Lecture 3 Physics 107

8/18/2019 Lecture 3 Physics 107

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Lecture 3 PHY 107)

SPRING 2016

INSTRUCTOR : SUBIR GHOSH, PHD

http://www.northsouth.edu/index.html


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Vectors

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A scalar quantity is specified by a single value with an appropriate unit and has no directiontemperature, mass, energy etc. )

A vector quantity has both magnitude and direction. (example displacement, velocity)


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Properties of Vectors

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1. Equality of Vectors:

Two vectors are equal if they have the same magnitude and point in the same

direction.

2. Adding Vectors:

The resultant vector is the vector that connects from the tail of a vector to the tip of another


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Vector Addition

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1. Commutative Law of Addition:

A+B = B+A

2. Associative Law of Addit

A+(B+C) = (A+B) +C


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Negative of a Vector

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The negative of a vector A is defined as the vector that when added to A gives zero for the v

A + (-A) = 0

The vectors A and –A have the same magnitude but point in opposite directions.

Subtracting Vectors:

A – B = A + (-B)


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Sample Problem

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A car travels 20.0km due north and then 35.0 km due west. Find the magnitude and directiresultant displacement.


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Components of a Vector

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•A component of a vector is the projection of the vector on an axis.

• The projection of a vector on x-axis is its x component and the projection

on y-axis is its y component.

• The process of finding the components of a vector is called resolving a

vector.

• Once a vector has been resolved into its components along a set of axes,the components themselves can be used in place of vector.


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Sample Problem

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A small airplane leaves an airport on an overcast day and is later sighted 215km away in a di

making an angle of 22 degree east of north. How far east and north is the airplane from the

sighted?


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Unit Vector

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• A unit vector is a vector that has a magnitude of exactly one and points in a particular dir

• It lacks both dimension and unit.

• A unit vector is denoted by a lower case letter with a hat.

• Its sole purpose is to point or specify a direction.

= +

= +

Vector Compon

ax, ay are scalar components.


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Adding Vectors by Components

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= + The vector is the same as the v

Each component of must be the same of the corresponding components of ( + ):

= +

= +

= +

Two vectors must be equal if their corresponding components are equal.


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Sample Problem

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Find the vector sum of the following three vectors:


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Sample Problem

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Two vectors must be equal if their corresponding components are equal.

Find the sum of two vectors A and B lying in the xy plane and given by

= 2.0 + 2.0 and B= 2.0 − 4.0


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Multiplying Vectors

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Multiplying a vector by a scalar:

If we multiply a vector by a scalar s, we get a new vector. Its magnitude is the product of m and the absolute value of s. Its direction is the direction of if s is positive but the opposs in negative.

Multiplying a vector by a vector:

(a) Scalar Product ( produces a scalar quantity)

(b) Vector Product (produces a vector quantity)


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Multiplying Vectors

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Scalar Product

. = ∅#1

#2

a is the magnitude of vector and b is the magnitude of vector ;∅ is the angle between the vectors

. = + +

. = ( + + ) ∙( + + )

. = .


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Sample Problem page 49)

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What is the angle φ between = 3.0 − 4.0 and = −2.0 +3 .0?


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Multiplying Vectors

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Vector Product (Also known as cross product)

The vector product of and , written as × , produces a third vector who

=

Where is the smaller of the two angles between of and .

×=−(×)

#1

#2 × = ( + + )×( + + )

× = − + − + ( −


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Multiplying Vectors

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If = 3.0 − 4.0 and = −2.0 +3 .0

, what is = × ?

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Lecture 3 Physics 107