Momentum & Energy

CONSERVATION OF ENERGY

Used generally when an object changes height, or when a spring is involved, etc.

  1. Choose the initial and final points for the energy conservation equation
  2. Determine what types of energies, KE, PE(gravitational), and PE(spring), are present at the initial and final positions,
    and if any work (W=F d cosq) is done between the two points
  3. Set the Initial energies plus any work done equal to the final energies.

KE + PE(gravitational) + PE(spring) + W = KE’ + PE’(gravitational) + PE’(spring)


CONSERVATION OF MOMENTUM

Used generally for all collisions

  1. Choose the initial and final points for the momentum conservation equation.
  2. Label a coordinate axis (x,y,z)
  3. Find the x, y, and z components of all the initial and final point velocities.
  4. For each direction (x,y,z), write a conservation of momentum equation using the initial and final momentums (p=mv) for each object obtained from the velocity components and the mass
    m1 v1x + m2 v2x = m1 v1x’ + m2 v2x’ (for x-direction)
    m1 v1y + m2 v2y = m1 v1y’ + m2 v2y’ (for y-direction)
    m1 v1z + m2 v2z = m1 v1z’ + m2 v2z’ (for z-direction)

REMEMBER:

  1. W = F d cosq, where q is the angle between the Force and the displacement. This indicates that if the force is in the opposite direction of the displacement, the Work is negative.
  2. Positive Work means that energy is being put into the system, while Negative Work means that energy is being removed from the system
  3. Conservation of Momentum equations can be used in all collisions without external forces.
  4. Conservation of KE can be used only when the collision is elastic.
  5. If there are any external forces on the system, momentum is not conserved for that system, thus a Conservation of Momentum equation should NOT be used between these two points.

 Page developed by CAPS Tutor, Tyson Schroeder 11/01/01