Download Stacey Carpenter

PPT
Vectors
Developer Notes
 Is time a vector quantity?
 Adding relative velocities of two different objects is different than finding the net velocity of
one object. This is confusing to me in the reading.
 More diagrams in the student reading would be nice
 There’s a lot of references to velocity but velocity hasn’t been covered yet according to the
new scope & sequence
Version
05
Date
2003/12/09
Who
dk
06
2003/06/22
sc
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Revisions
Added revision table and re-formatted
deleted definition of Newton, it's in the friction activity
deleted Newton from concepts introduced (in friction
activity)
Added “forces on backpack” example in tchrs section
Added note about how diagrams are helpful in student
reading
Some rephrasing
Added answers to exercises
Added general definitions of velocity and acceleration
in parentheses and a not that we’ll learn more later on
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Goals
 Students should understand that vectors have a magnitude and a direction.
 Students should know that vectors are represented by arrows, where the size indicates the
magnitude, and the point indicates the direction.
 Students should be able to sum vectors which are in a line.
 Students should understand that vectors can be at angles to each other.
 Students should understand that velocity, acceleration, and force are vector quantities, and
that speed, distance, and time are not.
Concepts & Skills Introduced
Area
physics
physics
physics
Concept
a vector quantity has a magnitude and a direction
examples of vector quantities include velocity, acceleration, force, and momentum
Introduces speed and velocity
Time Required
Warm-up Question
If you had to explain to someone which direction an object was going and how fast it was going,
but you couldn’t use words (written or spoken) how would you do it?
Presentation
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The point of the warm-up is to get the students to see the utility of an arrow to represent a vector
quantity.
From the friction activity, students should understand that friction is a force that resists motion.
They should also know that force causes motion. How do we represent force? With arrows.
Force is a vector quantity, both the magnitude and direction of a force are important. There is no
exploratory activity here other than class discussion. It’s hard to experiment on an idea. Lead a
discussion on how to show forces, which should lead to arrows and their size. Show the students
some examples on the board.
An example of why direction matters:
Two cars are driving on the road. One is going 30 mph, the other is going 31 mph. How fast is
one going relative to the other when they hit? The answer is 61 mph, 1 mph, or never, if they are
traveling along the same line, or anything in between, depending on their angle to each other.
Here’s another example. Revisit the friction lab. Pull on a backpack so that it does not move.
Ask about the forces involved and have the students try to draw a diagram of the situation. The
pulling force is equal in magnitude but opposite in direction of the static friction force. The
forces cancel each other out. There is no net (overall) force on the backpack.
Fpull
Ffriction
What about when the backpack starts to move? The pulling force is a little bit bigger than the
sliding friction force. Draw the vector diagram for this situation.
Vectors:
velocity (how fast and in what direction), acceleration, force, momentum
NOT vectors: speed (how fast), distance, time
Assessment
Writing Prompts
1.
Relevance
Summary
Answers to Exercises
1. Diagram should be similar to the example in the reading.
2. The push vector should be larger than the friction vector.
3. The resultant velocity of the canoe is 0 kph. It is not moving. The velocity vectors should
be equal in size and opposite in direction.
4. The sum of the forces in 5 N to the east. The car will move east.
5. 180 kph north
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6.
Challenge/ extension
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Background
Problem
Materials
Procedure
Summary
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Reading
Occasionally we’ve used arrows to indicate the force of something, and we’ve used bigger
arrows to indicate more force. Scientists and engineers often use arrows when they’re trying to
explain or describe something. What does the arrow show? It shows direction. And it can show
how much - the longer the arrow, the greater the quantity. Something that has direction and
magnitude (size, quantity) is called a vector quantity. It can be represented by an arrow.
Drawing diagrams can be very helpful for understanding certain situations in physics. We can
use arrows in our diagrams to represent the size and direction of specific vector quantities.
