Question

URGENT HELP NEEDED!!!

Two train cars are moving towards each other. The loaded car has a mass of 134,000 kg, and is moving north at a speed of 2.9 m/s. The unloaded car has a mass of 22,600 kg, and is moving south at a speed of 0.8 m/s. When the cars collide, they lock together, and move as a single unit. What is the velocity of the cars after they join together?

2.4 m/s north

2.1 m/s north

2.4 m/s south

2.1 m/s south

Answer 1

To find the final velocity of the train cars after they join together, we can use the principle of conservation of momentum.

Step-by-step explanation:

To find the final velocity of the train cars after they join together, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. We can calculate the momentum of each car using the formula: momentum = mass * velocity.

The momentum of the loaded car is (134,000 kg) * (2.9 m/s) = 388,600 kg m/s.

The momentum of the unloaded car is (22,600 kg) * (-0.8 m/s) = -18,080 kg m/s (negative because it is moving in the opposite direction).

Since momentum is conserved, the total momentum after the collision is equal to the total momentum before the collision:

Final momentum = initial momentum of loaded car + initial momentum of unloaded car.

Final momentum = 388,600 kg m/s + (-18,080 kg m/s) = 370,520 kg m/s.

To find the final velocity, we can divide the final momentum by the combined mass of the cars:

Final velocity = final momentum / (mass of loaded car + mass of unloaded car).

Final velocity = 370,520 kg m/s / (134,000 kg + 22,600 kg).

Final velocity = 370,520 kg m/s / 156,600 kg.

Final velocity = 2.36 m/s.

Answer 2

To solve this problem, we need to apply the principle of conservation of momentum, which states that the total momentum of a system remains constant if there is no external force acting on it.

The initial momentum of the loaded car moving north is:

p1 = m1 * v1 = 134,000 kg * 2.9 m/s = 388,600 kg*m/s (north)

The initial momentum of the unloaded car moving south is:

p2 = m2 * v2 = 22,600 kg * (-0.8 m/s) = -18,080 kg*m/s (south)

Note that we have used a negative velocity for the unloaded car, as it is moving in the opposite direction to the positive direction we have chosen (north).

When the cars collide, they lock together and move as a single unit. The final momentum of the joined cars is:

p = (m1 + m2) * v

where v is the final velocity of the joined cars.

Since the momentum is conserved, we can set the initial and final momenta equal:

p1 + p2 = (m1 + m2) * v

Substituting the values we have calculated:

388,600 kgm/s - 18,080 kgm/s = (134,000 kg + 22,600 kg) * v

370,520 kg*m/s = 156,600 kg * v

v = 2.366 m/s (north)

Therefore, the velocity of the cars after they join together is 2.4m/s north.

Note that this answer is between the initial velocities of the two cars, which makes sense since the collision causes the cars to slow down and move together in the north direction.