Vectors and 2-D motion Sept 29, 2009

Today’s Plan: Hand-back and go over test Vector Lecture – let the fun begin… Vector activity Vector lab Homework: Read Section ; worksheet; lab

Vectors – Let the fun begin…

Scalar Quantities Something that is completely described by size. Mass - 5 kg bag of peanuts Time - 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 size Example: Velocity Flying into a headwind…

Example: Force Gravity pulls down Friction 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 vectors Put 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 hour What 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 length are 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 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. c 2 = a 2 + b 2 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? Why?

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

Two scales? Hang same object from two scales What 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 speed Y = 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 review Projectiles Notes Projectile Lab! Homework assignment

Velocity of a projectile… Vertical and horizontal parts… They act independently!

Vertical Components Affected by gravity Decrease by 10 m/s per second Notice 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 = velocity x x time y = ½ at 2 = ½ (-10m/s 2 )t 2 y = -5 t 2

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 launches Two 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 Lab Projectiles with initial velocity Up and out Lab – More Projectiles Next time – review Next, 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 gt 2

Projectile Motion! The cannon ball drops from the line you initially aimed… By d = ½ gt 2

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… Velocity Second by second v x ? v y ? Position Second 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