An open train car, with a mass of 2150 kg, coasts along a horizontal track at the speed 2.29 m/s. The car passes under a loading chute and, as it does so, gravel falls vertically into it for 2.67 s at the rate of 441 kg/s. What is the car's speed after the loading is completed? Ignore rolling friction

The mass of gravel is

m2=441•2.67 = 1177.47 kg

The law of conservation of linear momentum
m1•v1= (m1+m2)v2
v2= m1•v1/(m1+m2) =
=2150•2.29/(2150+1177.47)=1.48 m/s

Well, that's quite a weighty situation! Let's calculate the change in momentum of the system before and after the loading takes place.

Before the loading, the momentum of the train car is given by:

momentum_before = mass * velocity = 2150 kg * 2.29 m/s = 4923.5 kg*m/s

The momentum change caused by the falling gravel can be calculated by multiplying the mass of the gravel by its velocity (which is vertically downward) and then dividing the result by the time interval:

momentum_change = (mass_rate_gravel * velocity_gravel * time_gravel) = 441 kg/s * (-9.8 m/s^2) * 2.67 s = -3160.362 kg*m/s

Note that the negative sign indicates a change in direction.

To find the final momentum, we can simply add the momentum change to the initial momentum:

momentum_final = momentum_before + momentum_change = 4923.5 kg*m/s - 3160.362 kg*m/s = 1763.138 kg*m/s

Now, we can find the final velocity of the train car by dividing the final momentum by its mass:

final_velocity = momentum_final / mass = 1763.138 kg*m/s / 2150 kg ≈ 0.819 m/s

So, the car's speed after the loading is completed is approximately 0.819 m/s. It seems like the car has picked up quite a bit of weight, but at least it's still rolling along!

To find the car's speed after the loading process, we need to apply the law of conservation of momentum. The total momentum of the system (train car + gravel) before and after the loading process will remain the same.

Step 1: Calculate the initial momentum of the train car:
Momentum = mass x velocity
Initial momentum of the train car = 2150 kg * 2.29 m/s

Step 2: Calculate the momentum of the falling gravel:
The mass of the gravel falling is given as 441 kg/s.
The time for which the gravel is falling is given as 2.67 s.
Momentum of the falling gravel = mass x velocity
Momentum = 441 kg/s * 2.67 s

Step 3: Calculate the total momentum before the loading:
Total momentum before loading = initial momentum of the train car + momentum of the falling gravel

Step 4: Calculate the mass of the train car after loading:
Mass after loading = mass before loading + mass of the falling gravel
Mass after loading = 2150 kg + (441 kg/s * 2.67 s)

Step 5: Calculate the final velocity of the train car:
Final momentum = total momentum before loading
Final velocity = final momentum / mass after loading

Follow these steps to find the car's speed after the loading is completed.

To find the car's speed after the loading is completed, we need to apply the principle of conservation of momentum.

Momentum is the product of an object's mass and velocity. The total momentum before the loading chute is equal to the total momentum after the loading chute.

Before the loading chute:
Total momentum before = mass of the car x velocity of the car

After the loading chute:
Total momentum after = (mass of the car + mass of the falling gravel) x final velocity of the car

Using the principle of conservation of momentum, we can set up an equation:

(mass of the car x velocity of the car) = (mass of the car + mass of the falling gravel) x final velocity of the car

Let's find the mass of the falling gravel first. We know that the gravel falls vertically into the train car for 2.67 seconds at a rate of 441 kg/s. Therefore, the mass of the falling gravel can be calculated as:

mass of the falling gravel = 441 kg/s x 2.67 s

Now, substituting the values into the equation:

(2150 kg x 2.29 m/s) = ((2150 kg + mass of the falling gravel) x final velocity of the car)

Substituting the found value for the mass of the falling gravel:

(2150 kg x 2.29 m/s) = ((2150 kg + (441 kg/s x 2.67 s)) x final velocity of the car)

Now, we can solve for the final velocity of the car.