Vectors and 2-D motion

Sept 29, 2009

Today’s Plan:

Hand-back and go over testVector Lecture – let the fun begin…Vector activityVector labHomework: Read Section 3.1-3.3; worksheet; lab

Vectors – Let the fun begin…

Scalar Quantities

Something that is completely described by size.

Mass - 5 kg bag of peanutsTime - 3 day trip to Disneyland

Scalar quantities

Simple addition and subtraction…

Vector Quantities

Requires magnitude and direction. Velocity of rocket

Adding vectors…

Must consider direction and sizeExample: VelocityFlying into a headwind…

Example: Force

Gravity pulls downFriction the other way

Hmm…

What if the vectors are not in the same direction or directly opposite?

Adding vectors…the “resultant”

1. Decide on a scale. Draw the vectors “to scale”

1 inch = 5 Newtons

2. Move 1 ray so that they sit head to tail.

3. Draw from the tail to the tip to enclose triangle This is the “resultant”

4. Measure diagonal using scale and determine direction.

Note – when moving ray, you must construct the line parallel.

More than 2 vectors?

If you are adding more than 2 vectorsPut all the vectors head to tail and measure the resultant.

Vectors – Simple Math

Take a trip north 2 miles, east 3 miles, south 4 miles, west 1 mile. What does it look like? What is the magnitude? What is the direction?

Abandon Ship!

The Polar Star is in the ice…The ice pack is moving at 3 miles per hour to the south.You are breaking through the ice to the east at 4 miles per hourWhat is your direction and speed?

You try it…the worksheet…

What if we have the resultant and want to find the vectors that make the resultant?

Use the process of “resolution” to determine the vertical and horizontal components.

One to think about…

An airplane makes a straight back-and-forth round trip, always at the same airspeed between 2 cities.If it runs into a steady tail wind going and the same head wind returning…WILL IT TAKE MORE TIME, LESS TIME, OR THE SAME TIME…as with no wind.

Back to the lab…

The vector of the day is force!You will measure the force and note its direction 4 different forces

Add them graphically

2 Dimensional Motion

Day 2 – more vectors!Oct 1

Vectors require

Magnitude and direction.The direction they are pointing

and the lengthare very important!!!!

To find the resultant

1. Decide on a scale.

1 inch = 5 Newtons

2. Move 1 ray so that they sit

head to tail.

3. Draw tip to tail diagonal to enclose triangle (called resultant).

4. Measure diagonal using scale and determine direction.

Note – when moving ray, you must have same angle… or construct a line parallel.

If you are dealing with more than 2 vectors, just put the vectors head to tail and measure the resultant.

Some Vector Tricks…A 45 degree triangle (right isosceles) will always have the hypotenuse or resultant equal to:

(length of side X square root 2)

5 N

5 N

7.1 N

For the record:Square root of 2 is 1.4

Some vector tricks…With a right triangle you can use the Pythagorean theorem to check your answer. c2 = a2 + b2

c = hypotenuse, a and b = sides.

7 N

3 N

Conceptual Question:

If B is added to A to get C When would the magnitude of C equal

the magnitude of A + the magnitude of B?

Conceptual Questions:

A student is adding 2 vectors with magnitudes of 55 and 25. Which of the following is a possible answer?• 85• 55• 20

Why?

Objects in equilibrium

Hanging and not moving…The forces are balanced Net force = zero

Two scales?

Hang same object from two scalesWhat would each scale read?

Forces in balance

We pull “up” the same amount…The amount we pull sideways on one rope cancels out the other sideways…

Components of weight:

W = weight factor (This is the hypotenuse!)X = vector affecting speedY = vector pressing against surface

Flat slope – 0 degrees

5 Newtons

Slope of 30 degrees

5 Newtons

Slope of 70 degrees

5 Newtons

An example…

Find the velocity of a helicopter flying at an angle 45 degrees to the ground, if it covers 100 km/hr over the ground?How fast is it climbing?

Lab 2

More experience with graphing vectors

October 3 - Projectiles

More than just vomit

My Mom’s good friend Vector…

Anybody see him? Football game? Dance? Running? Leaf blowing?

Today’s Plan:

Homework reviewProjectiles Notes Projectile Lab!Homework assignment

Velocity of a projectile…

Vertical and horizontal parts…They act independently!

Vertical Components

Affected by gravityDecrease by 10 m/s per secondNotice vector length.

Horizontal Component

Remains the same…Notice vector length!

Which one hits first?

One dropped or…One thrown horizontally?

A plane drops a package while flying over Lake Oswego…What will be the path of the package? Where will the package be with respect to the plane?

You tell me…

Bad design…

Truck mounted cannon shoots straight up…What is going to happen to the cannon ball?

Worksheet…

Take a look at what happens Second by second

x = velocityx x time

y = ½ at2 = ½ (-10m/s2)t2

y = -5 t2

True story…

Bentley the dog chases a stick off of the second story of the cabin… The wall is 4 meters high. The dog lands 2.5 meters away from

the wall.

How fast was the dog running?

Lab!

Horizontal launchesTwo different heights Calculate time to hit ground

t = √y/5 Measure distance traveled

Projectiles Day 2

October 7

Today’s Lab

After you collect data for a 20, 30 and 40 degrees… Make a prediction Get my initials before you

proceed.

And for today’s show…

Review HW and LabProjectiles with initial velocity Up and out

Lab – More Projectiles

Next time – reviewNext, next time – test!

Feeding monkeys in the tree Banana cannon

One monkey – Fred Likes to play games

What should the zookeeper do?

The Zookeeper

The zero gravity solution!

The fast gun…

Does speed matter?

So if there is some “up” velocity?

Imaging a cannon firing at an angle… In the direction of the initial velocity… Without gravity!

Now add gravity… d = ½ gt2

Projectile Motion!

The cannon ball drops from the line you initially aimed… By d = ½ gt2

Firing the cannon at 37 degrees?

Let’s look at something fired at 33 m/s At 37 degrees above horizontal

How fast is it going in the “x” direction? And the y direction?

We’ll determine by graphing it… TO SCALE!!!

Then calculate…

VelocitySecond by second vx ? vy ?

PositionSecond by second x ? y ?

Your turn!

Finish the other side of the worksheet I gave you Monday!

What about wind resistance?

What do you think happens when we consider air resistance?

Homework…

On back of sheet…Fill in the times as follows: I) 1.42 s II) 1.80 s III) 0.80 s