Upload
others
View
20
Download
0
Embed Size (px)
Citation preview
1
PHY131H1F - Class 4
Today:
• Vector Math
• Velocity and
Acceleration in 2-
dimensions
• Relative Velocity
• Constant Acceleration in
x and y
• Projectile Motion
• Motion on a Circular
Path
Clicker Question
• A large, light beach ball is falling
towards the beach on a windless day.
The force of gravity on the ball, 𝐹𝑔, is
greater than the upward drag force from
the air, 𝐹𝐷. Which of the following
directions is closest to the direction of
the net force 𝐹net = 𝐹𝑔 + 𝐹𝐷 on the ball?
A.North
B.East
C.South
D.West
E.The net force makes an angle of 90°
with respect to all four of these
directions.
𝐹𝐷
𝐹𝑔East
2
The Pointing Game
• There are three pairs of orthogonal directions in
this room.
• Within a pair, each direction is anti-parallel to the
other.
• Each pair is perpendicular to the other two pairs.
• Point with me:
North - South
West - East
Up - Down
Class 4 Preclass Quiz on MasteringPhysics
This was due this morning at 8:00am
92% answered correctly: In the study of physics, a scalar
is specified with a single number, but a vector is specified
using both a magnitude and direction.
Harlow note (based on student comments): A scalar can
have dimensions, or be dimensionless. ie: m = 5 kg. is a
scalar with dimensions of mass [M]. But π = 3.14 is a
dimensionless scalar (it is a ratio). Most vectors have
dimensions, but unit-vectors do not.
3
Class 4 Preclass Quiz on MasteringPhysics
88% answered correctly: The speed of the mouse
relative to the floor is the vector sum of the
mouse speed relative to the belt and the belt
speed relative to the floor (5 m/s)
88% answered correctly: Both bullets hit the
ground simultaneously!
84% answered correctly: When an object moves
in a circular path at a constant speed, the velocity
and acceleration vectors are perpendicular.
Student comments from Class 4 Preclass Quiz
“Was the mouse on the conveyor belt or was it on the edge
of the belt before it saw the cheese?”
Harlow answer: It was on the belt. The belt was the
mouse’s universe at that time – it didn’t care that the factory
floor was moving at a different velocity.
“I understand that in theory, both bullets should reach the
earth at the same time. However, doesn't the curvature of
the earth become a factor when firing a bullet over longer
distances? If so, would that not alter the height at which the
bullet being fired actually hits the ground?”
Harlow answer: YES! That’s a really good point! In fact,
due to the curvature of the earth, the fired bullet would take
slightly longer to hit the ground, because it would fall a
further distance.
4
Student comments from Class 4 Preclass Quiz
“I did this quiz without doing the assigned readings. I don't
even know what the assigned readings are, but I will find out
now and read it all posthaste.”
Harlow comment: Okay. Thank you for your honesty. Keep
in mind that you have defeated the entire purpose of the pre-
class quiz by doing this, though.
“Relative velocity seems like witchcraft. Please explain this
sorcery.”
“I just wonder what the rules are for this feedback section in
order to get the mark. Surely profanity is off the table, but
what about emoticons? Well, here goes nothing :P”
Student comments from Class 4 Preclass Quiz
“Confused why the section name includes 3-d motion, when
there isn't 3-d motion”
Harlow answer: 3-d motion exists. Most motion for this
course does happen in 2-D, which is a lot easier to draw.
But you should be aware that we live in a 3-D universe so, in
general, everything happens in 3-d.
“I like many people find frames of reference to be very
confusing. I watched the youtube video Frames of Reference
(1960) which helped me a lot with my understanding.
Surprisingly, this film was created in UofT many years ago.”
Harlow note: little known fact: Patterson Hume, one of the
two guys in that famous “Frames of Reference” video
https://youtu.be/aRDOqiqBUQY , was my grandmother’s first
cousin. (The taller one with straight hair.) I have hung out
with him on many family gatherings and he was a super-cool
guy.
