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Chapter 7 Learning Objectives

*Note: Type-setting limitations do not allow for arrows on the vector labels, so we have used boldface only.

Concepts and Skills to Review

  • Acceleration (Section 3.3)
  • Newton's second law: force and acceleration (Section 3.4)
  • Components of vectors in two dimensions (Section 4.2)
  • Velocity and acceleration (Section 4.4)
  • Kinetic energy (Section 6.3)
  • Conservation of mechanical energy (Section 6.6)

Summary

  • Definition of linear momentum:
     p = mv (7-1)
  • During an interaction, momentum is transferred from one body to another, but the total momentum of the two is unchanged.
     Δp2 = -Δp1 
  • Impulse is the average net force times the time interval. The impulse equals the change in momentum:
     Δp = FΔt (7-2)
  • A conserved quantity is one that remains unchanged as time passes.
  • Impulse is the area under a graph of force vs. time.
  • Force is the rate of change of momentum.
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/image7_4.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> (7-4)
  • External interactions may change the total momentum of a system
  • Internal interactions do not change the total momentum of a system
  • Conservation of linear momentum: if the net external force acting on a system is zero, then the momentum of the system is conserved.
  • The position of the center of mass of a system of N particles is
     <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/image7_9a.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>  
    and<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/image7_9b.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> (7-9)
    where M is the total mass of the particles:
     M = m1 + m2 + ... + mN 
  • The total momentum of a system is equal to the total mass times the velocity of the center of mass:
     p = p1 + p2 + ... + pN = MvCM(7-11)
  • No matter how complicated a system is, the center of mass moves as if all the mass of the system were concentrated to a point particle with all the external forces acting on it:
     ΣFext = MaCM(7-13)
  • The center of mass of an isolated system moves at constant velocity.
  • Conservation of momentum is used to solve problems involving collisions, explosions, etc. Even when external forces are acting, the momentum of the system just before a collision is nearly equal to the momentum just after if the collision interaction is brief. The impulse, and therefore the change in momentum of the system, is small since the time interval is small.





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