Esys  W  Q   psys  Fnet t   Lsys  nett Real vs. Point Particle System

July 13 2010 Chapter 9, Section 4-6 Real vs. Point: A cow

M = mass of cow

co2calculator.files.wordpress.com/2008/09/grazing-cow-1b.jpg Real System

 Use the actual physical shape of the object

 Contains all forms of energy in the system

 Translational, Rotational, Vibrational, Potential, Chemical, …

 Can have multi-object systems Point Particle System

 The system is a single point

 Located at Center of Mass

 Everything else is surroundings

 System only has Translational KE

 Work is done on the point f     K  W  F  dr  F  r trans  net cm net i Real vs. Point

 In both cases 1 K  Mv2 trans 2 cm  This is the same Kinetic Energy

 A real system will have additional behavior due to location of forces Example: The Jumper

F = mg Normal Normal Force Force

F = mg Clicker Question #1

 What force(s) contribute to total work in the Real System? F = mg

 A) Normal Force only Normal Force  B) Normal Force and Gravity

 C) Gravity only

 D) None, the feet never leave the ground so there is no work done Normal Force and Work

 Does not do work in real system

 A contact force

 Only exists when 2 objects touch

 Forces point of contact never moves

 Can do work in point system

 Can act on the COM over a distance

 Force is in contact at the COM, which moves Example: The Jumper

 Normal Force does not do work in real

system FN

Esys  Ktrans  EChem  Ethermal  mgh

 Normal Force does work in Point system

Ktrans  (FN  mg)h

Echem  Etherm  FN h

 Energy was used Example: Stretching a Spring

 Real System:

 Work done by each force separately

Espring  Wtot  Fl *rl  Fr *rr

 Point System

 Work done by net force only

Ktrans  W  Fnet *r  00 Why Use Point Particles

 Reduction in complexity

 Fewer forms of energy to worry about

 Allows easier calculation of vcm  Can make difficult problems simpler Limits of Point Particle

 Does not take into account all forms of energy

 Can’t give information about rotation, vibration, etc.

 Not Physical

 Does not indicate if the system is changing shape Example: Yo-Yo

 The hand moves up a distance d

 The Yo-Yo moves down a distance h

Esys  Ktrans  Krot  Whand WEarth

 Use point particle to

find Ktrans

 Then find Krot Yo-Yo –Point Particle

 System: yo-yo

 Surroundings

 Earth, Hand

Ktrans  W  Fnet ycm

ycm  h

Fnet  Fhand  mg

Ktrans  (mg  Fhand )h Yo-Yo –Real System

 System: yo-yo

 Surroundings

 Earth, Hand

Esys  Ktrans  Krot  Whand WEarth

Ktrans  Krot  Fhand d  (mg)(h)

Ktrans  (mg  Fhand )h

Krot  Fhand (d  h) Remember

 Point particles

 Have all of the forces acting on the object at the center of mass

 Only have Ktrans  Work done by net force

 Real system

 More general/physical

 Can have all available forms of energy

 Work done by individual forces