PHY131H1F - Class 6
• 4.5 Solving Force Problems
• 4.6 Newton’s Third Law
• The Normal Force
• Hooke’s Law
𝑎
A truck is pushing a car up an incline with a constant forward
acceleration 𝑎. The incline has an angle  with respect to the
horizontal. Note: the car and the truck remain in contact during
this acceleration. Which is larger, the magnitude of the force
the truck applies on the car or the magnitude of the force the
car applies on the truck?
A.
B.
C.
D.
E.
The magnitude of the force the truck applies to the car.
The magnitude of the force the car applies to the truck.
The magnitude of the two forces are the same.
We must know the angle  to answer this question.
We must know the masses of the truck and the car to
answer this question.
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Class 6 Preclass Quiz on MasteringPhysics
 This was due this morning at 8:00am
 47% of students answered correctly: “An object is at rest
on a tabletop. Earth pulls downward on this object with a
force equal in magnitude to mg. If this force serves as the
action force, what is the reaction force in the action–
reaction pair?” The object pulling upward on the Earth.
 90% of students answered correctly A large truck collides
head-on with a small car. The car is severely damaged as
a result of the collision. According to Newton's third law,
The force on the truck is equal to the force on the car.
 96% of students answered correctly A spring stretches by
21.0 cm when a 135 N object is attached. What is the
weight of a fish that would stretch the spring by 57.8 cm?
Answer = 371 N. [Use F2 = F1 (x2/x1) ]
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Class 6 Preclass Quiz Student Comments
 “Should the pair of action force and reaction force be on
the two same things and be attached with each other?”
 Harlow note: the 2 forces of an action-reaction-pair
always act on different objects! If it is a long range
force, then these objects need not be connected.
 “Will the k of a spring change?”
 Harlow note: No. For an ideal spring (which is all the
springs in this course) k is a constant for a particular
spring (unless you cut it in half or something!)
 "If you're in free fall, then Earth's gravity causes you to
accelerate toward Earth. Earth, too, accelerates toward
you." My mind is springing back and forth trying to
comprehend this.
Class 6 Preclass Quiz Student Comments
 “Does the midterm start at exactly 6, or the typical UofT
time of 6:10?”
 Harlow answer: 6:10
 “so far I've been studying the lecture notes and taking
notes on the information in the textbook, however when
I get to completing the homework and answering the
calculation questions, I'm completely lost. … My friends
don't even read the lecture notes or the textbook, they
go straight to the questions.”
 Harlow note: Both are important. But I would say being
able to solve homework and end-of-chapter type
problems is more important than a careful review of the
notes. This is a problem-solving course, not a contentremembering course.
 “I feel like anything I say won't be read anyway so ya....
Physics is fun”
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Newton’s Third Law
If object 1 acts on object 2 with a force,
then object 2 acts on object 1 with an
equal force in the opposite direction.


F1 on 2   F2 on 1
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Forces always come in pairs.
• Every force interaction involves two objects, and two
forces.
• These forces
– are equal in strength and opposite in direction.
– are always the same kind of force (ie gravity, normal,
friction, tension, etc.)
– always act on different objects.
Clicker Question
A Mack Truck drives North on the highway, and
collides head-on with a mosquito. Which is true?
A. The Mack Truck does more damage to the
mosquito than the mosquito does to the Mack
Truck.
B. The mosquito does more damage to the
Mack Truck than the Mack Truck does to the
mosquito.
C. The Mack Truck does the same amount of
damage to the mosquito as the mosquito
does to the Mack Truck.
D. Impossible to determine without knowing the
speeds of the truck and mosquito.
E. Don’t know or none of the above
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F = ma
or
a=F/m
• If the force is equal on the truck and the mosquito, is
the acceleration equal?
• Acceleration is higher if m is lower ( F divided by m)
• Mosquito accelerates more, so it receives more
damage.
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!”
ANSWER:
First sentence is correct: the wagon really does pull back on
you with an equal opposite force that you pull on the wagon!
Second and third sentences are not correct: forces cannot
cancel each other if they are on different objects.
The forward static friction on your feet is larger than the
backward rolling friction on the wheels of the wagon, so the
system of you and the wagon has a forward net force,
provided by the Earth (static friction). That is why you both
accelerate.
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Car/Earth Friction Interaction
• Consider an accelerating car.
• The tires of the car are pushing backward
on the Earth (static friction).
• The Earth is pushing forward on the tires
of the car (static friction).
Rocket/Gas Pressure Interaction
• Consider a rocket accelerating upward.
• The rocket is pushing down on the
expelled gas (pressure).
• The expelled gas is pushing up on the
rocket (pressure).
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Basketball/Earth Gravity Interaction
Clicker Question
• Consider a basketball in freefall.
• Gravity is pulling this ball down.
• What is the other force in this
interaction?
A. The thrower’s feet are pushing the
ground down.
B. The ground is pushing the thrower’s feet
up.
C. Gravity of Earth is pulling the thrower
down.
D. Gravity of the ball is pulling the Earth up.
E. Air is pushing the ball up.
Basketball/Earth Gravity Interaction
F
a=
m
m
a=
F
• The Earth is pulling down on the ball.
• The ball is pulling up on the Earth.
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𝑎
Remember this clicker question from the beginning?
