IOT POLY ENGINEERING 3-10 DRILL January __, 2009 With a partner, go over your solutions to last...

IOT

POLY ENGINEERING3-10

DRILL

January __, 2009

With a partner, go over your solutions to last night’s homework. Make sure all work is neat and any incongruence between answers is resolved.

Last night’s homework:1. Complete problems 4-6 on the Trig. Worksheet2. Complete problems 1-2 on the Vector Worksheet

IOT

POLY ENGINEERING3-9

N

IOT

POLY ENGINEERING3-9

IOT

POLY ENGINEERING3-8

Trigonometry and Vectors

Pythagorean Theorem:

r2 = x2 + y2

Trigonometry

A

B

C

y

x

r

HYPOTENUSE


Common triangles in Geometry and Trigonometry

3

4

5

1

Trigonometry and VectorsCommon triangles in Geometry and

Trigonometry

11

1

2

45o

45o

2

3

30o

60o

You must memorize these triangles

2 3

IOT

POLY ENGINEERING3-8


Trigonometric functions are ratios of the lengths of the segments that make up angles.

Trigonometric Functions

tan A = opposite adjacent

sin A = opposite

hypotenuse

cos A = adjacent

hypotenuse

IOT

POLY ENGINEERING3-8

Unless otherwise specified:

• Positive angles measured counter-clockwise from the horizontal.

• Negative angles measured clockwise from the horizontal.

• We call the horizontal line 0o, or the initial side

0

90

180

270

Trigonometry and VectorsMeasuring Angles

30 degrees

45 degrees

90 degrees

180 degrees

270 degrees

360 degrees

INITIAL SIDE

-330 degrees

-315 degrees

-270 degrees

-180 degrees

-90 degrees

=

=

=

=

=

IOT

POLY ENGINEERING3-9


1. Scalar Quantities – a quantity that involves magnitude only; direction is not importantTiger Woods – 6’1”Shaquille O’Neill – 7’0”

2. Vector Quantities – a quantity that involves both magnitude and direction

Vectors

How hard to impact the cue ball is only part of the game – you need to know direction too

Weight is a vector quantity

IOT

POLY ENGINEERING3-9


1. 5 miles northeast

2. 6 yards

3. 1000 lbs force

Scalar or Vector?

VectorMagnitude and Direction

ScalarMagnitude only


4. 400 mph due north

5. $100

6. 10 lbs weight




IOT

POLY ENGINEERING3-9


3. Free-body DiagramA diagram that shows all external forces acting on an object.

Vectors

friction force

force of gravity

(weight)

applied force

normal force

Wt

FN

Ff

IOT

POLY ENGINEERING3-9


4. Describing vectors – We MUST represent both magnitude and direction.

Describe the force applied to the wagon by the skeleton:

Vectors

45o40 lb

s

magnitude direction

F = 40 lbs 45o

Hat signifies vector quantity

IOT

POLY ENGINEERING3-9


2 ways of describing vectors…

Vectors

45o40 lb

s

F = 40 lbs 45o

F = 40 lbs @ 45o

Students must use this form

IOT



1. We can multiply any vector by a whole number.2. Original direction is maintained, new magnitude.

Vectors – Scalar Multiplication

2

½

IOT



1. We can add two or more vectors together. 2. Redraw vectors head-to-tail, then draw the resultant vector.

(head-to-tail order does not matter)

Vectors – Addition

IOT


March 14, 2010Drill: Draw these vectors

Find 2 a and a +b

y

x

b

aa

IOT


a

2 a

IOT


y

x

b

a aa+b

IOT


y

x

b

a

b

a+b

IOT


Trigonometry and VectorsVectors – Rectangular Components

y

x

F

Fx

Fy

1. It is often useful to break a vector into horizontal and vertical components (rectangular components).

2. Consider the Force vector below. 3. Plot this vector on x-y axis.4. Project the vector onto x and y axes.

IOT


Trigonometry and VectorsVectors – Rectangular Components

y

x

F

Fx

Fy

This means:

vector F = vector Fx + vector Fy

Remember the addition of vectors:

IOT



Vectors – Rectangular Components

y

x

F

Fx

Fy

Fx = Fx i

Vector Fx = Magnitude Fx times vector i

Vector Fy = Magnitude Fy times vector j

Fy = Fy j

F = Fx i + Fy j

i denotes vector in x direction

j denotes vector in y direction

Unit vector

IOT




From now on, vectors on this screen will appear as bold type without hats.

