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?
M1V1 + M2V2 = M1V + M2V.
14866*5-14866*5 = 14866V+14866V,
V = 0.
(M=18913 kg)6 m/s
850kg 30m/s
To find the final speed of the pair after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
To start, we need to find the initial momentum of the boxcars.
The momentum of an object can be calculated by multiplying its mass by its velocity. Since both boxcars have the same mass (m = 14866 kg) and are traveling in opposite directions, we can consider their velocities as negative and positive, respectively.
So, the initial momentum of the first boxcar (-m1v1) is given by:
m1 = 14866 kg (mass of the first boxcar)
v1 = -5 m/s (velocity of the first boxcar)
Similarly, the initial momentum of the second boxcar (m2v2) is given by:
m2 = 14866 kg (mass of the second boxcar)
v2 = 5 m/s (velocity of the second boxcar)
The total initial momentum (P_initial) is the sum of the individual momenta:
P_initial = m1v1 + m2v2
Now, since the boxcars collide and couple together, their masses combine, and we have a single final mass (M = 2m).
Let's calculate the final momentum of the coupled boxcars.
The final momentum (P_final) is given by:
P_final = Mv_final
Since the total momentum before and after the collision is conserved, we have:
P_initial = P_final
Therefore,
m1v1 + m2v2 = Mv_final
Substituting the values, we have:
14866 kg (-5 m/s) + 14866 kg (5 m/s) = (2 × 14866 kg) × v_final
Simplifying the equation:
-74330 kg m/s + 74330 kg m/s = 29732 kg × v_final
0 = 29732 kg × v_final
Dividing both sides by 29732 kg to solve for v_final:
v_final = 0 m/s
Therefore, the final speed of the pair after colliding and coupling together is 0 m/s.