collisions!bulldog2.redlands.edu/facultyfolder/eric_hill/phys231/lecture/lect 28 ppt.pdfmulti-step...

Wed.

Lab

Fri.

10.1-.4 Introducing Collisions Quiz 9

L9 Multi-particle Systems

10.6-.8 Scattering

RE 10.a

RE 10.b

Mon.,

Lab

Wed.,

Fri.,

10.9-.10 Collision Complications

L10 Collisions 1

10.5, .11 Different Reference Frames

1.1 Translational Angular Momentum Quiz 10

RE 10.c

EP9

RE 11.a; HW10: Pr’s 13*, 21, 30, “39”

Collisions! Short, Sharp Shocks

Collision: Operational definition: quick enough/strong enough interaction that all

others are negligible

Short, Sharp Example

System = ball

Can ignore Earth’s pull during “smack”.

Say an 0.5 kg ball is in contact is in contact with the

bat for 5 ms. During that time, it switches from going

forward at 100mph = 44.7 m/s to going 80 mph

backward = 35.8 m/s.

EF

Smack!

BF

EF

N050,8t

pFnet

s

smkgsmkg

005.0

/7.445.0/8.355.0

Of that, the Earth’s pull accounts for only

NsmkgmgF Eb 9.4/8.95.0 2

1-D Collision

A B

Pow! A B

Example

t

System = carts A & B

initially

finally

frictionAF

frictionBF

frictionAF

frictionAF

Often know initial motion, want to predict final motion

Two unknowns: and fAv .

fBv .

Generally need two equations to solve for them

0.. tFpFdt

pdextnetsystemextnet

system

A B

iAp .

iBp .

Pow! A B

fAp .

fBp .

Example

t


initially

finally

frictionAF

frictionBF

frictionAF

frictionAF

0

...)(

.

BA

frictionBfrictionABA

extnetsystemsystem

pp

tFFpp

tFp

If we look right before and right after collision

One of the Equations: Momentum Principle

1-D Collision

A B

iAp .

iBp .

Pow! A B

fAp .

fBp .

t


initially

finally

frictionAF

frictionBF

frictionAF

frictionAF

0 BA pp

0.... iBBfBBiAAfAA vmvmvmvm

csv '


1-D Collision

A space satellite of mass 500 kg

has velocity < 12, 0, –8 > m/s just

before being struck by a rock of

mass 3 kg with velocity

< –3000, 0, 900 > m/s.

After the collision the rock’s

velocity is < 700, 0, –300 > m/s.

Now what is the velocity of the

space satellite?

a. < –5100, 0, –400 > m/s

b. < –10.2, 0, –0.8 > m/s

c. < 10.2, 0, 0.8 > m/s

d. < –3688, 0, 1191 > m/s

e. < 3688, 0, –1192 > m/s


A B

iAp .

iBp .

Pow! A B

fAp .

fBp .

t


initially

finally

frictionAF

frictionBF

frictionAF

frictionAF

0 BA pp


csv '


1-D Collision

Special Case: “Maximally Inelastic” – hit & stick

Other Equations: for “Maximally Inelastic”

fBfAf vvv

A squishy clay ball collides in

midair with a baseball, and

sticks to the baseball, which

keeps going.

Initial momenta:

and

Final momentum of clay+ball :

Which equation correctly describes

this collision?

1)

2)

3) CLAYp _1

BALLp _1

2p

BALLCLAY ppp _1_12

BALLCLAY ppp _1_12

BALLCLAY ppp _1_12

A bullet of mass m traveling

horizontally at a very high speed

v embeds itself in a block of

mass M that is sitting at rest on

a nearly frictionless surface.

What is the speed of the block

just after the bullet embeds

itself in the block?

(1) (4)

(2) (5)

(3)

v

vM

m

vmM

m

vmM

m

vm

mM

m v

Initial

final

?

M

Maximally Inelastic

1-D Collision Special Case: “Maximally Inelastic” – hit & stick

Multi-step Example: A 60kg kid’s on a swing, say she’s gotten herself going so that at

her highest her center of mass is 4m above the ground and when she swoops down her

center of mass is just 0.5 m above the ground. On her down-sweep, she reaches down

and picks up her 3kg backpack that’s sitting on the ground (maybe her cell phone

started ringing).

How high will she get on her upswing with the pack in her lap?

A B C D

YA = 4m

YB= YC = 0.5m

YD= ?

mk = 60kg

mb= 3kg

A B

iAp .

iBp .

Pow! A B

fAp .

fBp .

t


initially

finally

Second Equations: Energy Principle

1-D Collision 0& BAE

BABBAABA UEKEKE &int.int.&

(2)

(3)

(4)

(5)

(1)

22

2

1

2

1if mvv)mM(

22

2

1

2

1if mvMv

2

internal

2

2

1)(

2

1if mvEvmM

2

internal2

1imvE

internal

22

2

1)(

2

1EmvvmM if

Which is an accurate energy equation for this collision

for the system of bullet + block?

m v

Initial final

? M

Maximally Inelastic

A squishy clay ball collides in midair

with a baseball, and sticks to the

baseball, which keeps going.

Initial kinetic energies:

K1clay, K1baseball

Final kinetic energy of clay+ball :

Which equation correctly describes

this collision?

1) Kclay+ball= K1clay + K1baseball

2) Kclay+ball> K1clay + K1baseball

3) Kclay+ball< K1clay + K1baseball

final initial

A B

iAp .

iBp .

Pow! A B

fAp .

fBp .

t


initially

finally

02

.212

.212

.212

.21 iBBfBBiAAfAA vmvmvmvm

csv '

Second Equations: Energy Principle

1-D Collision 0& BAE


Special Case: Perfectly Elastic (all internal changes ‘bounce back’)


02222

2

.

