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Newton 3 & Vectors. Action/Reaction. When you lean against a wall, you exert a force on the wall. The wall simultaneously exerts an equal and opposite force on you. . You Can OnlyTouch as Hard as You Are Touched. He can hit the massive bag with considerable force.

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Action reaction l.jpg
Action/Reaction

  • When you lean against a wall, you exert a force on the wall.

  • The wall simultaneously exerts an equal and opposite force on you.


You can onlytouch as hard as you are touched l.jpg
You Can OnlyTouch as Hard as You Are Touched

  • He can hit the massive bag with considerable force.

  • But with the same punch he can exert only a tiny force on the tissue paper in midair.


Newton s cradle l.jpg
Newton’s Cradle

  • The impact forces between the blue and yellow balls move the yellow ball and stop the blue ball.


Naming action reaction l.jpg
Naming Action & Reaction

  • When action is “A exerts force on B,”

  • Reaction is then simply “B exerts force on A.”


Vectors l.jpg
Vectors

  • A Vector has 2 aspects

    • Magnitude (r)

      (size)

    • Direction

      (sign or angle) (q)

  • Vectors can be represented by arrows

    • Length represents the magnitude

    • The angle represents the direction



Vector quantities l.jpg
Vector Quantities

How far in what direction?

  • Displacement

  • Velocity

  • Acceleration

  • Force

  • Momentum

  • (3 m, N) or (3 m, 90o)

How fast in what direction?


Vector addition finding the resultant l.jpg
Vector Addition Finding the Resultant

Head to Tail Method

Resultant

Equivalent Methods

Resultant

Parallelogram Method


A simple right angle example l.jpg
A Simple Right Angle Example

Your teacher walks 3 squares south and then 3 squares west. What is her displacement from her original position?

This asks a compound question: how far has she walked AND in what direction has she walked?

N

Problem can be solved using the Pythagorean theorem and some knowledge of right triangles.

3 squares

W

E

3 squares

Resultant

S

4.2 squares, 225o


Getting the answer l.jpg
Getting the Answer

  • Measure the length of the resultant (the diagonal). (6.4 cm)

  • Convert the length using the scale. (128 m)

  • Measure the direction counter-clockwise from the x-axis. (28o)

Resultant




Rope tensions l.jpg
Rope Tensions

  • Nellie Newton hangs motionless by one hand from a clothesline. If the line is on the verge of breaking, which side is most likely to break?


Where is tension greater l.jpg
Where is Tension Greater?

  • (a) Nellie is in equilibrium – weight is balanced by vector sum of tensions

  • (b) Dashed vector is vector sum of two tensions

  • (c) Tension is greater in the right rope, the one most likely to break



Resolving into components l.jpg
Resolving into Components

  • A vector can be broken up into 2 perpendicular vectors called components.

  • Often these are in the x and y direction.


Components diagram 1 l.jpg

N

W

E

S

Components Diagram 1

A = (50 m/s,60o)

Resolve A into x and y components.

Let 1 cm = 10 m/s

1. Draw the coordinate system.

2. Select a scale.

3. Draw the vector to scale.

5 cm

60o


Components diagram 2 l.jpg

N

W

E

S

Components Diagram 2

A = (50 m/s, 60o) Resolve A into x and y components.

  • 4. Complete the rectangle

    • Draw a line from the head of the vector perpendicular to the x-axis.

    • Draw a line from the head of the vector perpendicular to the y-axis.

Let 1 cm = 10 m/s

Ay = 43 m/s

Ax = 25 m/s

5. Draw the components along the axes.

6. Measure components and apply scale.


Vector components22 l.jpg
Vector Components

Vertical Component

Ay= A sin 

Horizontal Component

Ax= A cos 



X y to r l.jpg

(x,y) to (R,)

  • Sketch the x and y components in the proper direction emanating from the origin of the coordinate system.

  • Use the Pythagorean theorem to compute the magnitude.

  • Use the absolute values of the components to compute angle  -- the acute angle the resultant makes with the x-axis

  • Calculate  based on the quadrant


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