A 3800 kg open railroad car coasts along with a constant speed of 8.60 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.50 kg/min. ignoring friction with the tracks what is the speed of the car after 90.0 minutes?
Correct me if I'm wrong, but...
Momentum before = Momentum after
mv(before)=m'v'(after)
(mass of train before snow)(velocity of train before snow)=m'v'
(3,800 kg)(8.6 m/s)=(3,800 kg + added weight of snow)(v')
32,680=(3,800+315)(v')
32,680=4115(v')
v'= 7.94 m/s
momentuminitial=momentumfinal
3800*8.60=(3800+3.50*time)v(t)
solve for v(t) for t=90min
Well, since the snow is falling vertically, it won't affect the horizontal motion of the car. So the speed of the car will remain at a constant 8.60 m/s, no matter how much snow falls into it. Snow might make it look cooler, though!
To determine the speed of the car after 90.0 minutes, we need to consider the change in mass due to the snow accumulating in the car.
First, let's calculate the mass of the snow that accumulates in the car over the given time period. We are told that the snow accumulates at a rate of 3.50 kg/min. So in 90.0 minutes, the mass of snow that accumulates will be:
Mass of snow = (rate of accumulation) x (time)
= 3.50 kg/minute x 90.0 minutes
= 315 kg
Now, let's calculate the total mass of the car with the snow included. The initial mass of the car is given as 3800 kg. Adding the mass of the snow, the total mass becomes:
Total mass = initial mass + mass of snow
= 3800 kg + 315 kg
= 4115 kg
Next, we consider the conservation of momentum since there is no friction with the tracks. The momentum of the car before adding the snow is equal to the momentum of the car after adding the snow.
Momentum before = Momentum after
The momentum of an object is given by the product of its mass and velocity:
(Mass before) x (Velocity before) = (Mass after) x (Velocity after)
Plugging in the given values:
(3800 kg) x (8.60 m/s) = (4115 kg) x (Velocity after)
Solving for Velocity after:
Velocity after = (3800 kg x 8.60 m/s) / 4115 kg
= 7.939 m/s
Therefore, the speed of the car after 90.0 minutes is approximately 7.939 m/s.