For example, Fx = (4 lbs)i

Fy = (3 lbs)j

F = (4 lbs)i + (3 lbs)j

IOT




y

x

F

Fx

Fy

Each grid space represents 1 lb force.

What is Fx?

Fx = (4 lbs)i

What is Fy?

Fy = (3 lbs)j

What is F?

F = (4 lbs)i + (3 lbs)j

IOT




F

Fx

Fy

cos q = Fx / F

Fx = F cos q i

sin q = Fy / F

Fy = F sin q j

What is the relationship between q, sin q, and cos q?

q

IOT




y

x

F Fx +

Fy +

When are Fx and Fy Positive/Negative?

FFx -

Fy +

FFFx -Fy -

Fx +Fy -

IOT



Complete the following chart in your notebook:

III

III IV

Each grid space represents 1 lb force.

What is Fx?

Fx = (5 lbs)i

What is Fy?

Fy = (2 lbs)j

What is F?

F = (5 lbs)i + (2 lbs)jIOT




y

x

F

Fx

Fy

IOT

POLY ENGINEERING

Rewriting vectors in terms of rectangular components:

1) Find force in x-direction – write formula and substitute

2) Find force in y-direction – write formula and substitute

3) Write as a single vector in rectangular components Fx = F cos Qi Fy = F sin

Qj

IOT

POLY ENGINEERING

Fx = F cos Qi Fy = F sin Qj

IOT

POLY ENGINEERING


IOT

POLY ENGINEERING


IOT


Trigonometry and VectorsVectors – Resultant Forces

Resultant forces are the overall combination of all forces acting on a body. 1) sum of forces in x-direction

2) sum of forces in y-direction

3) Write as single vector in rectangular components

Fx = F cos Qi

= (150 lbs) (cos 60) i

= (75 lbs)i

SFx = (75 lbs)i

No x-component

IOT






Fy = F sin Qj

= (150 lbs) (sin 60) j

= (75 lbs)j

Wy = -(100 lbs)j

SFy = (75 lbs)j - (100 lbs)j

SFy = (75 - 100 lbs)j

3

3

3

IOT



R = SFx + SFy

R = (75 lbs)i + (75 - 100 lbs)j

R = (75 lbs)i + (29.9 lbs)j

3





IOT



IOT



IOT



IOT


IOT




F

Fx

Fy

cos q = Fx / F

Fx = F cos q i

sin q = Fy / F

Fy = F sin q j

What is the relationship between q, sin q, and cos q?

q

Problem 4a

IOT


100lbs

60

150lbsGravitySpace

Junk

Gravity: jiFgravity 1000

jiF junkspace 60sin15060cos150

jiF junkspace 2

3*150

2

1*150

Space Junk:

jiF junkspace 13075

JunkSpacegravityres FFF

jlbsilbsFres 23075

Problem 4b

IOT


28 lbs

5 lb

15lbs

Gravity


jiFfriction 05

jiFPulling 30sin1530cos15

Friction:

jiFPulling 5.713

PullingFrictiongravityres FFFF

jlbsilbsFres 5.208

Pulling Force30o

Friction

Pulling Force

Problem 4c

IOT


1 lbs

4 lb

110lbs

Gravity


jiFWind 04

jiFKick 45sin11045cos110

Wind:

jiFPulling 8.778.77

KickWindgravityres FFFF

jlbsilbsFres 8.768.73

Kick45o

Wind

Kick

Problem 4d

IOT


3500 lbs

55 lbs 800lbs

Gravity


jiFDrag 055

jiFCar 0800

Drag:

CarDraggravityres FFFF

jlbsilbsFres 3500745

CarDrag

Car:


IOT



IOT



CLASSWORK / HOMEWORK

Complete problem #4 on the Vector Worksheet

IOT


Date post:	01-Jan-2016
Category:	Documents
Upload:	drusilla-alexander
View:	214 times
Download:	0 times

IOT POLY ENGINEERING 3-10 DRILL January __, 2009 With a partner, go over your solutions to last...

Documents