Worksheet 1
Yang Li
August 20, 2012
PHYS 222 recitations, section 25 & 36
TA:
Yang LI (“Young”)
leeyoung@iastate.edu
A522 Zaffarano
294-5469
Recitation Hours:
(Section 25) Tuesday 1:10 - 2:00pm at Gilman 1051
(Section 36) Tuesday 3:10 - 4:00pm at Gilman 1312
Office Hours:
Helproom Hours (TBD), or by appointment
Course Website:
Homework:
the “Blackboard” (BB) http://bb.its.iastate.edu
on the “Mastering Physics”
B54 (in the basement)
recitation
• Recitation is the time for you to discuss, sketch, ask, explain, disagree and think aloud. You push
yourself to learn, actively.
• TA is here to help you through the problems, not to solve the problems for you.
• A recitation can be divided to two parts: 40 min worksheet (5 points) + 10 min. quiz (5 points);
worksheet
tentative plan for worksheet:
1. Questions on last week’s quiz and lecture (∼ 10 min) or homework (inform me the questions in advance)
2. Problem-solving in groups ( 4 people ); (∼ 25 min) the problems will be distributed or on board. a
student will explain the solution to the class on board ( Extra credits ).
If no one wants to or the whole class get the wrong answers, I’ll explain the answer.
quiz
• Each recitation includes a 10 min quiz except for the first week (but you do get a grade today);
• The quiz is made by the Prof. Anderson, based on materials of two previous homework assignments;
1
• There are four sets of quizzes and I randomly pick up one. don’t try to get information from students
of other sections;
• In the quizzes, you can bring your calculator and a formula sheet. The formula sheet is available on
BB. You can also bring your own formula sheet (or develop on the standard formula sheet) after my
inspection of it. Sharing calculator or formula sheet is not allowed.
• Quizzes are graded by TA and handed back to you at the next recitation. That’s when questions can
be asked;
• Missed quiz will be zero, unless with an excuse. The valid excuses include sickness, emergency, university sponsored activities. I need you to bring or email me the execuse note. I also recommand you to
drop me an email in advance. Your grade for excuse quiz will be the average of all other quizzes.
grading policies
• Recitation grades contribute to 10% of your total grade.
• We will have 10 points for each recitation, 5 pts for worksheet graded on your performance, and 5 pts
for your quiz.
1. Absence from recitation without valid excuse will give you a 0.
2. S/he who explains the problem on board will receive 2 extra points the group will receive 1 extra
point, upto 5 points.
3. Grading policies for quizzes:
– We grade on the development of the solution. A final answer alone is not acceptable.
– * We do no penalize you twice for the same mistake.
4. The grade will be posted on BB by every Thursday.
• Final recitation grades will be corrected by average of all students. (Some TAs are hard, some are
kind. So don’t get panic if your grade is not as good as students’ from other recitations.)
labs
• Labs are required to pass the course.
• If you have completed the 222 labs before, you can request a lab waiver on BB in the first week.
special needs
If you have special needs, please contact the instructor Prof. Ruslan Prozorov or Prof. Walter Anderson
ASAP.
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Inquiries can be directed to the Interim Assistant Director of Equal Opportunity and Compliance, 3280
Beardshear Hall, (515) 294-7612.”
2
vectors
Problem 1.1:
Vector ~a and ~b are seperated by an angle θab = 135◦. Their magnitudes are 5 and 4 respectively. What is
the angle between ~a + ~b and ~a − ~b?
~b
~a
|~b| = 4
θab = 135◦
|~a| = 5
b
Figure 1: problem 1.1
solution:
method 1, the easy way: Build coordinate system, and choose x-axis along ~a to make life easier. Then
~a = (5, 0). Take the component of ~b: ~bx = 4 · cos 135◦ = −2.83, ~by = 4 · sin 135◦ = +2.83.
~ ≡ ~a + ~b = (2.17, 2.83);
A
~ ≡ ~a − ~b = (7.83, −2.83);
B
~·B
~ = |A|
~ · |B|
~ · cos θAB
On the other hand, A
~
~
~
~
~ B|,
~ |B|
~ 2 = B 2 + B 2 ).
A · B = 8.98, |A| = 3.57, |B| = 8.32; (Use Pythagorean theorem for |A|&|
x
y
~ ~
A·B
◦
Therefore, θAB = arccos |A|·|
~ B|
~ = 72.4 .
method 2, the hard way: Use triangle (head-to-tail) method, or parallelogram method to get ~a + ~b
and ~a − ~b.
√
~ ≡ ~a + ~b, |A|
~ = a2 + b2 + 2ab cos θab = 3.57 (cross check);
A
~
~
~
in order to use triangle rule
√ to get ~a − b, we set d =p−b.
2
2
~
~
~
~
B ≡ ~a − b = ~a + d, |B| = a + d − 2ad cos θad = a2 + b2 − 2ab cos(180◦ − θab ) = 8.32 (cross check);
~
~
~
(~
a+b)·~
a
A·~
a
~
a·~
a+b·~
a
θAB = θAa + θaB . cos θAa = |A|·|~
~ a| = |A|·|~
~ a| = |A|·|~
~ a| ; cos θaB =
~a · ~a = a2 = 25; ~a · ~b = ab cos θab = 4 × 5 × cos 135 = −14.1;
~
~
a· B
~
|~
a|·|B|
=
~
a·(~
a−~b)
~
|~
a|·|B|
=
~
a·~
a−~
a·~b
~ ;
|~
a|·|B|
θAa = arccos 25+(−14.1)
= 52.4◦ ; θaB = arccos 25−(−14.1)
= 20◦ ; Therefore, θAB = 52.4◦ + 20◦ = 72.4◦.
3.57×5
5×8.32
method 3, the algebraic way
~ ≡ ~a + ~b, B
~ ≡ ~a − ~b.
A
~B
~
~·B
~ = |A|
~ · |B|
~ · cos θAB =⇒ cos θAB = A·
A
~ B|
~ .
|A|·|
2
~
~
~
~
~
~
A · B = (~a + b) · (~a − b) = ~a · ~a − b · b = 5 − 42 = 9.
~a · ~b = ab cos θab = −14.1.
~2=A
~ ·A
~ = (~a + ~b) · (~a + ~b) = ~a · ~a + ~b · ~b + 2 · ~a · ~b = 12.1;
|A|
~ 2 = ~a · ~a + ~b · ~b − 2 · ~a · ~b = 69.2.
similarly, |B|
9√
= 72.4◦ .
Therefore, θAB = arccos √12.1×
69.2
3