A sandbag in outer space moves at 3 m/s when it collides and sticks to a half-as-massive sandbag initially at rest. Compared with the kinetic energy of the moving sandbag before collision, the kinetic energy of the coupled sandbags after collision is

Question

Quizplus · Accepted Answer

The total mass of the sandbags after the collision is 1.5 times the mass of the original sandbag. Therefore, by conservation of momentum, the final velocity of the coupled sandbags is half of the initial velocity of the moving sandbag, which is 1.5 m/s.

The kinetic energy before the collision is:

KEi = 0.5 * m * v^2 = 0.5 * m * (3 m/s)^2 = 4.5 mJ

The kinetic energy after the collision is:

KEf = 0.5 * (1.5 m) * (1.5 m/s)^2 = 3.38 mJ

Therefore, the ratio of the kinetic energy after the collision to the kinetic energy before the collision is:

KEf / KEi = 3.38 mJ / 4.5 mJ = 0.75

So the kinetic energy of the coupled sandbags after collision is three-quarters of the kinetic energy of the moving sandbag before collision, which corresponds to answer B.

A Sandbag in Outer Space Moves at 3 M/s When