5
Student comments from Class 4 Preclass Quiz
“Q: What do you get when you cross a mosquito with a
mountain climber? A: You can’t cross a vector and a
scalar!”
“what is the prime of velocity, v'? (isn't that acceleration?)”
Harlow answer: No, no! This “prime” has nothing to do with
derivatives! It’s just a label to distinguish it from v.
“circular motion makes me dizzy”
Last day I asked at the end of class:
• Can you add a scalar to a vector?
• ANSWER: No. A 2-D vector is represented by a
pair of numbers (ie x- and y- components, or
magnitude and direction), and you can’t add a scalar
number to this.
• Can you multiply a vector by a scalar?
• ANSWER: YES! When you multiply a vector by a
scalar, you can either:
–Multiply both the x and y components by this
scalar, or
–Multiply the magnitude by the scalar, and keep the
direction unchanged (but you flip direction 180° for
a negative scalar)
6
Vectors
• There are two kinds of Physical quantities we will deal with:
–Scalar (Only has a size)
•Quantity that can be described with only one number.
•Examples: time, speed (just a magnitude say “5 m/s”)
–Vector: (Has size and a direction)
•Quantity that is described with two numbers:
–Magnitude
–Direction
•Examples: Position, velocity (magnitude say “5 m/s” and direction say “north”)
7
Distance vs Displacement Example
• From High Park, you ride
your bike 6 km East on
Bloor St, then 5 km North on
Yonge St to the corner of
Yonge and Eglinton.
a. What is the distance
traveled?
b. What is your displacement?
Which figure shows ? A A A1 2 3
Clicker Question:
8
Components
add and
subtract like
scalars!
Vector Components
9
Announcements
• The first term test will be on Tuesday Oct. 6, from 6:00pm
to 7:30pm.
• Test 1 will cover chapters 1-4 of Wolfson, plus what was
done in lectures and Practicals.
• You must bring a calculator and one 8.5x11’ aid sheet
which you prepare, double-sided
• If you have a conflict at that time with an academic activity
(test, lecture, tutorial, lab), you must register to write at the
Alternate Sitting of this test by going to portal and filling
out the online form no later than Sep. 29 by 4:00pm.
• (The Alternative Sitting is on Tuesday Oct. 6, from 4:30pm
to 6:00pm.)
10
Where to get good help for free
• Your classmates: form a study group
• Your two graduate student TAs. Learn their email
address, office hours, and office location.
• Me. After class, office hours are T10, R2, F11, and my
office is MP121-B.
• The Physics Drop-In Centre in MP125, back corner
MTWR 12-3, F11-2
• Academic Success Centre in Koffler 1st floor, inside the
Career Centre
Student Comments from Class 4 Preclass Quiz
“For the "cheat sheet" can we write some info too or is it
strictly equations?”
Harlow answer: You can write whatever you would like. I
will be providing helpful numbers such as conversion factors
on the front page, so you shouldn’t need those. You will
need to write whatever equations might be useful for
chapters 1-4 questions.
“Is there going to be anything about the labs asked on the
test/exam?”
Harlow answer: Yes! The material in Practicals is also
testable.
“Are we allowed to use graphing/programming calculators on
the tests and exams?”
Harlow answer: Yes!
11
Student comments from Class 4 Preclass Quiz
“Will these type of questions be asked on the exam? if not,
what is the purpose? "How much would it cost to cover the
entire land area of Canada with five dollar bills?“”
Harlow answer: Yes, there will be an estimation question on
test 1, and possibly on the final exam. It will be multiple
choice, where the five choices all differ by at least a factor of
10. You will be able to figure it all out using numbers and
simple equations which will be in the “possibly useful
information” on the front page of the test.
Are there assigned or recommended questions that we
should try out?
