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Section Summary

PhysicsSection Summary

8.1 Linear Momentum, Force, and Impulse

  • Linear momentum, often referenced as momentum for short, is defined as the product of a system’s mass multiplied by its velocity, p = mv.
  • The SI unit for momentum is kg m/s.
  • Newton’s second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes, F net = Δp Δt F net = Δp Δt .
  • Impulse is the average net external force multiplied by the time this force acts, and impulse equals the change in momentum, Δp= F net Δt Δp= F net Δt .
  • Forces are usually not constant over a period of time, so we use the average of the force over the time it acts.

8.2 Conservation of Momentum

  • The law of conservation of momentum is written ptot = constant or ptot = ptot (isolated system), where ptot is the initial total momentum and ptot is the total momentum some time later.
  • In an isolated system, the net external force is zero.
  • Conservation of momentum applies only when the net external force is zero, within the defined system.

8.3 Elastic and Inelastic Collisions

  • If kinetic energy is conserved, the collision is elastic. If they stick together, the collision is perfectly inelastic.
  • Kinetic energy is conserved in an elastic collision, but not in an inelastic collision.
  • The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes. Choose a coordinate system with the x-axis parallel to the velocity of the incoming particle.
  • Two-dimensional collisions of point masses, where mass 2 is initially at rest, conserve momentum along the initial direction of mass 1, or the x-axis, and along the direction perpendicular to the initial direction, or the y-axis.
  • Point masses are structureless particles that cannot spin.
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