Mon. Tues. Wed. Lab Fri.11

9.4-.5 (.9) The “Point Particle” approximation 10.1-.4 Introducing Collisions Quiz 9 L8 Multi-particle Systems 10.6-.8 Scattering

RE 9.c EP8, HW9: Ch 9 Pr’s 34, 40, 43 RE 10.a RE 10.b

Center of Mass

Center of Mass

Dp=? DE =?

Work and Translational Kinetic Energy

What is the net work done on a multi-particle system?

A

C

B

AnetF .

BnetF .

CnetF .

C B

A

Br

D

Cr

D

Ar

D

CCnetBBnetAAnetCnetBnetAnetnet rdFrdFrdFWWWW

......

Each integral for each external force over the displacement of it’s point of application.

systemEWnet D

internalnaltranslatio EKWnet DD

internal

2

21 EMvW cmnet DD

particles

particleparticlenetnet rdFW

.

Over what distance was the force applied?

a) 0.03 m b) 0.04 m c) 0.07 m d) 0.08 m e) 0.10 m

Assume no friction; say you pulled horizontally with a constant 0.5N force, then the total work done on the system / total change in energy of the system was

netWE D system

D handhandsystem rdFE

handhandsystem rFE DD

mNEsystem 08.05.0D Nm04.0

A

C

B

Work and Translational Kinetic Energy

How is that split between translational and internal energy?

dt

vdM

dt

pdF cmtotal

net

cmcm

cmnet rddt

vdMrdF

dt

rdvMdrdF cm

cmcmnet

cmcmcmnet vdvMrdF

cmcmcmnet vdvMrdF

2

21

cmcmnet MvrdF D

Just like for a point particle

C B

A

c.m.

c.m.

systemEWnet D

internalnaltranslatio EKWnet DD

internal

2

21 EMvW cmnet DD

naltranslatiocm KW D""

a) 0.03 m b) 0.04 m c) 0.07 m d) 0.08 m e) 0.10 m

Assume no friction; say both blocks have the same mass, 0.1 kg (and the spring is much less massive), and you pulled horizontally with a constant 0.5N force, then the change in translational kinetic energy associated with the center of mass motion was

cmhandtrans rFK DD

mNKtrans 07.05.0D Nm035.0

D cmnettrans rdFK What is the center of mass’s final speed?

2

.212

.21

icmsystemfcmsystemtrans vmvmK D

system

transfcm

m

Kv

D

2.

s

m59.01.0*2

035.02

kg

J

If both blocks have the same mass, then through what distance did the center of mass travel while the force acted?

Work and Translational Kinetic Energy

CnetF .

Br

D

Cr

D

Ar

D

internal

2

21 EMvW cmnet DD 2

21"" cmcmnetcm MvrdFW D

and

so

internal"" EWW cmnet D or internal"" EWW cmnet D

A

C

B

c.m.

AnetF .

BnetF .

C B

A

c.m.

If we can independently calculate the net work and the work of translating the center of mass, the difference is change in internal energy.

a) 0 J b) 0.005 J c) 0.035 J d) 0.040 J e) 0.075 J

If both blocks have the same mass, by how much did the internal (vibrational kinetic + spring potential) change?

netWE D system

D handhandsystem rdFE

handhandsystem rFE DD

mNEsystem 08.05.0D Nm04.0

cmhandtrans rFK DD

mNKtrans 07.05.0D Nm035.0

D cmnettrans rdFK

internaltranssystem EKE DDD

mr 07.0cm D

mr 08.0hand D

Work and Translational Kinetic Energy

internalErdF cmnet D

Example systemEWnet D

Earthfloorwallextnet FFFF

.

System: skater

Active surroundings: wall, floor, Earth

EarthF

floorF

wallF

internalEKrdF naltranslatio

i

iinet DD

internalEKrdF naltranslatiohandwall DD

Stationary on wall While force applied

internalEK naltranslatio DD

internalErdF cmwall D

Drcm

Say an average force of 10 N applied as her center of mass moves 0.3 m. What change in internal energy?

internal

internal

3

3.010

EJ

EmN

D

D If she was initially at rest, and her mass is 50 kg, with what speed does she (her c.m.) leave the wall?

naltranslatioKD

2

.

2

.21

int icmfcm vvmE D

smvkg

Jfcm /35.0

50

6.

fcmv

m

E.

int2

D

0

Example: Pulling spinning puck

If it started from rest, how fast was it going at the end? What was its rotational kinetic energy? If a uniform disc of radius r, what was its angular speed?

System: Puck Active surroundings: Hand

Fhand Fhand

07_twodiscs.py

Drhand = d + L

Drcm =d

Lstring

m

r

puckEWnet D

ernalnaltranslatiohandhand EKrdF intDD

transcmhand KrdF D

2

.

2

.21

icmfcmhand vvmdF

m

dFv hand

fcm

2.

irothandhand EdFLdF D

irothand ELF D

22

21

ifdischand ILF

2

21 mrIdisc

disc

handf

I

LF2

2

4

mr

LFhand

transhand KdF D

You pull up with constant force F What is the change in translational kinetic energy of the box? 1) F*b – mg*b 2) F*a – mg*b 3) F*(a+b) – mg*(b) 4) F*(a+b) – mg*(a+b)

You pull up with constant force F What was the net work done on the box? 1) F*b – mg*b 2) F*a – mg*b 3) F*(a+b) – mg*(b) 4) F*(a+b) – mg*(a+b)

You pull up with constant force F

So the change in internal energy is

internalnaltranslatio EKWnet DD

internalEmgbFbmgbabF D

internalEFa D

Exercise: You have a box containing a squishy mass on a spring (initially at its equilibrium length); when you pull it sideways, the spring extends until the mass squashes against the far wall of the box. In terms of the labeled properties, if the ball is much more massive than the box or spring, A) What’s the center of mass’s speed? B) What’s the increase in the ball’s internal energy?

ks

m

Drhand = d

s

Fhand Fhand

Friction

Fhand Fhand

Ffloor.friction Ffloor.friction

Drcm = d

transcmnet KrdF D

Center of Mass Motion

2

21

. cmfrictionflhand MvdFF DIf forces are equal, no change in kinetic – constant speed.

Total Work and Energy

systemEWnet D

inttrans EKrdFi

ii DD

frictionfrictionflhand rdFdF

.

Over what distance is friction applied?

Friction

Mon. Tues. Wed. Lab Fri.

9.4-.5 (.9) The “Point Particle” approximation 10.1-.4 Introducing Collisions Quiz 9 L8 Multi-particle Systems 10.6-.8 Scattering

RE 9.c EP8, HW9: Ch 9 Pr’s 34, 40, 43 RE 10.a RE 10.b

Center of Mass

Center of Mass

Dp=? DE =?