8.4 Elastic Collisions in One Dimension

8.4 Elastic Collisions in One Dimension

  • The electrocardiogram and the echocardiogram are used more often in the practice of cardiology.
  • It's useful in describing crashes.
    • Much of what we know about atomic and subatomic particles comes from collision experiments.
  • It is essential to our explorations of atomic and subatomic particles that the conserved of momentum principle is applied to the objects.
    • Researchers evaluate the results of giant machines throwing particles at one another by assuming a certain amount of momentum.
  • Particles and their properties are invisible to the naked eye, but can be measured with our instruments, and models of these particles can be constructed to describe the results.
    • Massless particles that compose light are considered to be a property of momentum.
    • The property of particles hints at an identity beyond the description of an object's mass.
    • Waves have a fundamental role to play in what we take and how we take them.
    • The conserved of momentum principle is valid when considering systems of particles.
    • This principle is used to analyze the mass and other properties of previously undetected particles, such as the nucleus of an atom and the existence of quarks that make up particles of nuclei.
    • This observation is considered nearly direct evidence of quarks because it implies a very small and dense particle makes up the protons.
    • The same principle that works well on the large scale was used in the analysis.
  • A particle moves backwards from a target particle.
    • In some experiments, electrons were seen to move backwards from a protons.
  • There are various types of two-object collisions.
    • Many of the physical principles involved in a collision are shown in these collisions.
    • The net external force on a system can't be used unless it's zero.
  • The elastic collision of two objects moving along the same line is a one-dimensional problem.
  • The only way to achieve elastic collisions is with subatomic particles.
    • It can be very nearly, but not quite elastic, because some energy can be converted into other forms of energy.
    • Two steel blocks on ice are nearly elastic.
    • There is a collision between two carts on an air track.
    • Icy surfaces and air tracks are more elastic than they used to be.
  • The energy of the internal and external is conserved.
  • The equations can be used to solve problems involving one-dimensional elastic collision between two objects.
  • An elastic collision conserves internal energy and the sum of energy before and after the collision equals the sum after the collision.
  • In a one-dimensional collision the equation is expressed.
  • If you visualize what the initial conditions mean, a small object strikes a larger object that is at rest.
  • Two independent equations are needed to find two unknowns.
    • The above two equations can be used because the collision is elastic.
    • Both can be simplified by the fact that object 2 is at rest.
    • We combine the equations to solve for unknowns once we simplify them.
  • To solve this problem, use the conserved of momentum.
  • Substituting this expression into the second equation eliminates the variable and leaves the equation as an exercise for the reader.
  • Both solutions may or may not be meaningful.
    • The first solution is the same as the initial one.
    • The situation before the collision is represented by the first solution.
    • Negative means that the first object bounces back.
  • The result is reasonable.
    • A small object hits a larger one at rest.
    • The larger one was knocked forward with a low speed.