A train is moving at 13 m/s and has a mass of 2363 kg. A broken down car (loaded with heavy bricks) is stopped on the train track. Upon impact, the train and car get tangled together and travel at a constant velocity of 3 m/s.
What is the mass of the broken down car?
answer please
2363kg for a train? That's some small train!
conserve momentum
2363(13) = (2363+x)(3)
kinda hard to ignore friction in such a scenario, right? Oh, well.
Given:
M1 = 2363kg, V1 = 13 m/s.
M2 = ?, V2 = 0.
V3 = 3 m/s = Velocity of M1 and M2 after collision.
Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V3.
2363*13 + M2*0 = 2363*3 + + M2*3,
2363*13-2363*3 = M2*3,
M2 = ?
To find the mass of the broken-down car, we can use the concept of conservation of momentum. The total momentum before the collision should be equal to the total momentum after the collision.
Before the collision:
The momentum of the train is given by the formula:
Momentum = mass × velocity
Momentum of the train = 2363 kg × 13 m/s = 30719 kg·m/s
The momentum of the broken-down car is zero since it is stopped.
After the collision:
The momentum of the tangled train and car is the sum of their individual momenta. Since they are traveling at a constant velocity of 3 m/s, their combined momentum can be calculated as:
Momentum of the tangled train and car = (mass of the train + mass of the car) × 3 m/s
According to the conservation of momentum, the total momentum before the collision (30719 kg·m/s) should be equal to the total momentum after the collision.
Therefore, we can set up the equation:
30719 kg·m/s = (mass of the train + mass of the car) × 3 m/s
To solve for the mass of the broken-down car, we need to rearrange the equation:
mass of the car = (30719 kg·m/s) / 3 m/s
mass of the car ≈ 10239.67 kg
Therefore, the mass of the broken-down car is approximately 10239.67 kg.