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2D Collision Vector Diagram

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About This Diagram

This visualization shows how momentum is conserved independently in both the x and y directions during a 2D collision. Adjust the angles of the incoming objects to see how the momentum vectors change.

Key Equations

For 2D collisions, momentum is conserved in each direction:

X-direction: \(\(m_1v_{1x,i} + m_2v_{2x,i} = m_1v_{1x,f} + m_2v_{2x,f}\)\)

Y-direction: \(\(m_1v_{1y,i} + m_2v_{2y,i} = m_1v_{1y,f} + m_2v_{2y,f}\)\)

Visual Elements

  • Blue Arrow: Object 1 velocity vector (2 kg)
  • Red Arrow: Object 2 velocity vector (3 kg)
  • Purple Arrow: Total momentum vector
  • Dashed Lines: Vector components (vx and vy)
  • Calculation Box: Shows momentum calculations

Controls

  • Object 1 Angle: Direction of first object's velocity (0-360°)
  • Object 2 Angle: Direction of second object's velocity (0-360°)

Key Observations

  1. Total momentum vector (purple) is the same before and after
  2. x-component of total momentum is conserved separately
  3. y-component of total momentum is conserved separately
  4. Individual object momenta can change, but the sum remains constant

Strategy for 2D Collision Problems

  1. Set up coordinate system (x and y axes)
  2. Resolve all velocities into components
  3. Apply conservation of momentum to x and y separately
  4. Solve the system of equations
  5. Convert back to magnitude and direction