Chapter 6

Applications of Newton’s Laws

What keeps Leo in his seat when the train stops?

Units of Chapter 6

• Frictional Forces

• Strings and Springs

• Translational Equilibrium

• Connected Objects

• Circular Motion

6-1 Frictional Forces

Kinetic Friction

Kinetic friction: the friction experienced by surfaces sliding against one another

Static Friction

Real-World Physics – Tires use Static Friction!

Static Friction

(6-2)

where

(6-3)

The static frictional force is also independent of the area of contact and the relative speed of the surfaces.

ConcepTest 6.4ConcepTest 6.4 FrictionFriction

1) the force from the rushing air pushed

it off

2) the force of friction pushed it off

3) no net force acted on the box

4) truck went into reverse by accident

5) none of the above

A box sits in a pickup truck

on a frictionless truck bed.

When the truck accelerates

forward, the box slides off

the back of the truck

because:

Generally, the reason that the box in the truck bed would move

with the truck is due to frictionfriction between the box and the bed.

If there is no friction, there is no force to push the box along, If there is no friction, there is no force to push the box along,

and it remains at rest.and it remains at rest. The truck accelerated away, essentially

leaving the box behind!!

ConcepTest 6.4ConcepTest 6.4 FrictionFriction

1) the force from the rushing air pushed

it off

2) the force of friction pushed it off

3) no net force acted on the box

4) truck went into reverse by accident

5) none of the above

A box sits in a pickup truck

on a frictionless truck bed.

When the truck accelerates

forward, the box slides off

the back of the truck

because:

Antilock brakes keep the

car wheels from locking

and skidding during a

sudden stop. Why does

this help slow the car

down?

1) k > s so sliding friction is better

2) k > s so static friction is better

3) s > k so sliding friction is better

4) s > k so static friction is better

5) none of the above

ConcepTest 6.5ConcepTest 6.5 Antilock BrakesAntilock Brakes

Antilock brakes keep the

car wheels from locking

and skidding during a

sudden stop. Why does

this help slow the car

down?

1) k > s so sliding friction is better

2) k > s so static friction is better

3) s > k so sliding friction is better

4) s > k so static friction is better

5) none of the above

Static friction is greater than sliding frictionStatic friction is greater than sliding friction, so

by keeping the wheels from skidding, the static

friction force will help slow the car down more

efficiently than the sliding friction that occurs

during a skid.

ConcepTest 6.5ConcepTest 6.5 Antilock BrakesAntilock Brakes

Example

• Leo goes down a playground slide that is inclined at an angle of 24.5˚ below the horizontal. Find his acceleration given that the coefficient of kinetic friction between the child and the slide is 0.375

6-2 Strings and Springs

6-2 Strings and Springs

ConcepTest 6.1aConcepTest 6.1a Tension ITension I

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

You tie a rope to a tree and you

pull on the rope with a force of

100 N. What is the tension in

the rope?

The tension in the rope is the force that the rope “feels”

across any section of it (or that you would feel if you

replaced a piece of the rope). Since you are pulling with

a force of 100 N, that is the tension in the rope.

ConcepTest 6.1aConcepTest 6.1a Tension ITension I

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

You tie a rope to a tree and you

pull on the rope with a force of

100 N. What is the tension in

the rope?

Follow-up:Follow-up: How hard is the tree pulling? How hard is the tree pulling?

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

Two tug-of-war opponents each

pull with a force of 100 N on

opposite ends of a rope. What

is the tension in the rope?

ConcepTest 6.1bConcepTest 6.1b Tension IITension II

This is literallyliterally the identical situation to the previous

question. The tension is not 200 N !!The tension is not 200 N !! Whether the other

end of the rope is pulled by a person, or pulled by a tree,

the tension in the rope is still 100 N100 N !!

1) 0 N

2) 50 N

3) 100 N

4) 150 N

5) 200 N

Two tug-of-war opponents each

pull with a force of 100 N on

opposite ends of a rope. What

is the tension in the rope?