Examples of vectors are:
 velocity (how fast and in what direction)– Speed is just how fast, but velocity includes
direction. Imagine you’re riding in a car at 30 miles an hour, and another car is going 31
mph, and they run into you. It makes a huge difference which direction they’re going! They
could hit you at 61 mph from in front or 1 mph from behind (or anything in between from
another direction). If they're in front of you, you'll never hit.
 acceleration (a change in velocity)– Are you accelerating forward (speeding up), backward
(slowing down), or sideways (turning)?
 force –If you’re trying to push a car out of the sand, it makes a difference how hard you push,
and whether you’re pushing on the front or rear of the car.
(Keep in mind that we will learn more about the concepts of velocity, acceleration, and force
later on)!
Examples of NON-vectors are:
 distance, time, speed
Vectors can be added together to get a resultant (sum) vector. For example, if two people push in
the same direction on a stalled car, their force vectors add up to a bigger force. But if one is
pushing from the front and the other is pushing just as hard from the rear, they both are applying
a force, but the two add up to zero and the car won’t move. It’s the same for an object sitting on
the floor: gravity is pulling it down, but the floor is pushing it up. You can only add the same
type of vectors, like force and force. You cannot add a velocity vector to a force vector.
Vectors are usually drawn with the tail on the object. They should be labeled with what they
represent (velocity, acceleration, or force) and with their quantity, although for discussion (not
calculation), larger arrows can represent larger quantities.
Here is a picture of the forces on a box sitting
on the floor. Note that the force of gravity is the
same size, but in the opposite direction, as the
force up from the floor, so they add up to zero.
They cancel each other out. There is no net
(overall) force on the box.
Ffloor
Fgravity
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Here’s a picture of a box being pulled,
but without the box moving. Note that
the force of the pull and the force of
friction add up to zero, so the box
doesn’t move.
Ffloor
Fpull
In the diagram, if Fpull was 15 N and
Ffriction was 10 N, then the net force
sideways would be Fpull – Ffriction, or 15
N – 10 N = 5 N to the left, and the box
would accelerate to the left.
Ffriction
Fgravity
Vectors don't always have to be in a line. Consider a boat crossing a river. One vector is the
velocity of the boat across the river. Another is the
vboat 4 kph
velocity of the river. Added together, they result in the
boat’s actual velocity. Vectors are added by drawing a
parallelogram and drawing the resultant from tail to head.
vriver 3 kph
For example, if the boat is going 4 kph across the river,
vtotal 5 kph
and the river is flowing at 3 kph, the vector sum is 5 kph
(Pythagorean theorem).
Exercises
1. Draw a diagram showing someone trying to push a box along the floor. However, the box is
too heavy, so it won’t move. Draw the vectors for the forces on the box, including gravity,
the floor, the push, and friction.
2. Now draw a diagram of someone pushing on a box as the box starts to move (accelerate).
Draw the vectors for the forces on the box, including gravity, the floor, the push, and friction.
3. If Leahi is paddling her canoe at a velocity of 3 kph straight south, and the current is flowing
at a velocity of 3 kph straight north, what is the resultant velocity of the canoe? Will it move?
Draw a picture of the canoe and the velocity vectors.
4. Vern's car ran out of gas. He wants to push it to a gas station, so he gets behind it and pushes
west with 100 N of force. Cal shows up and decides to help, pushing with 105 N of force.
They’re lacking in communication skills, however, and Cal pushes east. What is the sum of
forces on the car? Will the car move? Draw a diagram of the car and the forces on it.
5. If an airplane has a velocity of 200 kph straight north, but the wind is blowing straight south
at 20 kph, what is the airplane’s resultant velocity?
6. Morris is walking along with a helium balloon on a string. He's walking north at 3 kph, and
there is a wind blowing from the northeast (45) at 10 kph. Draw a diagram of Morris and the
balloon showing the wind vector from Morris' walking, the wind vector from the northeast,
and the resultant vector.
Challenge/ extension
Vocabulary
Vector – something that has both direction and magnitude, like velocity, acceleration, and force.
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