RECITATION
EF 151 Recitation
Solve Problems
Demonstrations
Team Projects
Recitation: What to bring
Textbook
Calculator
Pencil and Paper
Questions
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
learning
Several quiz questions will often be similar to the
homework
The best way to learn is to do; watching doesn’t
cut it
It is your responsibility to learn the material!
Problems - Portfolio
Keep a portfolio of all your problem solutions
Bring 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 other
Copying is a violation of the University
honor policy
It 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 Solving
Define 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 = 4pr3)
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 comp = Mag(cosq)
y comp = Mag(sinq)
y
q always measured:
q
x
counterclockwise from
positive x-direction
Origin is always located:
at tail of vector
Vectors - Components
y
A  Ax  Ay
A
Ay
A
A A
2
x
2
y
θ
x
Ax
q  tan
1
Ay
Ax
 arctan
Ay
Ax
Be careful with signs. Remember
tangent is sine/cosine.
Angle Determination
y
y
y
θ
θ
θ
θ
x
x
x
x+
y+
y
xy+
x
x+
y-
xy-
10
8
6
Tan( q )
4
2
0
-90
-2 0
90
180
-4
-6
-8
-10
q (deg)
270
360
Vector addition
Head
Tail
Vector sum is vector from
tail of first vector to head
of last vector (start to
end).
Ways to add vectors:
Graphically
Trigonometrically
Using components
Vectors - Forces
Determine the resultant (vector sum) of the forces acting
on the bolt.
60 lb
45º
Vector
Mag.
q
x-comp.
y-comp.
40 lb
1
60 lb
135°
-42.4 lb
42.4 lb
20º
2
40 lb
20°
37.6 lb
13.7 lb
-4.8 lb
56.1 lb
Sum
56.3 lb 94.9°
Module 1, Recitation 5
Vector component questions
ConcepTest
Vectors I
1) same magnitude, but can be in any
direction
such that A + B = 0,
2) same magnitude, but must be in the
what can you say about same direction
3) different magnitudes, but must be in the
the magnitude and
same direction
direction of vectors A
4) same magnitude, but must be in
and B?
opposite directions
5) different magnitudes, but must be in
opposite directions
If two vectors are given
ConcepTest
Vectors I
1) same magnitude, but can be in any
direction
such that A + B = 0,
2) same magnitude, but must be in the
what can you say about same direction
3) different magnitudes, but must be in the
the magnitude and
same direction
direction of vectors A
4) same magnitude, but must be in
and B?
opposite directions
5) different magnitudes, but must be in
opposite directions
If two vectors are given
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
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?
Vectors II
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
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?
Vectors II
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
Given that A + B =
C, and that lAl + lBl
= lCl , how are
vectors A and B
oriented with
respect to each
other?
Vectors III
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
Given that A + B = C,
and that lAl + lBl =
lCl , how are vectors A
and B oriented with
respect to each other?
Vectors III
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
Vector Components I
If each component of
1) it doubles
a vector is doubled,
2) it increases, but by less than double
what happens to the
angle of that vector?
3) it does not change
4) it is reduced by half
5) it decreases, but not as much as half
ConcepTest
Vector Components I
If each component of
1) it doubles
a vector is doubled,
2) it increases, but by less than double
what happens to the
angle of that vector?
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 q = 2y/2x, which is the same as tan q = y/x (the original
angle).
Follow-up: If you double one component and
not the other, how would the angle change?
ConcepTest
Vector Components II
A certain vector has x and y components
that are equal in magnitude. Which of
the following is a possible angle for this
vector, in a standard x-y coordinate
system?
1) 30°
2) 180°
3) 90°
4) 60°
5) 45°
ConcepTest
Vector Components II
A certain vector has x and y components
that are equal in magnitude. Which of
the following is a possible angle for this
vector, in a standard x-y coordinate
1) 30°
2) 180°
3) 90°
4) 60°
5) 45°
system?
The angle of the vector is given by tan q = y/x. Thus, tan q
= 1 in this case if x and y are equal, which means that the
angle must be 45°.
ConcepTest
Vector Addition
You are adding vectors of
1) 0
length 20 and 40 units. What is
2) 18
the only possible resultant
magnitude that you can obtain
out of the following choices?
3) 37
4) 64
5) 100
ConcepTest
Vector Addition
You are adding vectors of
1) 0
length 20 and 40 units. What is
2) 18
the only possible resultant
magnitude that you can obtain
out of the following choices?
3) 37
4) 64
5) 100
The minimum resultant occurs when the vectors
are opposite, giving 20 units. The maximum
resultant occurs when the vectors are aligned,
giving 60 units. Anything in between is also
possible, for angles between 0° and 180°.