Final answer:
To ensure that a 2000-kg freight car's speed does not go below 3.0 m/s when adding grain, we can use the conservation of momentum to calculate the maximum mass of grain that can be added. The maximum mass is found by equating the initial momentum of the train, prior to receiving the grain, with the final momentum after receiving the grain, ensuring the final velocity is at least 3.0 m/s.
Step-by-step explanation:
The Maximum Mass of Grain for a Freight Car
When dealing with a freight train and changes in its velocity due to added mass, we can use the principle of conservation of momentum. In this scenario, we have a 2000-kg freight car moving at a velocity of 4.4 m/s. The freight car is receiving grain, and we need to ensure its velocity does not fall below 3.0 m/s. The initial momentum of the car is its mass times its initial velocity (momentum = mass * velocity).
The initial momentum is therefore 2000 kg * 4.4 m/s. When grain is added, the momentum will be conserved, so we set up the equation with the initial momentum equal to the combined mass of the car and grain times the final velocity. The final velocity must not be less than 3.0 m/s, so using conservation of momentum:
2000 kg * 4.4 m/s = (2000 kg + mass of grain) * 3.0 m/s.
Solving for the mass of grain, we get a maximum mass that can be accepted without dropping below the minimum velocity. This approach incorporates concepts like conservation of momentum, mass, and velocity which are fundamental in physics, particularly in understanding the motion of objects.