A 2,000-kilogram railroad car moving at 5 m/sec to the east collides with a 6,000-kilogram railroad car moving at 3 m/sec to the west. If the cars couple together, what is their velocity after the collision?

So we wan't to know what is the velocity after a collision of two railroad cars, one moving to the east and the other moving to the west if m1=2000kg, v1=5m/s and m2=6000kg, v2=3m/s. We can find the solution using the law of conservation of momentum for plastic collisions that states that the momentum must remain constant before (left side of the equation) and after (right side of the equation) the collision: m1 v1+m2 v2=(m1+m2)*v. So now we simply plug in the numbers and get: 2000kg * 5m/s + 6000kg * 3m/s = (2000kg + 6000kg)*v. Now we can write: 10000 kgm/s + 18000 kgm/s = 8000kg * v. To get v, the velocity of both railroad cars after the collision we simply divide both sides of the equation with 8000 kg: so v=3.5m/s to the west.

Answered by W0lf93 | 2024-06-24

Using conservation of momentum, the final velocity of the coupled railroad cars is calculated to be 1 m/s to the west.
This problem involves the conservation of momentum principle.
When two objects collide and stick together, their combined momentum after the collision is equal to the sum of their momenta before the collision.
Calculate the initial momentum of both cars:
For the 2000 kg car moving east at 5 m/s:

Momentum = mass × velocity = 2000 kg × 5 m/s
Momentum = 10000 kg·m/s east

For the 6000 kg car moving west at 3 m/s:

Momentum = mass × velocity = 6000 kg × 3 m/s
Momentum = 18000 kg·m/s west

Determine the total initial momentum:

Total initial momentum = 10000 kg·m/s (east) - 18000 kg·m/s (west)
Total initial momentum = -8000 kg·m/s (negative sign indicates direction to the west)

The cars couple together, so their combined mass is:

Total mass = 2000 kg + 6000 kg
Total mass = 8000 kg

Using the conservation of momentum, the final velocity (v) can be found from:

Total momentum = Total mass × final velocity

Solve for the final velocity:

-8000 kg·m/s = 8000 kg × v

Therefore, the final velocity (v) is:

v = -8000 kg·m/s ÷ 8000 kg
v = -1 m/s

The final velocity of the coupled cars is 1 m/s to the west.

Answered by JamesCosmo | 2024-06-26

After the collision, the two railroad cars couple together and move at a velocity of 1 m/s towards the west. This is calculated using the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision, resulting in this final velocity.
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Answered by W0lf93 | 2024-10-31