7.12 - Interactive problem: shuffleboard collisions
The simulation at the right shows a variation of the game of shuffleboard. The red
puck has an initial velocity of í2.0 m/s. You want to set the initial velocity of the blue
puck so that after the two pucks collide head on in an elastic collision, the red puck
moves with a velocity of +2.0 m/s. This will cause the red puck to stop at the scoring
line, since the friction in the green area on the right side of the surface will cause it
to slow down and perhaps stop.
The blue puck has a mass of 1.0 kilograms. The red puck’s mass is 3.0 kilograms.
Use the fact that the collision is elastic to calculate and enter the initial velocity of
the blue puck to the nearest 0.1 m/s and press GO to see the results. Press RESET
to try again.
7.13 - Inelastic collisions
Inelastic collision: The collision results in a
decrease in the system’s total kinetic energy.
In an inelastic collision, momentum is conserved. But kinetic energy is not conserved.
In inelastic collisions, kinetic energy transforms into other forms of energy. The kinetic
energy after an inelastic collision is less than the kinetic energy before the collision.
When one boxcar rolls and connects with another, as shown above, some of the kinetic
energy of the moving car transforms into elastic potential energy, thermal energy and so
forth. This means the kinetic energy of the system of the two boxcars decreases,
making this an inelastic collision.
Acompletely inelastic collision is one in which two objects “stick together” after they
collide, so they have a common final velocity. Since they may still be moving,
completely inelastic does not mean there is zero kinetic energy after the collision. For
instance, after the boxcars connect, the two “stick together” and move as one unit. In
this case, the train combination continues to move after the collision, so they still have
kinetic energy, although less than before the collision.
As with elastic collisions, we assume the collision occurs in an isolated system, with no
net external forces present. You can think of elastic collisions and completely inelastic
collisions as the extreme cases of collisions. Kinetic energy is not reduced at all in an
elastic collision. In a completely inelastic collision, the total amount of kinetic energy
after the collision is reduced as much as it can be, consistent with the conservation of
momentum.
In Equation 1, you see an equation to calculate the final velocity of two objects, like the snowballs shown, after a completely inelastic collision.
This equation is derived below. The derivation hinges on the two objects having a common velocity after the collision.
Inelastic collisions
Collision reduces total KE
Momentum conserved
Completely inelastic collisions:
·Objects "stick together"
·Have common velocity after collision