RECITATION. EF 151 Recitation Solve Problems Demonstrations Team Projects.
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Transcript of RECITATION. EF 151 Recitation Solve Problems Demonstrations Team Projects.
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°.