a 6000 kg railroad car moving at 5 m/s collides into a staionary car with a mass of 4000 kg. i fthey couple togethether after the collision, what will be their combined velocity immediately after impact
To solve this problem, we can use the principle of conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Momentum (p) is defined as mass (m) multiplied by velocity (v).
Initially, the 6000 kg railroad car is moving at 5 m/s, so its momentum is:
Momentum of the railroad car = mass of the railroad car × velocity of the railroad car
= 6000 kg × 5 m/s
= 30000 kg·m/s
The stationary car has no initial momentum because its initial velocity is 0.
Therefore, the total momentum before the collision is 30000 kg·m/s.
After the collision, the two cars couple together and move with a combined velocity (v).
Therefore, the total momentum after the collision is the sum of the momentum of the two cars:
Total momentum after the collision = mass of the railroad car × velocity of the railroad car + mass of the stationary car × velocity of the stationary car
= 6000 kg × v + 4000 kg × 0
= 6000 kg · v
According to the principle of conservation of momentum:
Total momentum before the collision = Total momentum after the collision
30000 kg·m/s = 6000 kg · v
Dividing both sides of the equation by 6000 kg:
v = 30000 kg·m/s ÷ 6000 kg
v ≈ 5 m/s
Therefore, their combined velocity immediately after the impact is approximately 5 m/s.