Chapter 1:

Physical Quantities and Vectors

Chapter 2:

Linear Motion

Chapter 3:Curvilinear

Motion

Physics – the science that deals with matter, energy, motion and force.

Branches of Physics

(1) Thermodynamics (5) Quantum Physics

(2) Optics (6) Nuclear Physics

(3) Mechanics (7) Magnetism

(4) Acoustics (8) Electricity

Physical Quantities

Scalar Quantity – quantities specified by magnitude only

Ex. Time, Mass, Speed, Distance, Temperature, Volume, Area, Work, Energy.

Vector Quantity – quantities specified by both magnitude and directions.

Ex. Velocity, Displacement, Acceleration, Force, Weight, Momentum, Impulse.

Forces are analyzed in a number of ways; it is commonapproach to establish a coordinate system to quantifythe forces and their effects in a system or body. Since itis customary to assign the axes, the analysis may becoplanar (two-dimensional) or non-coplanar(three-dimensional).

A system of forces may be represented by aresultant force which has the same effect as thesystem.

The resultant force, much like any other force,has magnitude and direction. The geometric sumof the forces will yield the resultant.

Forces on an object

Equivalent Resultant Force

2N

1N

3N

2N4N

6N

Resultant =0

3N

6N

3N

Coplanar Force Systems analyze forces acting on abody by taking their components along twodesignated axes.

A force system can be identified into two main types:

concurrent

non-concurrent.

The resultant of concurrent forces must be definedby magnitude and direction. Magnitude representsthe length of the vector while the direction is referredfrom the defined axis.

Resultant Force

The equilibrant of the forces is a single vector that canbalance two or more vectors

- it is equal in magnitude as the resultant

- opposite the direction of the resultant

- acting along the same line of action as the resultantResultant Force

Equilibrant

Solutions to Vectors Problems:

(1) Graphical Method (with the aid of ruler andprotractor)

(a) Parallelogram

(b) Triangle Method (Tip-to-Tail Method)

(c) Polygon Method

(2) Analytical/Mathematical Method

(a) Use of Pythagorean Theorem

(b) Use of Sine/Cosine Law

(c) Component Method

Example 1: Given:

A = 150 lbs, 60ᵒ N of E

B = 200 lbs, 20ᵒ S of E

Find the resultant and its direction using

graphical and analytical method.

Example 2: Given:

A = 100 lbs, NE

B = 150 lbs, 30ᵒ N of W

C = 200 lbs, Due South

Find the resultant and its direction using

graphical and analytical method.

Example 3: In the final game of last year’s regular season,

south was playing New Greer Academy for the

Conference Championship. In the last play of the

game, star quarterback Avery took a snap from

scrimmage and scooted backwards (northwards)

8.0 yards. He then ran sideways (westward out of

the pocket for 12.0 yard before finally throwing a

34.0 yard pass directly downfield (southward) to

Kendall for the game-winning touchdown.

Determine the magnitude and direction of the ball’s

displacement.

Example 4: Four forces act concurrently at a point. Force

A has a magnitude of 70 lb and is directed 30ᵒ N

of E; force B has a magnitude of 60 lb and is

directed westward; force C has a magnitude of

50 lb and is directed southward; and force D has

a magnitude of 40 lb and is directed 20ᵒ E of S.

(a) What is the x-component and y-component

of the resultant of the four forces?

(b) What are the magnitude and direction of a

fifth force will produce equilibrium at the point?

Example 5: A group of physics students, after three days

of hiking, are 30 km north of their starting

position. On the first day they hiked 20 km east.

On the second day they hiked 30 km in a

direction 53ᵒ north of west. Using the component

method:

(a) Find the x-component and y-component of

their displacement vector on the third day.

(b) Find the magnitude and direction of their

displacement vector on the third day.

Example 6: A man walks one morning from his house to a store

that is 5000 m N40oE from his house. He startedcovering 1200 m NE; then goes 1000 m 10 o S of E;then saw a friend who is 800 m 30o E of N from wherehe is. Determine:

(a) How far and in what direction was his friend fromhis house?

(b) If he continued with his journey, how far and in whatdirection was his displacement from where his friendwas to finally get to the store?

(c) From the store, he first went to another friend’shouse before going back home. This friend’s house is950 m N50oW form the store. How far and in whatdirection from his house is his second friend’s house?

(Solve graphically or analytically)

Example 7: The force vector A has a magnitude of 20 lb and

points 25ᵒ east of north. The force vector B has a

magnitude of 35 lb and points 24ᵒ north of west.

The force vector C has a magnitude of 10 lb and

points south. Assuming that the force vectors are

coplanar and concurrent:

(a) Find the magnitude and direction of A+B + C.

(b) Find the magnitude and direction of 3A–2B–C.

(c) Find the magnitude and direction of 2A–B+3C.

Example 8: A boy scout continues walking 10 m SW from a

campsite, then 15 m 40oS of W, then saw a baby ape

9m S from where he is, and walks toward it. Use

graphical or analytical method to answer the following

questions, but use only one method to answer both.

(a) How far and in what direction was the baby ape

from the campsite?

(b) He then left the ape started to walk away from it to

a tree for some rest. When he reached the tree, his

position is now 20m S 30o E from the campsite.

Determine the magnitude and the direction of the last

displacement covered to get to the tree.

Example 9: X, Y, and Z are coplanar, concurrent forces.

If X = 150 lb, 35ᵒ W of S; Y = 220 lb, 21.5ᵒ N of W;

and X + Y + Z = 200lb, W:

(a) What is the magnitude and direction of Z?

(b) What is the magnitude of –X – 2Y + Z?

(c) What is the direction of –X – 2Y + Z?