ConcepTest 6.1bConcepTest 6.1b Tension IITension II

Springs

6-3 Translational Equilibrium

When an object is in translational equilibrium, the net force on it is zero:

(6-5)

6-3 Translational Equilibrium

Example

• A picture hangs on the wall suspended by two strings, as shown in the figure. The tension in string 1 is 1.7 N.– Find the tension in string 2– Find the weight of the

picture

Group Exercise

• A spring with a force constant of 120 N/m is used to push a 0.27-kg block of wood against a wall, as shown in the figure. (a) Find the minimum compression of the spring needed to keep the block from falling, given that the coefficient of static friction between the block and the wall is 0.46.

6-4 Connected Objects

When forces are exerted on connected objects, their accelerations are the same.

6-4 Connected Objects

We treat each box as a separate system:

6-4 Connected Objects

If there is a pulley, it is easiest to have the coordinate system follow the string:

Announcements, 10/8

• Homework due Friday

• Extra credit lecture: Today, right after class, Humanities auditorium– Remember to write up a 250 word essay

about what you learned and what it meant to you. Do this soon – you don’t want to forget!

Example

• Referring to the figure with masses shown, find the tension in the string connecting– m1 and m2

– m2 and m3. Assume the table is frictionless.

6-5 Circular Motion

An object moving in a circle must have a force acting on it; otherwise it would move in a straight line.

The direction of the force is towards the center of the circle.

Centripetal Force

This force may be provided by the tension in a string, the normal force, or friction, among others.

ConcepTest 6.9ConcepTest 6.9 TetherballTetherball1) Toward the top of the poleToward the top of the pole

2) Toward the groundToward the ground

3) Along the horizontal component of Along the horizontal component of the tension forcethe tension force

4) Along the vertical component of the Along the vertical component of the tension forcetension force

5) Tangential to the circleTangential to the circle

In the game of tetherball, In the game of tetherball,

the struck ball whirls the struck ball whirls

around a pole. In what around a pole. In what

direction does the direction does the net net

forceforce on the ball point? on the ball point?

W

T

The vertical component of the vertical component of the

tensiontension balances the weightweight. The

horizontal component of tensionhorizontal component of tension

provides the centripetal forcecentripetal force that

points toward the center of the

circle.

1) Toward the top of the poleToward the top of the pole

2) Toward the groundToward the ground

3) Along the horizontal component of Along the horizontal component of the tension forcethe tension force

4) Along the vertical component of the Along the vertical component of the tension forcetension force

5) Tangential to the circleTangential to the circle

In the game of tetherball, In the game of tetherball,

the struck ball whirls the struck ball whirls

around a pole. In what around a pole. In what

direction does the direction does the net net

forceforce on the ball point? on the ball point?

W T

W

T

ConcepTest 6.9 ConcepTest 6.9 TetherballTetherball

You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you?

(1) You are thrown to the right

(2) You feel no particular change

(3) You are thrown to the left

(4) You are thrown to the ceiling

(5) You are thrown to the floor

ConcepTest 6.10aConcepTest 6.10a Around the Curve IAround the Curve I

You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you?

(1) You are thrown to the right

(2) You feel no particular change

(3) You are thrown to the left

(4) You are thrown to the ceiling

(5) You are thrown to the floor

ConcepTest 6.10aConcepTest 6.10a Around the Curve IAround the Curve I

The passenger has the tendency to

continue moving in a straight line. From

your perspective in the car, it feels like

you are being thrown to the right, hitting

the passenger door.

(1) centrifugal force is pushing you into the door

(2) the door is exerting a leftward force on you

(3) both of the above

(4) neither of the above

During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?

ConcepTest 6.10bConcepTest 6.10b Around the Curve IIAround the Curve II

(1) centrifugal force is pushing you into the door

(2) the door is exerting a leftward force on you

(3) both of the above

(4) neither of the above

During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?

The passenger has the tendency to

continue moving in a straight line. There

is a centripetal force, provided by the

door, that forces the passenger into a

circular path.

ConcepTest 6.10bConcepTest 6.10b Around the Curve IIAround the Curve II

Centripetal Force

The magnitude of the force is given by:

Banked Roads and Dips

Summary of Chapter 6

• Friction is due to microscopic roughness.

• Kinetic friction:

• Static friction:

• Tension: the force transmitted through a string.

• Force exerted by an ideal spring:

Summary of Chapter 6

• An object is in translational equilibrium if the net force acting on it is zero.

• Connected objects have the same acceleration.

• The force required to move an object of mass m in a circle of radius r is: