sine Law we arrived at,

∆d = 5.2 km [N 18° E]

Finally, I listed the steps to add vectors using components.

Adding vectors with components

In some cases, this this easier than using the trigonometry methods mentioned above.

1. Write down the xy-components of vector A.
2. Write down the xy-components of vector B.
3. Add all the x-components.
4. Add all the y-components.
5. Done!

Homework

You should be able to do the homework from day 2,

• HW: Pg. 75 #5a, 8, 10, 12

Sept. 11 – Formative Quiz and VT Graphs

Today we did our formative quiz and took it up in class.

• Formative Quiz Solutions

Then we discussed VT graphs...

Velocity Time Graphs

Graphs with v on the y-axis, t on the x-axis

Example: Graph of wandering dog.

Question: What is the dog's displacement?

Answer: v = ∆d / ∆t  —> ∆d = v ∆t

• v ∆t is the AREA under the vt graph.
• displacement is the AREA between the vt graph and the x-axis.

Break up the area into 4 sections and calculate the area of each section.

d1 = (1 m/s)(4 s) = 4 m

d2 = (1 m/s)(2 s) ÷ 2 = 1 m

d3 = (-2 m/s)(4 s) ÷ 2 = -4 m

d4 = (-2 m/s)(3 s) = -6 m

∆d = d1 + d2 + d3 + d4

     = 4m +1m – 4m –6m

     = -5 m

Example:  What is the dog’s average velocity?

Average velocity = total displacement ÷ total time

v(average) = -0.4 m/s [forward]

Instantaneous Velocity

The velocity at any instant of time.

Examples:

The dog’s instantaneous velocity at 5s is 0.5 m/s [forward].

The dog’s instantaneous velocity at 12 s is -2 m/s [forward]. 

MORE ON VECTORS

Look at Monopoly board.

Write a vector that goes from “Free Parking” to “Jail”.

    A = 10 steps [down]

Challenge: Write a vector that goes from “Water Works” to “Jail”.

Sept. 10 – D-T graphs and V-T grarphs

Watch this...

Problem: How far away is the volcano?  The speed of sound is 340 m/s.

Time between explosion and sound can be found from watching the video.

Given:

∆t = 25 s – 12 s = 13 s

v = 340 m/s

Required:

∆d = ?

Analysis:

Isolate for ∆d.

v = ∆d / ∆t   —> rearrange —> ∆d = v ∆t

Solve:

∆d = (340 m/s)(13 s)

     = 4400 m

Statement:

The volcano is 4.4 km away.

Position-Time Graph (D-T graph)

• distance on the y-axis,
• time on the x-axis

The slope of the D-T graph represents speed (we recognized this from yesterday's activity)

If the ball is not moving, the slope is 0.

Speeding up and slowing down, give curved graphs.

Speeding up

 Slowing down

If the graph is a straight line (constant slope) we call it UNIFORM MOTION.

 - v is constant.

 - v= ∆d / ∆t  only works for uniform motion

y - intercept is the starting point of the motion

negative slope means the object is moving in the negative direction (backwards.)

Uniform Motion backwards

 Speeding up backwards

Slowing down backwards

Example: Describe the motion in this graph.

   - I leave my house and run 60 m.

   - I stop for 5 s.

   - I run back home and ran too far by 40 m.

   - I turn around and go back to home.

What is my total distance travelled?

d = 60 m + 0 m + 100 m + 40 m

   = 200 m

What is my displacement?

∆d = df  – di  = 0 m [forward] - 0 m [forward] 

                      = 0 m [forward]

Distance is the actual path travelled.

Displacement is the final change in position.

Example: Calculate the speed in each section of the trip.

Solutions:

v1 = 83 m/s

v2 = 42 m/s

v3 = 15 m/s

Velocity Time Graph (V-T graphs)

From the above data, we can draw a velocity time graph:

Homework

You should now be able to do homework from day 0 and day 1.

• HW:  Pg. 13 #1-4, 6,7
• HW:  Pg. 25 #1-3, 5-7, 9-13

Sept. 9 – Speed and Velocity

We continued with where we left off yesterday:

Displacement: a change in position.

Question: If I travel from Halifax to Vancouver, what is my displacement?

Vancouver is 3350 km West of Toronto.

Halifax is 1260 km East of Toronto.

Answer:   

                       = 3350 km [WEST] – 1260 km [EAST]

                       = 3350 km [WEST] – 1260 km [-WEST]

                       = 3350 km [WEST] + 1260 km [WEST]

                       = 4610 km [WEST]

Notice we can rewrite EAST as negative WEST!

SPEED is the change in distance over time.

                                       

VELOCITY is the change in displacement over time.

(Velocity is a VECTOR)

                                       

Then we went out into the hallway and measured the speed of a medicine ball as it rolled down the hall.  Here's our set up:

And here are the results from the first class:

and the second class:

Here's the handout on the activity:

• Kinematics Lab 1: Rolling a Ball

Homework

• Complete the lab handout
• Complete day 0 homework from the Unit Outline: P. 13 #1-4, 6, 7

Announcement

• There will be a FORMATIVE QUIZ tomorrow!

Sept. 8 – Vectors and Displacement

I handed out textbooks today!  This means you can now start doing the homework questions that are in the Unit Outline:

• Unit Outline

Then we started Unit 1.  If you have any questions about the previous homework or any of the review material, please let me know.

Unit 1: KINEMATICS

How things move.

Where is the dancer?  What do we need to know to describe her position?

How do we describe where things are located?

Ex: Where is Vancouver?

You need to know where you are starting from, a reference point.

If we use Toronto, we can say go WEST 3350 km.

Answer: Vancouver is 3350 km WEST of Toronto.

Ex: Halifax is 1260 km EAST of Toronto.

We need to describe the distance AND the direction to get a position.

This is an example of a VECTOR.

VECTOR = a quantity with a magnitude and direction

SCALAR = a quantity with magnitude

Here are some examples of vectors and scalars:

Scalars	Vectors
Distance, d Speed, v Mass, m   Time, t Volume, V Energy, E	Displacement                Velocity                Force                Magnetic Field

We can represent vectors with arrows:

Vancouver              Toronto    Halifax

<----------------------------x------------>

magnitude is represented by the length of the arrow.

The first vector we will talk about is called displacement.

DISPLACEMENT: a change in position.

displacement  =  final position – initial position

Example: If I travel from Halifax to Vancouver, what is my displacement?

Think about how you answer this question and what you would write to show your work.

Today was a short class, so this is as far as we got.  Tomorrow we will continue!