Download Slides posted after class - University of Toronto Physics

PHY131H1F - Class 5
4.1 Newton’s First Law
3.6 Uniform and
nonuniform circular
motion
4.2 Newton’s Second Law
4.3 The Fundamental Forces
4.4 The Force of Gravity
(No, it isn’t, Calvin. For an explanation of buoyancy
force, see Chapter 15..)
Clicker Question
• You toss a ball straight up in the air.
• Immediately after you let go of it, what
forces are acting on the ball?
1. The downward force of gravity from the Earth.
2. An upward throwing force from your hand.
3. A small downward drag-force from air
resistance.
A. 1, 2 and 3
B. 1 and 3
C. 1 and 2
D. 1 only
E. 2 and 3
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Test is coming up!!
• The midterm is Tuesday Oct. 6 from 6pm-7:30pm.
• It is based on Wolfson Chs.1-4 plus everything from
lectures, Practicals and MasteringPhysics.
• If you have a conflict with this time, you must sign up for
the alternate sitting on portal by tomorrow 4pm at the
latest!
• Click on “Alternative Sitting Registration”, fill out the form.
• If you fill out the form, you will be accepted into the
alternate sitting. April will send you an email soon –
probably Wednesday, letting you know what room the
test will be in.
Class 5 Preclass Quiz on MasteringPhysics
 This was due this morning at 8:00am
 78% of students answered correctly: When a constant
net force acts on an object, the object moves with a
constant acceleration.
 89% of students answered correctly: The same net force
is applied to two different objects. The second object
has twice the mass of the first object. The acceleration
of object 1 is twice the acceleration of object 2.
 71% of students answered correctly: A 1-lb block and a
100-lb block are placed side by side at the top of a
frictionless hill. Each is given a very light tap to begin
their race to the bottom of the hill. In the absence of air
resistance, the two blocks end in a tie.
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Class 5 Preclass Quiz Student Comments
“Is there any way I can take this course without
taking MAT135?”
Harlow Answer: No. If you drop MAT135 you
will be deleted from PHY131 as well because it
is a co-requisite.
 “what is the unit lb?”
Harlow Answer: “lb” is a short form for “pound”.
It comes from the Latin word “libra” which refers
to a pan balance. Anyway it’s a unit of force,
the conversion is: 2.2 lbs = 9.8 N. This is the
kind of conversion you will be given on page 1
of the test.
Class 5 Preclass Quiz Student Comments
 “We're no strangers to love
 You know the rules and so do I
 A full commitment's what I'm thinking of
 You wouldn't get this from any other guy
 I just want to tell you how I'm feeling
 Gotta make you understand
 Harlow comment: ONO!
You Rick-roll’d me on
MasteringPhysics!!
 [Chorus:]
 Never gonna give you up, never gonna let you down
 Never gonna run around and desert you
 Never gonna make you cry, never gonna say goodbye
 Never gonna tell a lie and hurt you
 …”
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Class 5 Preclass Quiz Student Comments
 “Do we need to memorize all formula we learned ?”
 Harlow Answer: No. You can just write it on your aidsheet.
 “Since the earth is orbiting around the sun, and so it's
constantly accelerating in uniform circular motion, how
come we on earth don't feel these effects but instead
seem to be in an inert frame of reference?”
 Harlow answer: Great question! There are two
reasons. #1 the effect of acceleration is pretty small –
0.006 m/s2. #2, it is quite steady. We already have g =
9.8 m/s2 as the acceleration due to the Earth’s gravity –
the extra accelerations from the orbit and rotation of the
Earth would only change our measurements of g, they
wouldn’t be noticed in any other way.
Class 5 Preclass Quiz Student Comments
 “Are our quizzes before class based on what you tell
use to read, or on the whole chapter?”
 Harlow answer: Just for what you needed to read. For
example, today’s was only sections 4.1-4.4.
 “Do you have any specific way in which you would want
us to draw free body diagrams? The textbook indicates
that the object should be represented with a dot, but
would a box be acceptable as well?”
 Harlow answer: For the tests and final exam, if you are
asked to draw a free-body diagram, it should look a lot
like what the book does. If you replace the dot with a
box, it should be a small box, with the forces emanating
from it (not pointing toward it).
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Uniform Circular
MotionAcceleration
Speed is constant.
𝑣=
2𝜋𝑟
𝑇
where T = Period [s]
Centripetal Acceleration
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Centripetal Acceleration
Clicker Question
A car is traveling East at a constant speed of 100
km/hr. Without speeding up of slowing down, it is
turning left, following the curve in the highway. What
is the direction of the acceleration?
N
W
E
S
A. North
B. East
C. North-East
D. North-West
E. None; the acceleration is zero.
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Nonuniform Circular Motion
• Any object traveling along a curved path has
centripetal acceleration, equal to v2/r.
• If, as it is traveling in a circle, it is speeding up or
slowing down, it also has tangential acceleration.
• The total acceleration is the vector sum of these two
perpendicular components
Nonuniform Circular Motion
• In nonuniform circular motion, speed and path radius can
both change.
• The acceleration has both radial and tangential
components:
a  ar  at
a  at2  ar2
• ar is perpendicular to v while at is tangential to v .
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Last day I asked at the end of class:
• 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?
• ANSWER: SAME – zero!
• The net force on any object is proportional to
its acceleration.
• In the case of these two books, they are both
traveling at a constant velocity, meaning
acceleration is zero.
• Any friction must be offset by some pushing
force, not mentioned in the question.
What is a force?
• A force is a push or a pull on an
object.
• Pushes and pulls are applied to
something
• From the object’s perspective, it has a
force exerted on it
• A force is either a contact force (like
normal) or a long-range force (like
gravity).
