Final answer:
The maximum mass of grain that a 2000-kg railway freight car can accept while maintaining a speed above 3.0 m/s is determined by using the principle of conservation of momentum and equating initial and final momentum values.
Step-by-step explanation:
To determine the maximum mass of grain that a 2000-kg railway freight car can accept without its speed dropping below 3.0 m/s, we can use the principle of conservation of momentum. The momentum before and after loading the grain must be equal since we are assuming there are no external forces acting on the system besides gravity, which only affects the vertical motion and not the horizontal momentum.
Initially, the momentum of the car is the product of its mass (2000 kg) and its velocity (4.4 m/s). Therefore, the initial momentum is 2000 kg × 4.4 m/s. After loading, the momentum of the system will be the sum of the momentum of the car and the grain. If m represents the mass of the grain and the velocity of the car is 3.0 m/s, the final momentum is (2000 kg + m) × 3.0 m/s. Setting the initial and final momentums equal to each other and solving for m gives us the maximum mass of grain the car can carry without going below the specified speed.