Two setups are available: an airtrack with gliders of various masses and a grooved track with low-friction carts. The airtrack is connected to an air blower that creates an air “pillow” for the gliders. The low-friction carts are silent and can be loaded with additional masses. The carts and the ends of the track have strong magnets to repel each other. Both setups demonstrate a variety of concepts including velocity, acceleration, conservation of momentum, elastic and inelastic collisions, etc.

Materials:

• Airtrack
• Gliders with magnets
• Air blower with connecting hose
• Wooden block for acceleration measurements
• Photogate timer
• Auxiliary timer
  And/or
• Flat track
• Low-friction carts
• Masses

Demo:

Two options are available:

• Air Track with Gliders: This demonstration can be used to model elastic and inelastic collisions between two masses in a low-friction system created by a cushion of air flowing beneath the gliders. The gliders and track are equipped with magnets on each end which can be used to attract or repel the gliders to or from one another (Figure 2)
• Low-friction Track with Variable Mass Carts: This demonstration models elastic collisions between variable masses in a low-friction system.  The track and carts are equipped with magnets to repel the carts from one another (Figures 1 and 3).

Explanation:

In an ideal and frictionless system, an elastic collision between two masses, m₁ and m₂, with initial velocities v and u, results in a transfer of momentum between the masses

(p_initial)_total = (p_final)_total 

m₁v + m₂u = m₁v’ + m₂u’

where v’ = u and u’ = v and m₁ = m₂, as follows

m₁v + m₂u = m₁u + m₂v.

In a system with constant potential energy (i.e., a level track), the kinetic energy before and after the collision looks like

½m₁v² + ½m₂u² = ½m₁v’² + ½m₂u’²

In this case, both kinetic energy and momentum are conserved, however in an inelastic collision, only momentum is conserved because some kinetic energy is converted into energy released by friction between the two masses.

In an inelastic collision, the two masses stick together and move off with a final velocity, V, becoming a single mass M,

M = m₁ + m₂

with their momentum combining linearly

m₁v + m₂u =  MV.

Note that for masses moving in opposite directions relative to one another, one of the velocities can be expressed as negative, reversing the direction of each mass in an elastic collision or decreasing the final velocity in an inelastic collision.

Notes:

• Level the tracks prior to use.
• The blower for the air track is noisy and disruptive to lecture.

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Written by Lydia Seymour