GENERAL PHYSICS (101 PHYS)...1) Add vectors A and B graphically by drawing them together in a head to tail arrangement. 2) Draw vector A first, and then draw vector B such that its

DR. MOHAMMED MOSTAFA EMAM

INAYA MEDICAL COLLEGE (IMC)PHYS 101- LECTURE 1

GENERAL PHYSICS(101 PHYS)

LECTURES & CLASS ACTIVITIES

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DR. MOHAMMED MOSTAFA EMAM 2

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GENERAL PHYSICS

(101 PHYS)PART I

PART I

Force, Vectors and

Newton’s law of motion

Vocabularies add to notes

Force:

Push or Pull (strength or energy).


Newton’s Laws of Motion

Background

Sir Isaac Newton (1643-

1727) an English scientist

and mathematician famous

for his discovery of the law

of gravity also discovered

the three laws of motion.


• A force is simply a push or a pull.

• All forces have both size and direction.

• Mass is a measure of the amount of “stuff” contained in an object;

MASS ONLY HAS SIZE AND IT DOES NOT HAS DIRECTION. (add to notes)


Remember…

FORCE


NET FORCES

When two or more forces are combined!


Some tips:1. Forces in the same direction- add the

two forces together.

+ =

1. Forces in different directions- subtract the two and figure out which direction was the stronger of the two.

- =


Balanced vs. unbalanced forces

• Unbalanced: when the net force on an object is not zero. These produce a change in motion.

• Balanced: when the net force on an object equals zero. These do NOT produce change in motion.


Vectors

An Introduction

There are two kinds of quantities• Scalars are quantities that have magnitude only,

such as

– position

– speed

– time

– mass

• Vectors are quantities that have both magnitude and direction, such as

– displacement

– velocity

– acceleration DR. MOHAMMED MOSTAFA EMAM 14

Notating vectors

• This is how you notate a vector…

• This is how you draw a vector…

R R

Rhead

tail DR. MOHAMMED MOSTAFA EMAM 15

Direction of Vectors

• Vector direction is the direction of the arrow, given by an angle.

• This vector has an angle that is between 0o and 90o.

Ax


Vector angle ranges

x

y

Quadrant 10 < < 90o

Quadrant 290o < < 180o




Direction of Vectors

• What angle range would vector B have?

• What would be the exact angle, and how would you determine it?

B

xBetween 180o and 270o

orBetween-90o and -180o


Magnitude of Vectors

• The best way to determine the magnitude (orsize) of a vector is to measure its length.

• The length of the vector is proportional tothe magnitude (or size) of the quantity itrepresents.


Sample Problem

• If vector A represents a displacement of three miles to the north, then what does vector B represent? Vector C?

A

B

C


Equal Vectors

• Equal vectors have the same length and direction, and represent the same quantity (such as force or velocity).

• Draw several equal vectors.


Inverse Vectors

• Inverse vectors have the same length, but opposite direction.

• Draw a set of inverse vectors.

A

-A


Graphical Addition and Subtraction of Vectors

II

Graphical Addition of Vectors

1) Add vectors A and B graphically by drawing themtogether in a head to tail arrangement.

2) Draw vector A first, and then draw vector B suchthat its tail is on the head of vector A.

3) Then draw the sum, or resultant vector, by drawinga vector from the tail of A to the head of B.

4) Measure the magnitude and direction of theresultant vector.


A

B

RA + B = R

Practice Graphical Addition

R is called the resultant vector!

B


The Resultant and the Equilibrant

• The sum of two or more vectors is called theresultant vector.

• The resultant vector can replace the vectorsfrom which it is derived.

• The resultant is completely canceled out byadding it to its inverse, which is called theequilibrant.


A

B

R A + B = R

The Equilibrant Vector

The vector -R is called the equilibrant.If you add R and -R you get a null (or zero) vector.

-R


Addition of Vectors – Graphical Methods

The parallelogram method may also be used;

here again the vectors must be “tail-to-tip.”


Graphical Subtraction of Vectors

1) Subtract vectors A and B graphically byadding vector A with the inverse of vectorB (-B).

2) First draw vector A, then draw -B suchthat its tail is on the head of vector A.

3) The difference is the vector drawn fromthe tail of vector A to the head of -B.


A

B

A - B = C

Practice Graphical Subtraction

-B

C


3-2 Addition of Vectors – Graphical Methods

For vectors in one

dimension, simple

addition and subtraction

are all that is needed.

You do need to be careful

about the signs, as the

figure indicates.


http://ia300139.us.archive.org/1/items/AP_Physics_B_Lesson_02/Container.html

H.W.

A man walks at40 meters Eastand 30 meters North. Find themagnitude of resultantdisplacement and its vector angle.Use Graphical Method.


Practice Problem

• You are driving up a long inclined road. After 1.5 miles younotice that signs along the roadside indicate that your elevationhas increased by 520 feet.

a) What is the angle of the road above the horizontal?

b) How far do you have to drive to gain an additional 150 feet of elevation?


Practice Problem

• Find the x- and y-components of the following vectors

a) R = 175 meters, = 95o

b) v = 25 m/s , = -78o

c) a = 2.23 m/s2 , = 150o


Practice Problem

• Vector A points in the +x direction and has amagnitude of 75 m. Vector B has amagnitude of 30 m and has a direction of30o relative to the x axis. Vector C has amagnitude of 50 m and points in a directionof -60o relative to the x axis.

a) Find magnitude and direction of A + B

b) Find magnitude and direction of A + B + C

c) Find magnitude and direction of A – B.


Component Addition of Vectors

1) Resolve each vector into its x- and y-components.

Ax = Acos Ay = Asin

Bx = Bcos By = Bsin

Cx = Ccos Cy = Csin etc.

2) Add the x-components (Ax, Bx, etc.) together to get Rx and the y-components (Ay, By, etc.) to get Ry.


Component Addition of Vectors

3) Calculate the magnitude of the resultant

with the Pythagorean Theorem (R = Rx2

+ Ry2).

4) Determine the angle with the equation = tan-1 Ry/Rx.


Practice Problems• In a daily prowl through the neighborhood, a cat makes a

displacement of 120 m due north, followed by a displacement of 72 mdue west. Find the magnitude and displacement required if the cat isto return home.

• If the cat in the previous problem takes 45 minutes to complete thefirst displacement and 17 minutes to complete the seconddisplacement, what is the magnitude and direction of its averagevelocity during this 62-minute period of time?


Sample problems

• A surveyor stands on a riverbank directly across the river from a tree onthe opposite bank. She then walks 100 m downstream, and determinesthat the angle from her new position to the tree on the opposite bank is50o. How wide is the river, and how far is she from the tree in her newlocation?

• You are standing at the very top of a tower and notice that in order tosee a manhole cover on the ground 50 meters from the base of thetower, you must look down at an angle 75o below the horizontal. If youare 1.80 m tall, how high is the tower?


WRITE DOWN THESE STATMENTS

• A quantity with magnitude and direction is a

vector.

• A quantity with magnitude but no direction is

a scalar.

• Vector addition can be done either graphically

or using components.

• The sum is called the resultant vector.

• Projectile motion is the motion of an object

near the Earth’s surface under the influence of

gravity.


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GENERAL PHYSICS (101 PHYS)...1) Add vectors A and B graphically by drawing them together in a head to tail arrangement. 2) Draw vector A first, and then draw vector B such that its