Freight Car Collision

In summary, in a collision between a 29000-kg railroad freight car and a stationary caboose car with brakes released, 10 percent of the initial kinetic energy is dissipated as heat, sound, vibrations, and so on. Using the equation m1v1=(m1+m2)vf and the energy equation, both with the same velocities, the mass of the caboose can be solved for, despite the lack of information provided.
  • #1
MooCow
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Homework Statement


A 29000-kg railroad freight car collides with a stationary caboose car with brakes released. They couple together, and 10 percent of the initial kinetic energy is dissipated as heat, sound, vibrations, and so on. What is the mass of the caboose?

This is the equation that I've gotten. However, there are to many variables so I don't know where to go from here. I plugged in the same velocities but the mass turned out negative.

m1v1=(m1+m2)vf

I posted this question exactly as it was written. I wish I had more information for those who asked for it, but that is all I was given- thus my confusion!

Any help would be great. Thanks.
 
Last edited:
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  • #2
You've got the first equation... you need one more... write the energy equation using the kinetic energies before and after the collision...

Then you'll have 2 equations with 2 unknowns (vf and the mass of the caboose).
 
  • #3


I understand your confusion as there are indeed several unknown variables in this problem. However, let's try to break it down and see what information we can gather.

First, we know that the initial kinetic energy (KE) of the system is equal to the final KE plus the energy dissipated. Mathematically, this can be written as:

KEi = KEf + Ed

We also know that the initial KE is equal to 1/2 * m1 * v1^2, where m1 is the mass of the freight car and v1 is its initial velocity. Similarly, the final KE is equal to 1/2 * (m1 + m2) * vf^2, where m2 is the mass of the caboose and vf is the final velocity of the coupled cars.

So, putting these together, we get the following equation:

1/2 * m1 * v1^2 = 1/2 * (m1 + m2) * vf^2 + Ed

Now, we also know that the energy dissipated is equal to 10% of the initial KE, so we can substitute this into the equation:

1/2 * m1 * v1^2 = 1/2 * (m1 + m2) * vf^2 + 0.1 * 1/2 * m1 * v1^2

Simplifying this, we get:

0.9 * 1/2 * m1 * v1^2 = 1/2 * (m1 + m2) * vf^2

Now, we can rearrange this equation to solve for m2, the mass of the caboose:

m2 = 2 * (0.9 * m1 * v1^2 - m1 * vf^2) / vf^2

Unfortunately, without knowing the specific values for the initial and final velocities, we cannot solve for the mass of the caboose. However, we can make some general observations:

1. The mass of the caboose will be directly proportional to the difference between the initial and final velocities. If the initial and final velocities are the same, then the mass of the caboose will be zero.

2. The mass of the caboose will also be directly proportional to the mass of the freight car. The larger the freight car, the larger the mass of the caboose will need to be in
 

1. What is a freight car collision?

A freight car collision is when two or more freight cars, which are used to transport goods on a train, collide with one another. This can happen due to various reasons, such as mechanical failures, human error, or adverse weather conditions.

2. What are the potential impacts of a freight car collision?

A freight car collision can result in damage to the train cars, loss of cargo, and potential injuries to train crew or bystanders. It can also cause delays and disrupt the transportation of goods.

3. How common are freight car collisions?

Freight car collisions are relatively rare, but they can occur from time to time. The frequency of collisions depends on various factors, such as the condition of the train cars, the experience of the train crew, and the safety protocols in place.

4. What measures are taken to prevent freight car collisions?

To prevent freight car collisions, train companies have strict safety protocols in place, including regular maintenance and inspections of train cars, training for train crew members, and the use of advanced technology such as signaling systems and GPS tracking.

5. What steps are taken after a freight car collision?

After a freight car collision, an investigation is conducted to determine the cause of the collision. Train companies may also implement additional safety measures to prevent similar incidents in the future. If there are any injuries or damages, appropriate actions will be taken to address them.

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