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PHY131H1F - Class 6

• 4.5 Solving Force Problems

• 4.6 Newton’s Third Law

• The Normal Force

• Hooke’s Law

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. The magnitude of the force the truck applies to the car.

B. The magnitude of the force the car applies to the truck.

C. The magnitude of the two forces are the same.

D. We must know the angle to answer this question.

E. We must know the masses of the truck and the car to

answer this question.

𝑎

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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 content-

remembering 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.

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1 on 22 on 1 FF

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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.

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

A Mack Truck drives North on the highway, and

collides head-on with a mosquito. Which is true?

Clicker Question

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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

• 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.

Clicker Question

Basketball/Earth Gravity Interaction

• The Earth is pulling down on the ball.

• The ball is pulling up on the Earth.

a =Fm

a =F

m

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Remember this clicker question from the beginning?

𝑎

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.

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

Clicker Question

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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

• 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.

𝐹𝑠 = −𝑘𝑥

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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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• 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?

Hooke’s Law: Two springs “in series”

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

• Alternate sitting students will receive a separate email by

Oct.2 letting you know the room and time.

• EX is the Exam Centre at

255 McCaul Street

• GB is the Galbraith

Building at 35 St. George

Street.

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?