Question

A load of gravel is dumped straight down into a 30 000-kg freight car coasting at 2.2 m/s on a straight section of a railroad. If the freight car’s speed after receiving the gravel is 1.5 m/s, what mass of gravel did it receive?

a) 12,000 kg
b) 15,000 kg
c) 7,000 kg
d) 9,000 kg

Answer 1

The mass of the gravel that was dumped into the freight car is calculated using the conservation of momentum. The final answer, after solving the equation for the unknown mass, is 12,000 kg, which corresponds to option (a).

Step-by-step explanation:

The student's question involves calculating the mass of the gravel that a freight car received based on the change in its velocity. This is an application of the conservation of momentum, which states that in the absence of external forces, the total momentum of a system remains constant. In this case, the system consists of the freight car before and after it receives the load of gravel.

To solve the problem, we use the equation: initial momentum = final momentum, resulting in (mass of freight car × initial velocity) = (total mass after receiving gravel × final velocity). You would use the given masses and velocities to find the unknown mass of gravel. After plugging in the numbers:

• Initial momentum = 30,000 kg × 2.2 m/s
• Final momentum = (30,000 kg + mass of gravel) × 1.5 m/s

By solving for the mass of the gravel, we can determine the correct answer to be 12,000 kg, which is option (a).