PHYSICS: Mechanical Equilibrium

“Victor” was my nerd name…

Now my name is…

“VECTOR!”

Let’s review…

PH-YSICS PH-LASHBACKR

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PH-YSICS PH-LASHBACK

SCALAR QUANTITYA scalar quantity is something that does not require a direction. It is a quantity that only has magnitude.

Examples of scalar quantities include:

Distance… Speed… Time… Mass… Volume… Density…

Scalar quantities can be added, subtracted, multiplied, and divided like normal numbers.

PH-YSICS PH-LASHBACK

VECTOR QUANTITYA vector quantity is something that does require a direction. It is a quantity that has both magnitude and direction.

Examples of vector quantities include:

Displacement… Velocity… Acceleration… Force…

Vector quantities cannot necessarily be combined together as easily as scalar quantities.

Combining Vectors

It’s now time for…the

“WELL…DUH” statement of the day.

“Vectors are used to illustrate vector quantities.”

?

??

???

DUH…

Combining VectorsVectors are handy for illustrating the

motion of an object.A vector is an arrow that represents two

things:

1) DIRECTION OF MOTION2) MAGNITUDE OF THE VECTOR

The arrow points in the direction of the motion, and the relative length of the arrow gives an indication

of the size of the quantity.

Combining VectorsEXAMPLE #1: Bob drives his car 5 miles east and then drives 12 miles west. What is Bob’s displacement?

+5

-12

0

-7 or 7 miles W

Resultant

East (+)

Combining Vectors

PHYSICS According to

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Vectors are not always that easy…

Anyway…in most cases, you cannot

just add or subtract!

This is where basic trig ideas come into play.

…kind of like being Mr. Dillon’s kid…it can be

pretty rough…

Combining VectorsEXAMPLE #2: Bob drives his car 5 miles north and then drives 12 miles west. What is Bob’s displacement?

+5

-12

013 miles, 67° W of N

Resultant

North/East (+)

QUESTIONS AND ANSWERS WITH EINSTEIN

Q: What are the parts of a vector called?

A: The COMPONENTS are the pieces that are combined together

to get the resultant.

A: The RESULTANT is the final vector that illustrates the motion

of the object.

QUESTIONS AND ANSWERS WITH EINSTEIN

Q: What are the ways that we work with vectors?

A: One situation is when you know the components and you

are trying to figure the resultant.

A: The other situation is when you know the resultant and you

break it into the components.

Rules for Combining VectorsThere are two rules that can be used for

combining vectors together…

RULE #1 – PARALLELOGRAM RULEPut the “tails” of the vectors together and draw the rest of the

parallelogram. The resultant is the diagonal of the parallelogram.

This rule works good when you have two vectors to work with. It also works

well when the vectors that are

acting at the same time.

Rules for Combining VectorsThere are two rules that can be used for

combining vectors together…

RULE #2 – HEAD TO TAIL RULELine the vectors up head to tail. The resultant vector is a vector

arrow that connects the starting point and the ending point.

This rule works good when you have two or more vectors to work with. It also works well when the

vectors that are acting at different

times.

Combining VectorsEXAMPLE #3: A plane flies 100 kph east while a tail wind pushes at 25 kph north. What is the resultant velocity of the plane?

+25

+1000

103.1 kph, 14° N of E

Resultant

North/East (+)

+25

PHYSICS IS

PHUN!