vectors notes & exercise

Physics Grade X:Chapter 2: Vectors

Notes & Exercise

By: Devilim, SMA IBC

(credit to Serway, Physics 6th ed)

pretest

• What is a vector?

• Give three examples of quantities that are vectors.

• What is a scalar?

• Give three examples of quantities that are scalars.

Vector vs Scalar

What is the difference?

> Jessica walks 5 meter

> Jessica walks 5 meter to east

Scalar magnitude + unit

Vector magnitude + unit + direction

Symbol of Vector

• How to write & draw vector?

• How to write magnitude of vector?

• How about negative of vector?

COMPONENTS OF VECTOR

• Just like Cartesian Coordinate (x and y)

Addition of Vectors

• METHOD : GRAPHING

– PARALLELOGRAM

– POLYGON

• METHOD : ANALYTICAL

Find the resultant of vectors

• A vector

– magnitude of vector?

QuizDraw the vector in Cartesian.

1. �⃗ = 2�� + 3��

2. � = 3�� − 2��

3. �⃗ = −2�� − 4��

4. � = −2�� − 3��

5. � = −�� + 3��

6. �⃗ = 2�� − ��

7. �⃗ = 4�� + 5��

8. � = 2�� − 2��

Find the components of vector

Vector A has magnitude of 2 meter and direction of 30o from +x direction

What is the components of vector A?

Use trigonometry: sine, cosine, tangent

Find x and y component of the vector

1. �⃗ = 4�, 210�

2. � = 6�, 240�

3. �⃗ = 8�, 300�

4. � = 10�, 330�

5. � = 6�, 120�

6. �⃗ = 2�, 315�

7. �⃗ = 4�, 135�

8. � = 20�, 270�

Find the magnitude and direction of the vector

1. �⃗ = 2 3�� − 2��

2. � = 3�� − 3��

3. �⃗ = −2�� − 2 3��

4. � = − 2�� − 2��

5. � = − 3�� + ��

6. �⃗ = 5 3�� − 5��

7. �⃗ = 4�� − 4��

8. � = 10�� − 10 3��

By drawing, find the magnitude and direction of:

1. �⃗ + �

2. �⃗ -�

�� + �

Try several combinations of addition or subtraction using the vectors above. Try it out yourself.

More about addition of vectors using analytical method

Consider the following vectors:

�⃗ = 2 2�, 225�

� = 3�� − 2��

Find the resultant of : �⃗ + �

APPLICATIONS OF VECTORS

• Find resultant of velocities

• Find force needed to hang a picture (tension)

• Velocity and direction of a boat when it needs to cross river a Ferry in Kapuas River

• Shooting aim for the target

• Parasailing or glider

• Playing angry birds

EXERCISE:

1. You go for a walk and take 20 steps in the north direction (90°).

a) Draw the vector represented your steps.

b) Next, you turn left and walk 10 steps to the west. Add the two vectors. How far from where you started did you end up?

2. You are going for a drive, but a detour takes you out of the way of your destination. You drive north for 10 miles, turn right and drive east for 5 miles, turn to the north and drive for 3 miles, drive west for 10 miles, and arrive at your destination.

a) How far from where you started did you end up?

b) If you wanted to travel directly to your destination without following the streets (“as the crow flies”), what angle would you take? What direction would a compass read?

3. You are flying a hang glider at 14 mph in the northeast direction (45°). The wind is blowing at 4 mph from due north.

a) What is your airspeed?

b) What angle (direction) are you flying?

c) The wind increases to 14 mph from the north. Now what is your airspeed and what direction are you flying? If your destination is to the northeast, how would you change your speed or direction so you might make it there?

In Figure P3.66 a spider is resting after starting to spin its web. The mass of spider is 0.20 newton down. The spider is supported by different tension forces in the two strands above it, so that the resultant vector force on the spider is zero. The two strands are perpendicular to each other, so we have chosen the x and y directions to be along them. The tension Tx is 0.173 newton. Find (a) the tension Ty , (b) the angle the x axis makes with the horizontal, and (c) the angle the y axis makes with the horizontal.