• The S.I. unit of force is the Newton
(N)
• N is not a fundamental unit; it can be
broken down into fundamental units:
1 N = 1 kg m s −2
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Drawing force vectors
A Short Catalog of Forces
The forces we deal with most
often in PHY131/132 are:
• Gravity (Fg = mg)
•
Electric
• Normal Force
•
Magnetic
• Tension
•
Thrust (like from a
rocket)
• Static Friction
•
Drag (fluid resistance)
• Spring Force
•
Muscle
• Kinetic Friction ( fk = μkn)
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Gravity
• 𝐹𝐺 = 𝑚𝑔 when the object is
near the surface of Earth
N

FG
• 𝑔 = 9.80 kg , 𝑑𝑜𝑤𝑛
• Also called “weight”
“The Earth exerts a gravity
force on the angry bird.”
Normal Force
“The diving board exerts a
normal force on the dog.”
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Tension
“The rope exerts a tension
force on Harlow.”
An Even Shorter Catalog of Forces
The fundamental forces in the universe are:
1. Gravity (Fg = mg)
2. Electric & Magnetic
3. “Weak Nuclear” – governs beta-decay
4. “Strong Nuclear” – holds the nucleus
together
• Every force you can experience is a
manifestation of one or more of the above.
• It has been shown that #2 and #3 are diferent
aspects of the same, more fundamental force,
called “electroweak”.
• So there are truly only three fundamental
forces.
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A Person Exerts a
Force on A Wall
This contact force is an
example of:
A. Gravity Force
B. Electric & Magnetic Force
C. Weak (radioactive decay)
D. Strong (holds nucleus
together)
E. None of the above
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1
Newton’s First Law
The natural state of an object with no net external force on
it is to either remain at rest or continue to move in a
straight line with a constant velocity.
What is Mass?
•
•
•
Mass is a scalar quantity that describes an object’s inertia.
It describes the amount of matter in an object.
Mass is an intrinsic property of an object.
•
It tells us something
about the object,
regardless of where the
object is, what it’s doing,
or whatever forces may
be acting on it.
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Momentum
Momentum is the product of a particle’s mass and
velocity, has units of kg m/s, and is given by
An object can have a larger momentum if it is:
• moving faster or,
• has more mass
Note: Momentum is a vector quantity. It has both x and
y components.
Examples
• A 1000 kg car travels west at 25 m/s.
What is its momentum?
• A 0.01 kg bullet is fired straight up,
and leaves the gun with a muzzle
speed of 1000 m/s. What is its
momentum?
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2
Newton’s Second Law
The rate at which a body’s momentum changes is equal to the net
force acting on the body:
𝐹net
2
𝑑𝑝
=
𝑑𝑡
Newton’s Second Law
𝑝 = 𝑚𝑣
𝐹net
𝑑
𝑑
𝑑𝑣
=
𝑝 =
𝑚𝑣 = 𝑚
𝑑𝑡
𝑑𝑡
𝑑𝑡
𝐹net = 𝑚𝑎
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Clicker Question
Three forces act on an object. In which
direction does the object accelerate?
Projectile Motion Example
• An angry bird of mass m = 0.12 kg is flying
through the air. His wings are tucked in,
and air resistance is negligible.
• What is the acceleration of the bird?
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Problem Solving Strategy
• Acceleration is the link between dynamics and
kinematics.
• From Fnet, find a.
• From a and initial conditions, find vx, vy, x, y.
• a = 0 is the condition for equilibrium.
• Equilibrium occurs if and only if Fnet = 0.
Clicker Question
• A green ball swings back and forth between
positions 1, 2 and 3. Fg is the magnitude of
the force of gravity on the ball. T is the
magnitude of the tension force on the ball.
At the instant the ball is in position 2,
A. Fg > T
B. Fg < T
C. Fg = T
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• Newton’s Laws only apply in a “inertial
reference frames”. They are not valid if
your reference frame is accelerating!
• An inertial reference frame is one that
is not accelerating.
Clicker Question
• You are in a plane which is accelerating forward on a runway.
• Some careless person has left a tennis ball in the aisle. You notice this
tennis ball is accelerating toward the back of the plane.
• Newton’s Second Law states that Fnet = ma, so there must be a net force on
the tennis ball. What is the source of this backward net force?
A. Air resistance
B. The plane must be at an angle, so a component of gravity provides
the net force toward the back of the plane.
C. The inertial force
D. The normal force
E. Newton’s second law is not valid in your reference frame.
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Gravity for Earthlings
If you happen to live on the surface of a large planet
with radius R = 6370 km and mass M = 5.97 × 1024 kg,
then there will be a force acting on every object of mass
m called its “weight”:
𝑤 = 𝑚𝑔
Where 𝑔 = 9.80 m/s2 toward the centre of the planet. (ie
“down”).
Clicker Question
• When I stand on a scale in my
bathroom it reads 185 pounds.
2.2 pounds = 9.8 Newtons, so
this means the upward force on
my feet when I am standing still is
185 lbs (9.8 N / 2.2 lbs) = 824 N.
• If I ride an elevator which is
accelerating upward at 1.5 m/s2,
what is the upward force on my
feet?
• With no calculations, take a wild
guess from this list:
A. 824 N
B. 950 N
C. 698 N
D. 0 N
E. –824 N
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Before Class 6 on Wednesday
• Please finish reading Chapter 4.
• The midterm is Tuesday Oct. 6 from 6pm-7:30pm. If
you have a conflict with this time, you must sign up
for the alternate sitting on portal by tomorrow at the
latest! Click on “Alternative Sitting Registration”
• Consider the following reasoning, and identify the
mistake:
• “When you pull a wagon, Newton’s 3rd law states that
the wagon pulls back on you with an equal and
opposite force. These forces should cancel each
other. So it is impossible to accelerate the wagon!”
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