RECITATION

EF 151 Recitation

Solve ProblemsDemonstrationsTeam Projects

Recitation: What to bring

TextbookCalculatorPencil and PaperQuestions

Attendance and Grading Policy

Today

Introduce you to course website and online homework

Take pictures and Meyers-Briggs test

Practice algebra and trigonometry

Online Homework

ef.engr.utk.edu

Need to be within 1% of correct answer to get credit. Enter three significant figures.

On-line Homework Problems

On-line HW is graded. You should work out the solution on paper prior to submitting your answers.Working the homework will improve your learningSeveral quiz questions will often be similar to the homeworkThe best way to learn is to do; watching doesn’t cut itIt is your responsibility to learn the material!

Problems - Portfolio

Keep a portfolio of all your problem solutionsBring the portfolio when you come to help sessions This will enable us to provide better help Students with their portfolios receive priority at

help sessions

Being able to look at the work you have done will aid in reviewing for quizzes and the final exam

Working Together?

Work together only if you are truly learning from each otherCopying is a violation of the University honor policyIt is your job to maintain your integrity, and to learn the material

Module 1, Recitation 3

Estimate amount of paint needed to paint supports of Jumbotron.

Put in picture of Jumbotron supports

Problem SolvingDefine the problem

Identify the critical data of the problem. Do not be misled by data that is extraneous, erroneous, or insignificant.

Diagram A diagram or schematic of the system being analyzed is

often very helpful, and may be required.Governing equations

Determine what type of problem is being solved. Recognize when certain equations apply and when they do not apply. The governing equations should be written out in symbolic form before substituting in numerical quantities.

Calculations Carry out your calculations only after you have completed

the first three steps. Check to make sure units are consistent.

Solution check Make sure you solved the problem that was posed. If

possible, use an independent method or equation to check your result. Check to see that your solution is physically reasonable. Make sure both the magnitude and sign of the answer makes sense.

Problem Philosophy

Documentation -- must be NEAT. Clearly state all relevant assumptions. Provide diagrams where needed. List fundamental relationships in symbolic terms (e.g., V = 4r3) Always provide units with your answers. Ensure that your answer makes sense.

Module 1, Recitation 4

Review of vector properties

Vectors - Components

Generalize from previous slide

x

y

q

Mag

x comp =

y comp =

always measured:

Origin is always located:at tail of vector

counterclockwise from positive x-direction

Mag(cos)

Mag(sin)

Vectors - Components

x

y

θ

A

xA

yA

yx AA

A

Be careful with signs. Remember tangent is sine/cosine.

A

22yx AA

x

y

x

y

A

A

A

Aarctantan 1

Angle Determination

-10

-8

-6

-4

-2

0

2

4

6

8

10

-90 0 90 180 270 360

(deg)

Tan

( )

x +y +

x -y +

x -y -

x +y -

x

y

θx

y

θ

x

y

θx

y

θ

Vector addition

Ways to add vectors:GraphicallyTrigonometricallyUsing components

Tail

Head Vector sum is vector from tail of first vector to head of last vector (start to end).

Vectors - Forces

Determine the resultant (vector sum) of the forces acting on the bolt.

60 lb

40 lb

20º45º

Vector

Mag. x-comp. y-comp.

1 60 lb 135° -42.4 lb 42.4 lb

2 40 lb 20° 37.6 lb 13.7 lb

Sum56.3

lb94.9

°-4.8 lb 56.1 lb

Module 1, Recitation 5

Vector component questions

If two vectors are

given such that A + B

= 0, what can you say

about the magnitude

and direction of

vectors A and B?

1) same magnitude, but can be in any direction2) same magnitude, but must be in the same direction3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions5) different magnitudes, but must be in opposite directions

ConcepTest ConcepTest Vectors IVectors I

If two vectors are

given such that A + B

= 0, what can you say

about the magnitude

and direction of

vectors A and B?

1) same magnitude, but can be in any direction2) same magnitude, but must be in the same direction3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions5) different magnitudes, but must be in opposite directions

The magnitudes must be the same, but one vector must be pointing

in the opposite direction of the other, in order for the sum to come

out to zero. You can prove this with the tip-to-tail method.

