Physics 1600 8. Systems of particles

from Physics 1600 Review Plan

Physics 1600 8. Systems of particles 8.1 Basic formulation …227

• Divide forces into internal and external
  • The boundary of the “system” here is arbitrary.
  • On that basis, the sum of internal forces is 0.
  • Therefore, if we consider a collection of particles as a single system, we can focus on the external forces only in the discussion.
  • 8.2 Center of mass…232
• External Force = 0 and
• Center of Mass Frame
• 
• Consider the motion of multiple objects in the center of mass frame.
  • At this time, if there is no external force, the momentum in the center of mass frame is 0. This can be said by using the Galilean transformation.
    • → Does this mean it becomes an elastic collision?
    • It doesn’t matter, momentum is conserved anyway, and whether KE is conserved depends on the situation.
  • ==COM velocity is constant = total momentum is constant = No external force==
• reduced mass
  • 
  • It is commonly seen, so let’s use a symbol for it. 8.3 Examples…235 8.3.1 Perfectly inelastic collisions …236
• If momentum is conserved, the COM velocity is constant, I see.
  • No external force and acceleration, so I understand.
  • At this point, KE is not conserved. 8.3.2 Inverse inelastic collisions …237 8.3.3 Gravitational and other external forces … … … . 240 8.3.4 The “push-me-pull-you”…241 8.4 Momentum and energy…245
• Check the implications here (blu3mo) 8.4.1 How to catch an egg…246 8.5 Mass and momentum flow problems …249 8.5.1 Rocket propulsion…250
• Whole system: p(t+Δt)-p(t) = external force * Δt
  • Mass does not change.
  • Gravity, etc. become external forces.
• 
• In Newtonian mechanics, we cannot handle changes in mass, but here we are dealing with systems with constant mass, so it’s safe.
  • I see (blu3mo) (blu3mo)
• As a technique, you can eliminate the infinitesimal limit squared term like dmdt.
  • If you don’t differentiate more than dp/dt, it will eventually become 0 no matter what you do. 8.5.2 Falling raindrop…253 8.5.3 Momentum transport by stream of particles … … . 254
• Is this essentially the same as air drag? (blu3mo) (blu3mo) (blu3mo)
  • square 8.5.4 Gas Pressure…257 8.6 Energy in systems …259
• Does energy remain the same even if the coordinates change? (blu3mo)
• 
  • No, V changes with Galilean transformation.

8.6.1 Formulation …259 8.6.2 Forces and potential energy …267 8.6.3 Energy using COM coordinates …270 8.7 Simultaneous application of momentum and energy techniques 271 8.7.1 Scattering processes…272 8.8 Center of mass of continuous mass distributions … … . . 275