Question

A railway car with a mass of 2880 kg moves along horizontal tracks at a constant speed of 5.28 m/s. It rolls under a grain terminal, which dumps grain directly down into the freight car after which the car's speed decreases to 2.5 m/s. Calculate the force applied by the grain terminal.

Answer 1

To find the force applied by the grain terminal, we can use the conservation of momentum. By setting the initial momentum equal to the final momentum, we can calculate the mass of the grain to be approximately 960 kg.

Step-by-step explanation:

To calculate the force applied by the grain terminal, we can use the concept of conservation of momentum. The initial momentum of the railway car before the grain is dumped is given by:

Initial momentum = mass of the car × initial velocity

Using the given values, the initial momentum can be calculated as:

Initial momentum = 2880 kg × 5.28 m/s = 15206.4 kg•m/s

The final momentum of the car after the grain is dumped is given by:

Final momentum = mass of the car + mass of the grain × final velocity

Let's assume the mass of the grain is m kg. So, the final momentum can be calculated as:

Final momentum = (2880 kg + m kg) × 2.5 m/s

According to the conservation of momentum, the initial momentum and the final momentum should be equal. Setting the two equations equal to each other and solving for the mass of the grain, we get:

15206.4 kg•m/s = (2880 kg + m kg) × 2.5 m/s

m kg = (15206.4 kg•m/s / 2.5 m/s) - 2880 kg

After solving this equation, we find the mass of the grain to be approximately 960 kg.