Final answer:
The question involves calculating the final velocity of a loaded freight car and the kinetic energy lost using conservation of momentum principles. By equating the momentum before and after loading, the final velocity is determined to be approximately 0.1821 m/s. The kinetic energy lost is the difference in kinetic energy before and after the freight car is loaded.
Step-by-step explanation:
Conservation of Momentum and Energy Loss
When adding 30 loaded coal cars to a train, the placement of the cars can be a complex task involving practical considerations that might be addressed differently depending on the specific rules and practices of the railway. However, regarding the sample physics problem provided about a 30,000-kg freight car coasting at 0.850 m/s under a hopper that dumps 110,000 kg of scrap metal into it:
- The final velocity of the loaded freight car can be calculated using the conservation of momentum.
- The kinetic energy lost can be determined by calculating the kinetic energy before and after the scrap metal is dumped, and then finding the difference.
Assuming there's no external force on the system, the total momentum before and after the dumping should be equal. To find the final velocity (v_f) of the freight car:
Momentum before = (mass of freight car) x (initial velocity of freight car)
Momentum after = (mass of freight car + mass of scrap metal) x v_f
Setting these equal to each other to solve for v_f:
(30,000 kg x 0.850 m/s) = (30,000 kg + 110,000 kg) x v_f
v_f = (30,000 kg x 0.850 m/s) / (140,000 kg)
v_f = 0.1821 m/s (approximately)
To find the kinetic energy lost:
Kinetic energy before = 0.5 x (mass of freight car) x (velocity of freight car)^2
Kinetic energy after = 0.5 x (mass of freight car + mass of scrap metal) x (final velocity)^2
Subtract the kinetic energy after from the kinetic energy before to get the kinetic energy lost.