A 3400 kg open railroad car coasts along with a constant speed of 7.50 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 5.10 kg/min.Ignoring friction with the tracks, what is the speed of the car after 85.0 min ?
After 85 min, 433.5 kg has been added to the railroad car. The momentum will stay the same because there is no friction (or so they say). The new mass of the car with snow in it is 3833.5 kg.
Use the law of conservation of momentum.
3400 * 7.50 = 3833.5 * Vfinal
Whoever dreamed up this problem is out of touch with the real world. There is no way a railroad car can go 85 minutes on a level track without friction. Friction will slow it down more than the falling snow that fills it.
To determine the speed of the car after 85.0 minutes, we need to consider the additional mass added by the snow and conserve the momentum.
First, let's find the mass of snow added to the car in 85.0 minutes. Given that the snow fills the car at a rate of 5.10 kg/min, we can use the following formula:
Mass of snow = Rate of snowfall × Time
Mass of snow = 5.10 kg/min × 85.0 min
Mass of snow = 433.5 kg
Now, let's determine the initial momentum of the system, which is given as the product of the car's mass and its velocity:
Initial momentum = Mass of car × Velocity of car
Initial momentum = 3400 kg × 7.50 m/s
Initial momentum = 25500 kg·m/s
Since there is no external force acting on the system other than the snowfall, the total momentum should remain constant.
Final momentum = Initial momentum
(Mass of car + Mass of snow) × Velocity final = Mass of car × Velocity initial
(3400 kg + 433.5 kg) × Velocity final = 3400 kg × 7.50 m/s
(3833.5 kg) × Velocity final = 25500 kg·m/s
Velocity final = (25500 kg·m/s) / (3833.5 kg)
Velocity final ≈ 6.65 m/s
Therefore, the speed of the car after 85.0 minutes is approximately 6.65 m/s.