Harlow answer: Yes, suggested end-of-chapter items from
Wolfson chapters 1-4 have been posted on the portal page
for this course under “Extra Study Materials”
Projectile Motion
12
Projectile Motion
Projectile motion is made up of two independent motions:
• uniform motion at constant velocity in the horizontal direction and
• free-fall motion in the vertical direction.
The kinematic equations that describe these two motions are:
13
Clicker Question
A C
B
• A tennis ball is launched at an angle, and flies through the
air in a parabolic path, as shown, A B C.
• At point B
A. the velocity is horizontal, and the speed is maximum.
B. the velocity is horizontal, and the speed is minimum.
C. the velocity is horizontal, but the speed is neither a
maximum nor a minimum.
D. the velocity is not horizontal, but the speed is minimum.
E. the velocity is not horizontal, and the speed is neither a
maximum or minimum.
Monkey and Hunter Demonstration (and clicker question)
The classic problem: “A monkey hanging from the branch of a
tree is spotted by a hunter. The monkey sees that the barrel
of the gun is pointed directly at him. At the exact instant the
gun is fired, the monkey lets go of the branch. Will the bullet
(A) go above the monkey, (B) go below the monkey, or (C) hit
the monkey?
Our demonstration uses a
pressurized tennis ball
launcher. The laser is aimed
directly at the monkey, which
is supported by an
electromagnet. As the tennis
ball leaves the launcher, it
breaks a connection that
releases the magnet.
14
Joke: Why Did the Chicken Cross
the Road?
Aristotle (330 BC):
“Because it is the nature of chickens to cross roads.”
Newton (1687):
“Because there is no external net force causing the chicken’s velocity across the road to change.”
Einstein (1905):
“Is the chicken crossing the road, or is the road moving under the chicken?”
[image downloaded 9/30/2013 from http://afgg.tumblr.com/post/3126636261/when-the-chicken-crossed-the-road ]
Relative Motion
15
Relative Motion
If we know an object’s velocity measured in one reference
frame, S, we can transform it into the velocity that
would be measured by an experimenter in a different
reference frame, S´, using the Galilean transformation of
velocity.
Or, in terms of components,
Example: You are running on flat
ground at 7 m/s when you throw a
ball to a friend in front of you. In
your own reference frame, you
launch the ball at an angle of 45°
above the horizontal at a speed of
12 m/s. What is the ball’s initial
velocity relative to the ground?
16
A. 40 m/s, West
B. 20 m/s, West
C. zero
D. 20 m/s, East
E. 40 m/s, East
• You are on an Eastbound subway train going at 20 m/s.
• You notice the Westbound train on the other track.
• Relative to the ground, that Westbound train has a speed
of 20 m/s.
• What is the velocity of the Westbound train as measured
by you?
Clicker Question
[image from http://www.cbc.ca/news/canada/toronto/ttc-closes-downtown-subway-loop-for-the-weekend-1.1347919 ]
17
Analyzing the acceleration vector An object’s acceleration
can be decomposed into
components parallel and
perpendicular to the velocity.
𝑎|| is the piece of the
acceleration that causes the
object to change speed
𝑎⊥ is the piece of the
acceleration that causes the
object to change direction
An object changing
direction always has a
component of acceleration
perpendicular to the
direction of motion.
Acceleration
Uniform Circular
Motion
Speed is constant.
where T = Period [s]
𝑣 =2𝜋𝑟
𝑇
18
Centripetal Acceleration
Centripetal Acceleration
19
Before Class 5 on Monday
• Please read Chapter 4, sections 4.1
through 4.4 of Wolfson.
• Problem Set 1 is based on Wolfson
Chapters 1 and 2: it is due this Friday by
11:59pm.
• Something to think about: A paperback novel
has a mass of 0.3 kg and slides at a
constant velocity. A chemistry textbook has
a mass of 3.0 kg, and slides at the same
constant velocity. How does the net force on
the textbook compare to the net force on the
novel?