2

.2

.

2

.

B

iB

B

fB

A

iA

A

fA

m

p

m

p

m

p

m

p

Which of the following is a property of all “elastic” collisions?

(1) The colliding objects interact through springs.

(2) The kinetic energy of one of the objects doesn’t change.

(3) The total kinetic energy is constant at all times -- before, during, and after the

collision.

(4) The total kinetic energy after the collision is equal to the total kinetic energy

before the collision.

(5) The elastic spring energy after the collision is greater than the elastic spring

energy before the collision.

1-D Collision

A B

Pow! A B

Example


initially

finally

frictionAF

frictionBF

frictionAF

frictionAF

Often know initial motion, want to predict final motion

Two unknowns: and fAv .

fBv .

Generally need two equations to solve for them

0& BABA ppp

True for all collisions

0&& BABABA UEEE

BB EK .intAA EK .int

A B

iAp .

iBp .

Pow! A B

fAp .

fBp .


initially

finally

02

.212

.212

.212

.21 iBBfBBiAAfAA vmvmvmvm csv '

1-D Collision



02222

2

.

2

.2

.

2

.

B

iB

B

fB

A

iA

A

fA

m

p

m

p

m

p

m

p

iBiAfBfA pppp ....

Equation 1

Equation 2

0

11

2

11

2

1 ..

2

....

2

.

A

iBiA

BA

iB

A

iAiBfB

BA

fBm

pp

mm

p

m

ppp

mmp

Deriving relation for Final Speed

1-D Collision

02222

2

.

2

.2

.

2

.

B

iB

B

fB

A

iA

A

fA

m

p

m

p

m

p

m

p

fBiBiAfA pppp ....

2...

2

. fBiBiAfA pppp


Equation 1

Equation 2

fBiAfBiBiBiAfBiBiAfA pppppppppp ......

2

.

2

.

2

.

2

. 222

Form of 0.

2

. cbpap fBfB Solved by a

acbbp fB

2

42

.

Ack!

0

11

2

11

2

1 ..

2

....

2

.

A

iBiA

BA

iB

A

iAiBfB

BA

fBm

pp

mm

p

m

ppp

mmp

Extra special case: Say B is initially stationary

1-D Collision Special Case: Perfectly Elastic (all internal changes ‘bounce back’)

A B

Pow! A B

fAp .

fBp .


initially

finally

011

2

1 ..

2

.

A

iAfB

BA

fBm

pp

mmp

BA

A

iAfB

mmm

pp

112 .

.

AB

iAB

mm

pm

.2

1



A B

Pow! A B

fAp .

fBp .


initially

finally

AB

iABfB

mm

pmp

.

. 2

fBiAfA ppp ...

AB

iABiAfA

mm

pmpp

.

.. 2

iA

AB

BAfA p

mm

mmp ..

iA

AB

AfB v

mm

mv ..

2

iA

AB

BAfA v

mm

mmv ..



A B

Pow! A B

fAp .

fBp .


initially

finally

iA

AB

A vmm

m.

2

iA

AB

BA vmm

mm.

iAv .2

iAv .

1 iAv .

0

𝑣 𝐵.𝑓 𝑣 𝐴.𝑓

𝑚𝐵

𝑚𝐴

Initially Stationary

𝑣 𝐴.𝑓 𝑣 𝐵.𝑓

Wed.

Lab

Fri.

10.1-.4 Introducing Collisions Quiz 9

L9 Multi-particle Systems

10.6-.8 Scattering

RE 10.a

RE 10.b

Mon.,

Lab

Wed.,

Fri.,

10.9-.10 Collision Complications

L10 Collisions 1

10.5, .11 Different Reference Frames

1.1 Translational Angular Momentum Quiz 10

RE 10.c

EP9

RE 11.a; HW10: Pr’s 13*, 21, 30, “39”

Collisions! Short, Sharp Shocks

P

mp

ipp .

T

mT

0. iTp

T

P

fpp .

fTp .

Fast (v~c) Collision

P

mp

0,0,.. ipip pp

T

mT

0. iTp

T

P

0,sin,cos ... pfppfpfp ppp

p

0,sin,cos ... TfTTfTfT ppp T

Conservation of Momentum


00sinsin:ˆ

0coscos:ˆ

0

..

...

...

TfTpfp

ipTfTpfp

ipfTfp

ppy

pppx

ppp

P

mp

0,0,.. ipip pp

T

mT

0. iTp

T

P


p



where

21cv

vmp


00sinsin:ˆ

0coscos:ˆ

0

..

...

...

TfTpfp

ipTfTpfp

ipfTfp

ppy

pppx

ppp

P

mp

0,0,.. ipip pp

T

mT

0. iTp

T

P


p



Conservation of Energy

0.... iTipfTfp EEEE

where

21cv

vmp


00sinsin:ˆ

0coscos:ˆ

0

..

...

...

TfTpfp

ipTfTpfp

ipfTfp

ppy

pppx

ppp

where

2

2

1cv

mcE

P

mp

0,0,.. ipip pp

T

mT

0. iTp

T

P


p



Conservation of Energy

0.... iTipfTfp EEEE

where

21cv

vmp


00sinsin:ˆ

0coscos:ˆ

0

..

...

...

TfTpfp

ipTfTpfp

ipfTfp

ppy

pppx

ppp

where

2

2

1cv

mcE

CW: show

By plugging that into it and

recovering that.

222mcpcE

collisions!bulldog2.redlands.edu/facultyfolder/eric_hill/phys231/lecture/lect 28 ppt.pdfmulti-step...

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