Question

which of the following describes a nearly perfect elastic collision between two items? (1 point)
two glass marbles roll toward each other, collide, and roll away again at the same speeds.
a glass marble falls into sand and stops moving.
two glass marbles roll toward each other, collide, and stop moving.
a glass marble falls onto a wooden floor, and then bounces back to half its starting height.

Explanation:

In a nearly perfect elastic collision, both momentum and kinetic energy are conserved. When two glass marbles roll toward each other, collide, and roll away again at the same speeds, kinetic energy is conserved (since speed is same, \(KE=\frac{1}{2}mv^{2}\) remains same for each marble if mass is constant) and momentum is conserved (direction changes but magnitude of momentum for each marble remains same if mass and speed are same).

• For a marble falling into sand and stopping, kinetic energy is lost (converted to heat, sound etc. due to sand's resistance), so not elastic.
• When two marbles collide and stop, kinetic energy is lost (as they come to rest, \(KE = 0\) after collision while it was non - zero before), so not elastic.
• When a marble bounces back to half its starting height, potential energy at the maximum height after bounce (\(mgh_{2}\)) is half of the initial potential energy (\(mgh_{1}\), \(h_{2}=\frac{h_{1}}{2}\)), so kinetic energy is not conserved (as potential energy is related to kinetic energy in free - fall, \(KE = mgh\) at the point of impact and rebound).

Answer:

Two glass marbles roll toward each other, collide, and roll away again at the same speeds.