Two identical boxcars (m = 14866 kg) are traveling along the same track but in opposite directions. Both boxcars have a speed of 5 m/s. If the cars collide and couple together, what will be the final speed of the pair?
See previous post: Tue, 10-18-16, 8:27 AM.
To find the final speed of the pair of boxcars after they collide and couple together, we can use the principle of conservation of momentum.
The momentum before the collision is given by the sum of the momenta of the two boxcars. Since the boxcars are identical and have the same speed, the momentum of each boxcar is given by:
momentum = mass x velocity
For each boxcar, the mass (m) is 14866 kg and the velocity (v) is 5 m/s. Therefore, the momentum of each boxcar is:
momentum_boxcar = m x v = 14866 kg x 5 m/s = 74330 kg·m/s
Since the boxcars are traveling in opposite directions, their momenta will have opposite signs. So, the total momentum before the collision is:
total momentum before collision = momentum_boxcar1 - momentum_boxcar2
Since the boxcars have the same momentum magnitude but opposite directions, their momenta will cancel out:
total momentum before collision = 74330 kg·m/s - 74330 kg·m/s = 0 kg·m/s
According to the conservation of momentum, the total momentum after the collision should also be zero.
The formula for the final velocity of the pair after the collision can be derived from:
total momentum after collision = (total mass of the pair) x (final velocity of the pair)
Since the two boxcars couple together and move as a single unit, the total mass of the pair is simply twice the mass of a single boxcar:
total mass of the pair = 2 x mass of a single boxcar = 2 x 14866 kg = 29732 kg
Since the total momentum after the collision is zero, we can say that:
0 kg·m/s = (29732 kg) x (final velocity of the pair)
Simplifying the equation, we find:
final velocity of the pair = 0 kg·m/s / 29732 kg = 0 m/s
Hence, the final speed of the pair of boxcars after they collide and couple together is 0 m/s.