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?
To find the final speed of the pair of boxcars after they collide and couple together, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v). The formula for momentum is:
p = m * v
Let's calculate the total momentum before and after the collision:
Total momentum before collision = momentum of boxcar A + momentum of boxcar B
Total momentum before collision = (mass of boxcar A * velocity of boxcar A) + (mass of boxcar B * velocity of boxcar B)
Total momentum before collision = (14866 kg * 5 m/s) + (14866 kg * -5 m/s) [Since the boxcars are traveling in opposite directions, the velocity of one car will be negative]
Total momentum before collision = 0
Since the total momentum before the collision is equal to 0, according to the conservation of momentum, the total momentum after the collision should also be 0.
Total momentum after collision = momentum of the coupled boxcars
Total momentum after collision = mass of the coupled boxcars * final velocity of the pair
The masses of the boxcars are identical, so the mass of the coupled boxcars will be the sum of the masses of the individual boxcars.
Mass of the coupled boxcars = mass of boxcar A + mass of boxcar B
Mass of the coupled boxcars = 14866 kg + 14866 kg
Mass of the coupled boxcars = 29732 kg
Total momentum after collision = 29732 kg * final velocity of the pair
Since the total momentum after the collision is 0, we can find the final velocity of the pair by rearranging the formula:
0 = 29732 kg * final velocity of the pair
Solving for the final velocity of the pair, we get:
final velocity of the pair = 0 m/s
Therefore, the final speed of the pair of boxcars after they collide and couple together will be 0 m/s.