Question

Wo loaded train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 1.50×10^5 kg and a velocity of (0.30 m/s)ˆi, and the second having a mass of 1.10×10^5 kg and a velocity of −(0.12 m/s)ˆi. What is their final velocity?

a) 0.09 m/s ˆi
b) 0.18 m/s ˆi
c) -0.09 m/s ˆi
d) -0.18 m/s ˆi

Answer 1

Using the conservation of linear momentum, the final velocity of the coupled train cars was calculated to be 0.18 m/s in the direction of the first train car's initial motion, which is represented as 0.18 m/s î.

Step-by-step explanation:

To determine the final velocity of the two coupled train cars, we can use the conservation of linear momentum. The law of conservation of momentum states that the total momentum of a closed system of objects (which in this case is the two train cars) is conserved. In the absence of external forces, the momentum before the collision equals the momentum after the collision.

Let's calculate the momentum of each train car before the collision:

Momentum of car 1 (p₁) = mass₁ * velocity₁ = 1.50×105 kg * 0.30 m/s = 4.50×104 kg·m/s

Momentum of car 2 (p₂) = mass₂ * velocity₂ = 1.10×105 kg * -0.12 m/s = -1.32×104 kg·m/s

The total initial momentum (Pinitial) is the sum of p₁ and p₂.

Now we calculate the final velocity (Vf) of the system using the combined mass of both cars (total mass) and the total initial momentum:

Pinitial = Pfinal

Vf = Pfinal / (mass₁ + mass₂)

Vf = (4.50×104 kg·m/s + (-1.32×104 kg·m/s)) / (1.50×105 kg + 1.10×105 kg)

Vf = (4.50×104 kg·m/s - 1.32×104 kg·m/s) / 2.60×105 kg = 0.18 m/s

The final velocity of the system of two coupled train cars is 0.18 m/s in the direction of the first train car's initial motion, which is represented by the vector 0.18 m/s î.