Pi From Collisions

Key formulas

• $$N_{\text{collisions}} = \lfloor \pi \cdot 10^{N} \rfloor$$

  π from colliding blocks

  $N_{\text{collisions}}$

  Number of collisions

  $N$

  Mass ratio exponent: the big block is 100ᴺ times heavier

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• $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$

  Conservation of momentum

  $m_1$

  Mass of body 1kg

  $u_1$

  Velocity of body 1 beforem/s

  $m_2$

  Mass of body 2kg

  $u_2$

  Velocity of body 2 beforem/s

  $v_1$

  Velocity of body 1 afterm/s

  $v_2$

  Velocity of body 2 afterm/s

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• $$K = \tfrac{1}{2} m v^{2}$$

  Kinetic energy

  $K$

  Kinetic energyJ

  $m$

  Masskg

  $v$

  Speedm/s

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