Solve Compression Distance for Mass Spring Train Collision

[katysmith]

i have a question in which a train collides with a buffer stop of mass 1.5 tons that asks how far the buffer stop is compressed. this is similar to a block and spring question, except the spring has mass. how is this included in the equation to solve for compression distance?

 

[Mindscrape]

Well, what do your conservation laws tell you? You know that momentum is conserved, and since there are no non-conservative forces at work, then energy will also be conserved.

 

[kyle8921]

To solve for the compression distance in this scenario, we can use the principles of conservation of energy and Hooke's law. First, we need to determine the initial kinetic energy of the train before the collision. This can be calculated using the mass of the train and its velocity.

Next, we need to consider the energy lost during the collision. This energy is converted into potential energy stored in the compressed spring. The mass of the spring needs to be taken into account, as it will also contribute to the potential energy.

Using Hooke's law, we can then calculate the amount of compression in the spring based on the force applied and the spring constant. This will give us the distance that the buffer stop is compressed.

In summary, to solve for the compression distance in a mass-spring train collision, we need to consider the initial kinetic energy of the train, the energy lost during the collision, and the contribution of the spring's mass to the potential energy. By using the principles of conservation of energy and Hooke's law, we can accurately calculate the compression distance of the buffer stop.