e₁ = length of elastic + cradle (from point of attachment to point where handle touches the table) without tension
e₂ = additional length of elastic + cradle with tension
h₁ = height of table
h₂ = height of attachment point of the elastic above the table
l = distance from front edge of table to point where foam atom hits the floor
m_c = mass of cradle assembly
m_a = mass of foam atom
theta = angle between surface of table and (elastic + cradle) just before release
v(t) = velocity of atom at time t
v_x(t) = x component of velocity at time t
v_y(t) = y component of velocity at time t

The foam atom handle touches the table at time of release.
Neglect air resistance to movement. This is a pretty good, but not perfect, assumption. [The mass spectrometer performs pretyy much as expected for foam atoms with cores. However, a piece of foam by itself is so light that the air resistance effects cause it not to travel very far -- a clear violation of this assumption.]

KE(0) = energy stored in stretching the elastic = ½ k(e₂)² where k = the force constant of the elastic Note: we do not have to know the KE(0) in order distinguish atoms of differing weights. If one keeps e₂ constant for a series of experiments, KE will be constant. The (0) refers to "time = 0". This is the time at which the elastic has reached zero tension and no longer provides additional energy to the cradle and foam atom,

KE(0) = (1/2)(m_a + m_c)v(0)²

NOTE: If m_c >> m_a, then v(0) is barely affected by the value of m_a. In this case, the trajectories for foam atoms with different weights are nearly the same. This is why is is necessary to keep the weight of the cradle assembly as small as possible.

theta = arcsin(h₂/(e₁ + e₂))

y(0) = h₁ + (h₂ – e₁sin(theta))

x(0) = - e₁cos(theta)

vy(0) = v(0)sin(theta)

v_x(0) = v(0)cos(theta)

v_y(t) = v_y(0) – gt

v_x(t) = v_x(0)

y(t) = y(0) + v_y(0)t – 1/2gt²