Final answer:
The maximum mass of grain a 1875-kg freight car can accept while moving at 5 m/s without falling below 2.7 m/s is approximately 1601.85 kg, calculated using conservation of momentum principles.
Step-by-step explanation:
The question posed involves using the principle of conservation of momentum to determine the maximum mass of grain that a railway freight car can accept without its speed falling below a certain threshold. The principles of momentum conservation are commonly applied in physics problems involving collisions and transfers of mass.
According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces act on it. Therefore, the initial momentum of the freight car is equal to the final momentum of the freight car plus the grain. Using the formula:
Initial momentum = Final momentum
The freight car's initial and final velocities (vi and vf, respectively), along with its initial mass (mc) and the mass of the grain (mg), can be plugged into the equation:
mcvi = (mc + mg)vf
To solve the problem, we rearrange the formula to solve for mg:
mg = mc(vi - vf) / vf
Given the initial speed (vi = 5 m/s), the final speed (vf = 2.7 m/s) of the freight car, and its mass (mc = 1875 kg), the calculation yields:
mg = 1875 kg * (5 m/s - 2.7 m/s) / 2.7 m/s = 1875 kg * 2.3 m/s / 2.7 m/s
mg = 1601.85 kg
Therefore, the maximum mass of grain the car can accept is approximately 1601.85 kg before its speed would drop below 2.7 m/s.