Final answer:
The maximum mass of grain that can be added to a 2000-kg railway freight car to maintain a minimum speed of 3.0 m/s, using conservation of momentum, is 1466.67 kg.
Step-by-step explanation:
The maximum mass of grain that a 2000-kg railway freight car can accept without the speed going below 3.0 m/s can be calculated using the principle of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system. The initial momentum of the freight car is the product of its mass and velocity (2000 kg × 4.4 m/s). After the grain is dumped, the final momentum will be the sum of the momentum of the freight car and the added grain, which we can represent as (2000 kg + m) × 3.0 m/s, where 'm' is the mass of the grain. Setting the initial momentum equal to the final momentum allows us to solve for 'm'. Using the equation 2000 kg × 4.4 m/s = (2000 kg + m) × 3.0 m/s, and solving for 'm', we find that the maximum mass of grain that can be added without dropping below the 3.0 m/s threshold is 1466.67 kg.