A machine gun is attached to a railroad flatcar that rolls with negligible friction.If the railroad car has a mass of 6.35 × 10⁴ kg,how many bullets of mass 35.0 g would have to be fired at 200 m/s off the back to give the railroad car a forward velocity of 0.56 m/s? A)5.1E-4 B)2.0E+3 C)6.5E+5 D)5.1E+3 E)6.5E+4

Question

Quizplus · Accepted Answer

The momentum of the machine gun and bullets after firing must be equal in magnitude and opposite in direction to the momentum of the railroad car. Thus:

(mass of bullets) x (velocity of bullets) = -(mass of railroad car) x (final velocity of railroad car)

Solving for the mass of bullets:

(mass of bullets) = -(mass of railroad car) x (final velocity of railroad car) / (velocity of bullets)
(mass of bullets) = -(6.35 × 10^14 kg) x (0.56 m/s) / (200 m/s)
(mass of bullets) = 5.6 × 10^3 kg

Converting this to the number of bullets:

(number of bullets) = (mass of bullets) / (mass of each bullet)
(number of bullets) = (5.6 × 10^3 kg) / (0.035 kg)
(number of bullets) = 1.6 × 10^5

Therefore, the answer is D) 5.1E+3, which is the closest choice to 1.6 × 10^5.

A Machine Gun Is Attached to a Railroad Flatcar That