Question

A railway car with a mass of 3680kg moves along horizontal tracks at a constant speed of 4.32m/s . It rolls under a grain terminal, which dumps grain directly down into the freight car after which the car's speed decreases by 2.59m/s .

Answer 1

To find the maximum mass of grain that the loaded freight car can accept, we need to use the principle of conservation of momentum. By equating the initial and final momenta, we can calculate the mass of the grain.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of momentum. The initial momentum of the railway car before the grain is dumped into it is equal to its final momentum after the grain is dumped. The momentum of an object can be calculated by multiplying its mass by its velocity.

First, let's calculate the initial momentum. Since the car is moving at a constant speed of 4.32 m/s, its initial momentum is given by:

Initial momentum = mass of car * initial velocity

Next, we need to find the final velocity of the loaded freight car. We know that the speed of the car decreases by 2.59 m/s, so the final velocity would be:

Final velocity = initial velocity - speed decrease

Now, using the principle of conservation of momentum, we can equate the initial and final momenta to find the mass of the grain:

(mass of car * initial velocity) = (mass of car + mass of grain) * final velocity
mass of grain = (mass of car * initial velocity - mass of car * final velocity) / final velocity

Substituting the given values into the equation, we can calculate the mass of the grain that the car can accept.