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PHY131H1F - Class 8

• 5.1 Problem Solving with

Newton’s Second Law

• 5.2 Objects Connected by

Ropes and Pulleys

• 5.3 Circular Motion

Clicker Question

• A ball is whirled on a string in a vertical

circle. As it is going around, the tension

in the string is

A.greatest at the top of the motion

B.constant.

C.greatest at the bottom of the motion

D.greatest somewhere in between the top

and bottom.

Last day at the end of class I asked:

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2015 Nobel Prize in Physics

• Neutrinos are ubiquitous

subatomic particles with

almost no mass and

which rarely interact with

anything else, making

them very difficult to

study.

• Takaaki Kajita and Arthur

McDonald led two teams

which made key

observations of the

particles inside big

underground instruments

in Japan and Canada.

http://www.bbc.com/news/science-environment-34443695

Preparation for Practicals next

week:

• Take a ride on the Burton

Tower elevators!

• All 4 elevators in the 14-storey

tower of McLennan Physical

Labs are equipped with a

hanging spring-scale.

• It measures the upward force

necessary to support a 750 g

mass. (a.k.a. “weight”)

• You may find that the

measured weight of this object

changes as you accelerate –

record the numbers you see on

the way up and down.

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Self-adjusting forces

• The force of gravity, FG, has an equation for it which predicts

the correct magnitude (it’s always mg here on Earth).

• Normal force, Tension and Static friction are all self-adjusting

forces: there are no equations for these!!

• Normal force is whatever is needed to keep the object from

crashing through the surface.

• Tension is whatever is needed to keep the string or rope

from breaking.

• Static friction is whatever is needed to keep the object from

slipping along the surface.

• In all these cases, you must draw a free-body diagram and

figure out by using equilibrium and Newton’s 2nd law what

the needed force is.

Bob stands under a low concrete arch, and presses

upwards on it with a force of 100 N. Bob’s mass is 82

kg. He is in equilibrium. What is the total normal force

of the ground on Bob? (Note that 82 × 9.8 = 800.)

A. 800 N, upward

B. 800 N, downward

C.900 N, upward

D.700 N, upward

E. 900 N, downward

Clicker Question

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A cart of mass M is on a track

which is at an angle of θ above the

horizontal.

The cart is attached to a string

which goes over a pulley; the other

end of the string is attached to a

hanging mass, m.

What is the acceleration of the cart?

A ball rolls along a

frictionless track on a

horizontal table, as seen

from above in the figure.

The track is curved in ¾

of a circle. The ball rolls

clockwise around this

track and then emerges

onto the flat, frictionless

table. Which dashed

line most closely

represents the path of

the ball when it emerges

from the track?

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A string is attached to the rear-view mirror of

a car. A ball is hanging on the other end of

the string. The car is driving around in a

circle, at a constant speed. Which of the

following lists gives all of the forces directly

acting on the ball?

A. Tension

B. Tension, gravity, the centripetal force and

friction

C. Tension and gravity

D. Tension, gravity and the centripetal force

Clicker Question

Every curve has a radius

r = 75 m

r = 410 m

r = 730 m

Intersection of Highway 427

And Highway 401

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Unbanked Curve

Top View

Back View

r

What horizontal force acts

on the car to keep it on the

curved path?

A. Gravity

B. Normal

C.Kinetic Friction

D.Static Friction

E. Rolling Friction

Clicker Question

Banked Curve Example

A highway curve of radius 70.0

m is banked at a 15° angle. At

what speed v0 can a car take

this curve without assistance

from friction?

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A. n > w

B. n < w

C. n = w

D. We can’t tell about n without knowing v.

A car is rolling over the top of a hill at speed v. At this instant,

Clicker Question

A car is driving at the bottom of a valley at speed v. At this instant,

Clicker Question

A. n > w

B. n < w

C. n = w

D. We can’t tell about n without knowing v.

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Fictitious Forces

• If you are riding in a car that makes a sudden stop, you

may feel as if a force “throws” you forward toward the

windshield.

• There really is no such force!

• The real force is the backwards force of the dashboard

on you when you hit it.

• Some books (not Wolfson) describe the experience in

terms of what are called fictitious forces.

• These are not real, but they help describe motion in a

noninertial reference frame.

• Wolfson avoids fictitious forces by doing all the

calculations in inertial frames (better).

• This is what really happens in a sudden stop (no

forward forces on passenger):

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“Centrifugal Force” (a fictitious force)

• If the car you are in turns a

corner quickly, you feel

“thrown” against the door.

• The fictitious “force” that

seems to push an object to

the outside of a circle is

called the “centrifugal force”.

• It helps describe your

experience relative to a

noninertial reference frame.

• In the inertial frame of the

ground, the only real force is

toward the centre not away.

Reality:

Why Does the Water Stay in my coffee cup?

• Watch Harlow swing a cup of water over his head. If

he swings the cup quickly, the water stays in. But the

students in the front row will get a shower if he swings

too slowly.

•The minimum speed of the coffee up at the top of the

vertical path is that at which gravity alone is sufficient

to cause circular motion at the top.

𝑣𝑚𝑖𝑛 = 𝑔𝑟

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The point is: Normal force must always be away

from the surface. It can never be toward the

surface (unless the surface is covered with glue!)

More than enough angular speed

𝑣 > 𝑣𝑚𝑖𝑛

Just enough angular speed

𝑣 = 𝑣𝑚𝑖𝑛

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Not enough angular speed

𝑣 < 𝑣𝑚𝑖𝑛

Before Class 9 on Wednesday Oct. 14

• Please read the rest of Wolfson Chapter 5, and/or watch

the Pre-Class Video, now on portal.

• MasteringPhysics Problem Set 3 is due on Friday

evening.

• Something to think about:

Does friction always slow things down? Can friction ever

speed things up?

Happy Thanksgiving!