Free-body Diagram of truck:
Free-body Diagram of car:
Clicker Question
•
The figure shows two blocks with two forces acting on the
pair. The net force on the larger block is
A. less than 2 N.
B. equal to 2 N.
C. greater than 2 N.
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Example
Three blocks are being accelerated
upward at 3.2 m/s2 by a force F applied
to the bottom block as shown in the
diagram. The mass of the bottom block
is 7.0 kg, the mass of the middle block
is 14 kg, and that of the top block is 21
kg. (a) Find the magnitude of F.
(b) What is the magnitude of the
normal force that the top block exerts
on the middle block?
Example
Three blocks are being accelerated
upward at 3.2 m/s2 by a force F applied
to the bottom block as shown in the
diagram. The mass of the bottom block
is 7.0 kg, the mass of the middle block
is 14 kg, and that of the top block is 21
kg. (a) Find the magnitude of F.
(b) What is the magnitude of the
normal force that the top block exerts
on the middle block?
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Ropes and Pulleys
• The tension in a taught
string or rope is a positive
scalar number, T, in
Newtons.
• If we can neglect the mass
of the string compared to the
other objects in the problem,
each end of the string pulls
inward with the same force,
of magnitude T.
• If the string is wrapped over
a frictionless pulley, and we
can neglect the mass of the
pulley, then the string has
the same tension T on both
sides of the pulley.
Clicker Question
In the figure to the right, is
the tension in the string
greater than, less than, or
equal to the force of
gravity on block B?
A. Equal to
B. Greater than
C. Less than
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Elasticity
• A solid object subjected to external forces may
undergo changes in shape and/or size.
• A body’s elasticity is a measure of how much it
changes when a deforming force is exerted on it
and how well it returns to its original shape.
[Image retrieved Jan. 11 2013 from http://en.wikipedia.org/wiki/File:Office-pink-erasers.jpg ]
Hooke’s Law
• For an ideal spring (one that is not “overstretched”, for
example) the restoring force is directly proportional to the
distance the end of the spring is pulled or pushed away from
equilibrium.
• If x is the position, and x = 0 is the equilibrium position,
then the force exerted by the spring is
𝐹𝑠 = −𝑘𝑥
• where Fs is the x-component of the restoring force, and k is
the spring constant of the spring.
• The minus sign reminds you that it is a restoring force.
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Elasticity
Hooke’s law: The extension of a spring is directly
proportional to the force applied to it.
𝐹𝑠 = −𝑘𝑥
Hooke’s Law: Two springs “in parallel”
•
•
•
Consider a spring that stretches an amount
x1 = F/k1 when a load of weight F is
suspended from it.
(a) How much will the spring stretch if two
identical springs support the same single
weight as shown?
(b) What is the “effective” spring constant of
the double-parallel spring?
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Hooke’s Law: Two springs “in series”
•
•
•
Consider a spring that stretches an amount
x1 = F/k1 when a load of weight F is
suspended from it.
(a) How much will the spring stretch if two
identical springs support the same single
weight as shown?
(b) What is the “effective” spring constant of
the double-series spring?
Term Test 1 Info
• The first term test in PHY131H1F will be written
on Tuesday, Oct 6, from 6:10 to 7:30 pm.
• It will be based on Wolfson Chapters 1-4, plus the
related material in classes 1-6, practicals 1 and 2,
and MasteringPhysics problem sets 1 and 2.
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Term Test 1 Info
• The room you will write in is based on the first few letters
of your last name. You must attend the correct room, or
you will not be allowed to write the test:
•
•
•
•
•
•
•
A – HN: EX100
HO – N: EX200
O – SA: EX300
SE – TO: EX310
TR – W: EX320
X – YO: GB404
YU - Z: GB405
• EX is the Exam Centre at
255 McCaul Street
• GB is the Galbraith
Building at 35 St. George
Street.
• Alternate sitting students will receive a separate email by
Oct.2 letting you know the room and time.
Term Test 1 Info
• Please be sure to bring your T-Card, as invigilators will be
collecting signatures and checking your photo-ID.
• Allowed aids include a pocket calculator with no
communication ability, a single hand-written aid-sheet
prepared by you, no larger than 8.5”x11”, written on both
sides, a hard-copy English translation dictionary, and a
ruler.
• If you wish to see the first page of the test and read the
instructions, I have posted it at
http://www.physics.utoronto.ca/~jharlow/teaching/phy131f
15/test1FirstPages.pdf . (See the announcement today on
portal.)
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Term Test 1 Info
• During the test, you must leave your other belongings at
the designated location (front or back) of the room.
• You may bring a small sized paper or plastic bag to
contain your valuables (wallets, powered-off electronic
devices such as cell-phone and tablet, etc.) under your
seat.
• At the end of the test at 7:30 pm, you must stop writing
and put your pen/pencil down the very moment the
invigilators declare the test over.
• Immediately put your answer sheet inside the question
paper and have it ready to hand to the invigilator who will
be picking it up.
• Please remain seated until you are told you can leave.
Before Class 7 on Monday
• Please read "Introduction to Uncertainty in
Physical Measurements".
• I have placed the document in the "Class Slides"
section on portal.
• This material will not be on test 1 on October 6,
but it will be included on test 2 on Nov.17, and the
final exam.
• Something to think about: If your height is 150
cm, is there necessarily an uncertainty in that
number?
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