Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling...

55
Chapter 6 Applications of Newton’s Laws

Transcript of Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling...

Page 1: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

Chapter 6

Applications of Newton’s Laws

Page 2: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 2

Applications of Newton’s Laws

• Friction

• Drag Forces

• Motion Along a Curved Path

• The Center of Mass

Page 3: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 3

The microscopic area of contact is proportional to the

normal force.

The normal force is the same in both of the above orientations.

Microscopic Surface Area

Page 4: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 4

Microscopic Surface Area

• When one flat surface rests on another it is only the

high points of each surface that are actually in

physical contact.

• The actual physical contact area can be less than 1%

• This has important consequences for heat ransfer in

a vacuum.

Page 5: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 5

83µm

Polished Steel Surface

The diameter of a human hair is on average 100µm.

The vertical scale is expanded 10x relative to the horizontal

scale.

Page 6: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 6

Computer Graphic of Nickel Probe on

Gold Substrate

Gold atoms adhere to the nickel probe after contact.

This is a microscopic example of the adhesion that contributes

to the force of frition

Page 7: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 7

Static and Kinetic Friction

Static friction has a range of values up to a maximum

Page 8: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 8

Frictional Coefficients

Page 9: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 9

Rolling Friction

r rf = µ N

Page 10: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10

Rolling Friction

The tire will adhere to the road to some extent. The

peeling away of the tire from the road is the source of

rolling friction

r

r

µ

µ

≤ ≤

≤ ≤

0.01 0.02 Tires on concrete

0.001 0.002 Steel wheels on a steel rail

Page 11: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 11

Finding µs with Tanθ

s s

s

f =µ mgcosθ = mgsinθ

mgsinθ sinθµ = = = tanθ

mgcosθ cosθ

Page 12: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 12

Is This Analysis Realistic?

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MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 13

Force Diagram for - Is It Realistic?

• Part of T, the vertical component,

is offsetting the weight of the sled

and reducing the size of the

normal force.

• The horizontal component of T

appears larger than the frictional

force f.

• The unbalanced force in the x-

direction causes an acceleration of

the sled. Can old Dad keep the

tension constant?

Page 14: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 14

With Friction - All Set to Slide

µk = 0.54

m1 = 7 kg

m2 = 5 kg

Find µs and the acceleration

Page 15: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 15

All Set to Slide means fs = fsmax

1 2 1 2

1 2

2

1

( )

0

50.71

7

x s

s

s

F m g m g m m a

m g m g

mm

µ

µ

µ

= − + = +

− + =

= = =

2

1 2 1 2

2 1

1 2

( )

1.0

k

k ms

m g m g m m a

m ma g

m m

µ

µ

− + = +

−= =

+

Static friction

Dynamic friction

Page 16: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 16

The Toboggan Problem is the Milk Carton

Problem

Except we didn’t want the milk carton to travel

with the table cloth but we do want the children to

travel with the toboggan.

Page 17: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 17

The Runaway Buggy

Questions: What is the minimum stopping distance, D?

What is the force exerted on the buggy?

There is only friction between the skates and the ice while the buggy slides

with no friction

Page 18: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 18

The Runaway Buggy

Two masses loosely coupled together. Only the

adult’s skates experience friction.

Treated as one mass for inertial purposes

Treated as separate masses for normal force

and friction considerations.

fk

Na

N

magmg

Page 19: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 19

The Runaway Buggy - The Buggy Alone

Two masses loosely coupled together. Only the

adult’s skates experience friction.

Treated as one mass for inertial purposes

Treated as separate masses for normal force

and friction considerations.

N

mg

FYB

a

Page 20: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 20

The Runaway Buggy - A Neater Solution

∑k k a k a

x k a

k a a

k a

a

f = µ N = µ m g

F = - f = (m + m)a

-µ m g = (m + m)a

-µ ma = g

m + m

N

mg

FYB

a

kYB

a

µ mF = m a = g

m1+

m

Page 21: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 21

The Runaway Buggy - Stopping Distance

Let D be the stopping distance. Since we have velocities,

acceleration and a distance we choose the following:

2 2

f o

2

o

2 2

o o

a k

v = v + 2a∆x

0 = v + 2aD

-v vmD = = 1+

2a m 2µ g

Page 22: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 22

The Runaway Buggy Example

⇒B

Y a

m m

m m

Page 23: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 23

Air Resistance

Page 24: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 24

Air Resistance

When the drag force due to

air resistance equals the force

due to gravity the net force on

the falling object is zero

There is no more acceleration.

The velocity stays constant

from that point on. This is

referred to as the terminal

velocity.

Page 25: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 25

Air Resistance

The force of air resistance is proportional to a power of the

velocity of the falling object.

Page 26: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

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212

0ρ= − =∑ yF mg C Av

12

2

ρ

=

mgv

C A

( ) =F v bv

∑ yF = mg - bv = 0

mgv =

b

( ) 212

ρ=F v C Av

where ρ is the density of the medium through which the object falls,

A is the cross sectional area of the object, and C is a constant known

as the drag coefficient and is related to the shape and texture of an

object.