ConcepTest ConcepTest Vectors IVectors I

Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other?

1) they are perpendicular to each other

2) they are parallel and in the same direction

3) they are parallel but in the opposite direction

4) they are at 45° to each other

5) they can be at any angle to each other

ConcepTest ConcepTest Vectors IIVectors II

Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other?

1) they are perpendicular to each other

2) they are parallel and in the same direction

3) they are parallel but in the opposite direction

4) they are at 45° to each other

5) they can be at any angle to each other

Note that the magnitudes of the vectors satisfy the Pythagorean Theorem. This suggests that they form a right triangle, with vector C as the hypotenuse. Thus, A and B are the legs of the right triangle and are therefore perpendicular.

ConcepTest ConcepTest Vectors IIVectors II

Given that A + B = C, and that lAl + lBl = lCl , how are vectors A and B oriented with respect to each other?

1) they are perpendicular to each other

2) they are parallel and in the same direction

3) they are parallel but in the opposite direction

4) they are at 45° to each other

5) they can be at any angle to each other

ConcepTest ConcepTest Vectors IIIVectors III

Given that A + B = C, and that lAl + lBl = lCl , how are vectors A and B oriented with respect to each other?

1) they are perpendicular to each other

2) they are parallel and in the same direction

3) they are parallel but in the opposite direction

4) they are at 45° to each other

5) they can be at any angle to each other

The only time vector magnitudes will simply add together is when the direction does not have to be taken into account (i.e., the direction is the same for both vectors). In that case, there is no angle between them to worry about, so vectors A and B must be pointing in the same direction.

ConcepTest ConcepTest Vectors IIIVectors III

If each component of

a vector is doubled,

what happens to the

angle of that vector?

1) it doubles

2) it increases, but by less than double

3) it does not change

4) it is reduced by half

5) it decreases, but not as much as half

ConcepTest ConcepTest Vector Components IVector Components I

If each component of

a vector is doubled,

what happens to the

angle of that vector?

1) it doubles

2) it increases, but by less than double

3) it does not change

4) it is reduced by half

5) it decreases, but not as much as half

The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan = 2y/2x, which is the same as tan = y/x (the original angle).

Follow-up:Follow-up: If you double one component and If you double one component and not the other, how would the angle change?not the other, how would the angle change?

ConcepTest ConcepTest Vector Components IVector Components I

A certain vector has A certain vector has xx and and yy components components

that are equal in magnitude. Which of the that are equal in magnitude. Which of the

following is a possible angle for this following is a possible angle for this

vector, in a standard vector, in a standard x-yx-y coordinate coordinate

system?system?

1) 30°

2) 180°

3) 90°

4) 60°

5) 45°

ConcepTest ConcepTest Vector Components IIVector Components II

A certain vector has A certain vector has xx and and yy components components

that are equal in magnitude. Which of the that are equal in magnitude. Which of the

following is a possible angle for this following is a possible angle for this

vector, in a standard vector, in a standard x-yx-y coordinate coordinate

system?system?

1) 30°

2) 180°

3) 90°

4) 60°

5) 45°

The angle of the vector is given by tan = y/x. Thus, tan

= 1 in this case if x and y are equal, which means that

the angle must be 45°.

ConcepTest ConcepTest Vector Components IIVector Components II

ConcepTest Vector Addition

You are adding vectors of

length 20 and 40 units. What

is the only possible resultant

magnitude that you can obtain

out of the following choices?

1) 01) 0

2) 182) 18

3) 373) 37

4) 644) 64

5) 1005) 100

ConcepTest Vector Addition

You are adding vectors of

length 20 and 40 units. What

is the only possible resultant

magnitude that you can obtain

out of the following choices?

1) 01) 0

2) 182) 18

3) 373) 37

4) 644) 64

5) 1005) 100

The minimumminimum resultant occurs when the

vectors are oppositeopposite, giving 20 units20 units. The

maximummaximum resultant occurs when the vectors

are alignedaligned, giving 60 units60 units. Anything in

between is also possible, for angles

between 0° and 180°.