Chapter 5Forces in Equilibrium

VectorsQuantity with both strength (magnitude)

And direction.

Examples: Force

Acceleration

Velocity

Momentum...

Non-vectorsThese are called “scalars”

Temperature

Pressure

Mass

Energy

Power

Writing VectorsA force pushing 2 N left and 5 N up would be written: <-2, 5>

A force pushing 7 N right and 3 N down would be <7, -3>

Write these vectors in numbers:

8 right and 2 up

4 right and 6 down

7 right

9 up

Drawing vectorsA = <-3, 1>

B = <1, 5>

C = <2, -2>

D = <1, 0>

E = <0, -3>

F = <-2, 4>

Adding VectorsTo add vectors, find both sets of components

Add the x-components

That’s the x-component of the sum

Add the y-components

That’s the y-component of the sum

The vector you get is called the “resultant”.

Adding vectorsA = <-3, 1> B = <1, 5>C = <2, -2> D = <1, 0>E = <0, -3> F = <-2, 4>

A + B =

C + D =

E + F =

A + C + E =

B + D + F =

Vector InteractivesGet a computer and go to the class website on the Physics tab.

Click on the Vectors and Projectiles link.

Play with Name That Vector and Vector Guessing Game.

Finding Magnitude and DirectionThe “magnitude” of the vector is the length, representing the strength of the force or the speed of the velocity, etc.

The direction is the angle it points.

If you have components, the “magnitude” of the vector is the hypotenuse c if the components are a and b from the Pythagorean Theorem.

The direction comes from the trigonometric Tangent function.

Examples.If A = <-3, 4>

|A| = √(32 + 42) = 5

tan( ) = 4/3

= tan-1(4/3) = 53.1 degrees

Direction can be written “north of west”

Or it could be 36.9 degrees west of north.3

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Examples.If A = <10, -3>

|A| = √(102 + 32) = 5

tan( ) = 3/10

= tan-1(3/10) = 16.7 degrees

Direction can be written “south of east”

Or it could be 73.3 degrees east of south.

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Vector Addition ActivityUse the Vector Addition interactive to do the assignment to turn in.