Air Resistance Models

Linear Model Quadratic Model

Page 27: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

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Vertical Position

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0 0.5 1 1.5

Tim e (sec)

He

igh

t (m

)

Air Resistance

Free Fall

Air Resistance

The free fall curve has a term proportional to t2. With air

resistance the acceleration goes to zero. Its distance curve is

proportional to t.

Page 28: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 28

Vertical Velocity

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 0.5 1 1.5

Tim e (sec)

Ve

loc

ity

(m

/s)

Vertical Velocity

Free Fall

Air Resistance Time Constant

122

ρτ

=

m

gC A

• The time constant represents the

characteristic time interval in the

problem. This is the size of the time

interval over which important event in the

problem take place.

• It takes a time interval about three (3)

time constants in length for the velocity of

the filter to reach 95% of terminal

velocity. This time is indicated by the first

vertical line in the Distance and Velocity

graphs.

• The second vertical line represents the

total fall time of the filter.

• The interval between these two lines is

the time period available for making

measurements of the terminal velocity.

Page 29: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 29

Vertical Velocity

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 0.5 1 1.5

Tim e (sec)

Ve

loc

ity

(m

/s)

Vertical Velocity

Free Fall

Air Resistance - Velocity vs

Time Graph

Page 30: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 30

Movement Along a Curved Path

Page 31: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 31

Movement Along a Curved Path

The derivation shows that

the centripetal acceleration

is 2

c

va =

r

If there is circular motion

then the acceleration has

this form.

Page 32: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 32

Relationships for Circular Motion

2

c

va =

r

2πω= 2πf =

T

v is the linear (tangential)

velocity (m/s).

r is the radius of the motion

f is the frequency (rev/s)

T is the period of the

motion (s)

Page 33: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 33

Centripetal Force

∑ r PW r

PW r

2

PW

F = F + mg = ma

F = ma - mg

vF = m - g

r

Page 34: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 34

∑ r PW r

PW r

2

PW

F = F + mg = ma

F = ma - mg

vF = m - g

r

∑ r PW r

PW r

2

PW

F = F - mg = ma

F = ma + mg

vF = m + g

r

Page 35: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 35

Roller Coaster

H

Page 36: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 36

Conical Pendulum

Page 37: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 37

Conical Pendulum

y

2

x x

2

2

F = Tcosθ - mg = 0

mgT =

cosθ

vF = Tsinθ = ma = m

r

mg vsinθ = m

cosθ r

vgtanθ =

r

v = rgtanθ

Page 38: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 38

Banked Tracks

Page 39: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 39

Banked Track - No Friction

Page 40: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 40

Banked Track - No Friction

The component of the

normal force along the x-

axis is the centripetal

force. This is Fnsinθ.

Fn is equal to mg/cosθ.

Fnsinθ = mgsinθ/cosθ2

2

mv= mgtanθ

r

vtanθ =

rg

The same results as the conical pendulum

Page 41: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 41

Flat Tracks

Page 42: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 42

Flat Track - With Friction

In a flat track situation

the driver relys on

friction between his tires

and the track to stay on

the curve.

For some reason the

author ignores his center

of mass obsession on a

problem where it might

be usefulWhere should r be measured?

Inner tires, outer tires, center of

mass?

Page 43: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 43

Flat Track - With Friction

Require: 1 complete loop

in 15.2s without skidding

Page 44: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 44

Flat Track - With Friction

Require: 1 complete loop

in 15.2s without skidding

Page 45: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 45

Center of Mass Motion

Page 46: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 46

The Center of Mass

The center of mass follows a parabolic path.

Page 47: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 47

The Center of Mass

1 1 2 2

1 21 2

cm

cm

Mx mx m x

m mx x x

M M

= +

= +

The CM is a mass weighted displacement

Page 48: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 48

The Center of Mass

For equal masses the CM is mid way between them.

For unequal masses the CM is closer to the larger

mass.

Page 49: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 49

Problems

Page 50: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 50

The Sliding Block Problem

What is the scale reading while the block is sliding?

The forces don’t depend on the velocity.

Page 51: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 51

The Sliding Block Problem

The center of mass

approach is unnecessary

since the incline isn’t

moving.

The inclined problem is

analyzed with a non-rotated

coordinate system.

Then an acceleration result

from a rotated system is

pulled in. A component of

the result is then taken to

get the desired projection.

Page 52: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 52

The Sliding Block Problem

In the end the simplicity of

the situation is obscured.

Page 53: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 53

The Sliding Block Problem

The scale reading is just

the normal force of both

blocks. How much of their

weight is directed straight

down?

For m2 it is the entire

weight m2 g. For m1 it is

just the vertical projection

of m1gcosθ which is

m1gcos2θm2 g

m1gsinθ

m1gcosθ

( )2

n 1 2F = m cos θ + m g

Page 54: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 54

Extra Slides

Page 55: Chap 06H More Newton Newton.pdfMFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 10 Rolling Friction The tire will adhere to the road to some extent. The peeling away of the

MFMcGraw - PHY 2425 Chap_06H-More Newton-Revised 1/11/2012 55