1. Solve for - ROOM 216sshs216felix.weebly.com/.../scalars_and_vectors_1.pdf1. Solve for x. 19.2...

P11 Kinematics 1 Scalars and Vectors Bundle.notebook

1

July 27, 2013

1. Solve for x.

19.2

13.7x

2. Solve for θ.

θ

7.4

6.2


2

July 27, 2013

Directions in Two Dimensions

23o north of east 55o west of south

17o south of east 88o west of north

[E23oN] [S55oW]

[E17oS] [N88oW]


3

July 27, 2013

Unit 1-Kinematics

Kinematics is the study of how things move.

Physics 112

We will study such terms as:scalars, vectors, distance, displacement, speed, velocity and acceleration.


4

July 27, 2013

Module 1.1- Position, Distance, Displacement

This module is an introduction to some basic kinematics terminology that will be important throughout the entire unit, as well as in future units.


5

July 27, 2013

Types of Quantities: Scalars vs. Vectors


6

July 27, 2013

Scalars and Vectors

Scalar quantities are quantities that do not have a direction associated with them. They have a magnitude (size) only.

Vector quantities have two parts to them:A Magnitude, or size of the quantity, andA direction


7

July 27, 2013

A scalar is a physical quantity that is described by a single number (with its appropriate unit).

distance, time, temperature, speed

Types of Physical Quantities

A vector is a physical quantity that has both size and a direction.

The size or length of a vector is called its magnitude.

Examples

Many quantities have a directional quality and cannot be described by a single number.

http://www.youtube.com/watch?v=KbrEBpCw3Ag


8

July 27, 2013

Examples

force, position, velocity, acceleration

http://www.youtube.com/watch?v=EUrMI0DIh40

http://www.youtube.com/watch?v=GxURTJ_JDT8&feature=related


9

July 27, 2013


10

July 27, 2013

Drawing Vector Quantities

We can graphically represent a vector as an arrow.

The arrow is drawn to point in the direction of the vector quantity, and the length of the arrow is proportional to the magnitude of the vector quantity.

tip of the arrow

tail of thearrow

20 N

Example


11

July 27, 2013

Adding Vectors Graphically

Suppose that a child walks 200 m east, pauses, and then continues 400 m east. To find the total displacement, or change in position of the child, we must add the two vec tor quantities.

Vectors are added by placing the tail of one vector at the tip of the other vector. The diagram below, drawn to scale, shows the addition of the two segments of the child's walk.

It is very important that neither the direction nor the length of either vector is changed during the addition process. A third vector is then drawn connecting the tail of the first vec tor to the tip of the second vector. This third vector represents the sum of the first two vectors.

This third vector is called the resultant, R. The resultant is always drawn from the tail of the first vector to the tip of the last vector.

To find the magnitude of the resultant, R, measure its length using the same scale used to draw the first two vectors.

200 m 400 m

Scale: 1 division = 100 m

Scale: 1 division = 100 m

200 m 400 m


12

July 27, 2013

When vectors are added, the order of addition does not matter. The same vector sum will result.

NOTE!!!

200 m400 m

If the child had turned around after moving 200 m east and then walked 400 m west, the change of position would have been 200 m west. Note that the vectors are added tip to tail.

Two vectors can have opposite directions.

200 m

400 m

200 m

400 m

200 m

400 m

R


13

July 27, 2013

Vector Addition: The Order Does Not Matter

http://www.physicsclassroom.com/mmedia/vectors/ao.cfm


14

July 27, 2013

Add the following forces. Sketch a graphical solution. State the magnitude and direction of the resultant.

2.5 N

A2.0 N

B

1.5 N

C

5.0 N

D+ +

+

A 2.5 N North B 2.0 N EastC 1.5 N [W40oS]D 5.0 N [W55oN]

5.9 N [W70oN]

Example

Let 1 cm = 1 N


15

July 27, 2013


16

July 27, 2013

100 Aker Wood


17

July 27, 2013

When a vector is multiplied by a positive scalar, c, the magnitude of the vector will change. The direction of the vector is not affected.

Multiplication of a Vector by a Scalar

Examples

1. If A = 15 m east and c = 0.5, then

A15 m

cA7.5 m


18

July 27, 2013

2. If B = 30 m/s at 52o

and

c = 2

then

cB = 2 x 30 m/s at 52o cB = 60 m/s at 52o

B

cB


19

July 27, 2013

The Negative of a Vector

The negative of a vector is a vector of the same magnitude but opposite direction. In other words, the vector will rotate 180o.

A B

How do we subtract two vectors?

We have to rewrite the expression as a sum of two vectors.

A + (B)

A B

A B

BA

A B=


20

July 27, 2013


21

July 27, 2013


22

July 27, 2013


23

July 27, 2013


24

July 27, 2013

Vectors and Trigonometry

Trig Basics

θ

The longest side, opposite to the right angle, is the

hypotenuse.

This is the side adjacent

to the angle.

This is the side opposite

to the angle. H

A

O

The sine, cosine, and tangent of angle θ are defined as ratios of the sides of the triangle:

sin θ = opp hyp

cos θ = adj hyp

tan θ = opp adj

We can determine the magnitude of the resultant vector from the Pythagorean Theorem.

H2 = O2 +A2

Adding Perpendicular Vectors

http://www.youtube.com/watch?v=PPhL_c3JtR8


25

July 27, 2013

Sample Problem 1Earl walks 3.2 m east and then 9.4 m south. Determine his resultant displacement. Include a labelled vector diagram.


RR

3.2 m

3.2 m

9.4 m 9.4 mθ α

H2 = O2 +A2

R2 = (3.2m)2 + (9.4m)2

R =

R = 9.9 m

tan θ = opp adj

tan θ = 9.4m 3.2m

θ = 9.4m x 1 3.2m tan

θ = 71o

His resultant displacement is 9.9 m E 71o S or 9.9 m 71o south of east

or 9.9 m S 19o E or 9.9 m 19o east of south.


26

July 27, 2013

A dog walks 23.7 m west and then 14.9 m south looking for his yoyo.

a) How far did the dog walk?b) What is the dog's resultant displacement?

Sample Problem 2

a) Distance = 23.7 m + 14.9 m = 38.6 m

b) 23.7 m

14.9 m θ

The dog's Resultant Displacement = 38.6 m W 32.2o S or 38.6 m 32.2o south of west or

38.6 S 57.8o W or 38.6 m 57.8o west of south,

tan θ = opp adj

tan θ =14.9m 23.7m

θ = 14.9m x 1 23.7m tan

θ = 32.2o


27

July 27, 2013

A camel walks 12.0 km east, 23.0 km northand finally 3.00 km west. What is the resultant displacement of the camel?

Sample Problem 3

12km

3km

23km

(123)km

Distance =

= 24.7 m

θ

tan θ = opp adj

tan θ =23 m 9 m

θ = 23 m x 1 9 m tan

θ = 69o

The resultant displacement of the camel is 24.7 m E 69O N or

24.7 m N 21 O E


28

July 27, 2013

Practice Problems Vector Addition

1. Two vectors A and B are added together to form vector C. The relationship between the magnitudes of the vectors is given by: A2 + B2 = C2. Which statement concerning these vectors is true?

a) A and B must have equal lengths. b) A and B must be parallel. c) A and B must be going in the same direction. d) A and B must be at right angles to each other.

2. An escaped convict runs 1.70 km due east of the prison. He then runs due north to a friend’s house. If the magnitude of the convict’s resultant displacement is 2.50 km, what is the direction of his total displacement? a) 42.8o south of east b) 47.2o north of east c) 42.8o east of south d) 47.2o east of north

P11 Kinematics


29

July 27, 2013

3. A 7 N force and a 8 N force act concurrently on an object. Which of the following forces is not a possible resultant?

a) 0 N b) 1 N c) 11 N d) 15 N

4. A groundhog named Murray reluctantly leaves his hole and walks 11 km north and then 16 km west.

a) How far did Murray travel? b) What is Murray’s resultant displacement from his hole?

19 km [W35oN] or 19 km 35o north of west

19 km [N55oW] or 19 km 55o west of north


30

July 27, 2013

5. Bubba is flying a plane due north at 225 km/h as a wind carries it due east at 65.0 km/h. Find the magnitude and direction of the plane’s resultant velocity.

6. Baby Bear can’t find Mama Bear. What is his resultant displacement if he walks 2.0 m north, 3.0 m east, 1.0 m south, 5.0 m west, 4.0 m south and then 2.0 m east?

234 km/h [E73.9oN] or 234 km/h [N16.1oE]

3.0 m south


31

July 27, 2013

7. Beulah and Bertha kick a soccer ball at exactly the same time. Beulah’s foot exerts a force of 66 N south. Bertha’s foot exerts a force of 88 N west. What is the resultant force on the ball?

1.1 x 102 N [W37oS] or 1.1 x 102 N [S53oW]


32

July 27, 2013

a) The speed of the vehicle along its descent path is 65 m/s.

b) 58o to the right of the vertical

R35 m/s

55 m/s

θ

8. A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 35 m/s. At the same time it has a horizon tal velocity of 55 m/s to the right.

a) At what speed does the vehicle move along its descent path? b) At what angle with the vertical is this path?


33

July 27, 2013

9. Mr. Whipple is in a boat traveling 3.8 m/s east straight across a river 2.40 x 102 m wide. The river is flowing at 1.6 m/s south.

a) What is Mr. Whipple’s resultant velocity? b) How long will it take Mr. Whipple to cross the river?

a) 4.1 m/s [E23oS] or 4.1 m/s [S67oE]

b) It will take Mr. Whipple 63 s to cross the river.

3.8 m/s

1.6 m/sRθ

2.40 x 102 m


34

July 27, 2013

Module Summary

In this module, you should have become familiar with some of the basic terminology. At this point, you should know the following:• The difference between a scalar and a vector.• How to draw vector quantities• How to add and substract vector quantites graphically• How to multiply a vector by a scalar• How to use trigonometry to solve vector quantity problems.

Attachments


Vector Addition: The Order Does Not Matter

http://www.youtube.com/watch?v=PPhL_c3JtR8

http://www.physicsclassroom.com/mmedia/vectors/ao.cfm

1. Solve for - ROOM 216sshs216felix.weebly.com/.../scalars_and_vectors_1.pdf1. Solve for x. 19.2...

Documents

Transcript of 1. Solve for - ROOM 216sshs216felix.weebly.com/.../scalars_and_vectors_1.pdf1. Solve for x. 19.2...