# Energy and Momentum: Elastic Collision of 2 Trains

• yummallory
In summary, Thomas the train and Diesel were involved in an elastic collision where a 2.5 kg Thomas was at rest and approached head-on by a 5.0 kg Diesel moving at 0.60 m/s. The total kinetic energy before and after the collision can be calculated by solving for the initial and final velocities using conservation of momentum and energy equations. The velocity of each train at minimum separation can be determined by finding the point on the force-separation graph where the forces acting on each train are equal and opposite. The total kinetic energy at minimum separation can be found by calculating the area under the force-separation graph. The energy stored at minimum separation is equal to a portion of this area. The minimum separation distance between
yummallory

## Homework Statement

Thomas the train and Diesel are involved in an elastic collision. A 2.5 kg Thomas is, at rest but is approached head-on by a 5.0 kg Diesel moving at 0.60 m/s. The force-separation graph for the ensuing collision is given: http://tinypic.com/r/2zyftae/7

a. What is the total kinetic energy before the collision? After?
b. What is the velocity of each train at minimum separation?
c. What is the total kinetic energy at minimum separation?
d. How much energy is stored at minimum separation?
e. What is the minimum separation distance between the trains? Hint: The energy temporarily stored at minimum separation equals a portion of the area under the above graph. The collision starts when the centers of the trains are separated by 0.03 m as shown on the above graph at which time the collision force is 15 N. But this force increases to 30 N and then eventually 45 N.
f. What is the magnitude of the force acting on each mass at minimum separation?

## The Attempt at a Solution

I have no idea how to even start these questions, so if someone could help me with at least some of them or show me how to start them that'd be great..thank you!

hi yummallory!

surely you know how to do a. ?

for the rest, you have a force against distance graph,

so the area under it will be the integral of force times distance, which is … ?

## 1. What is an elastic collision?

An elastic collision is a type of collision in which the kinetic energy and momentum of the system are conserved. This means that the total energy and momentum before the collision are equal to the total energy and momentum after the collision.

## 2. How does an elastic collision differ from an inelastic collision?

In an inelastic collision, some or all of the kinetic energy is lost as the objects stick together or deform. In an elastic collision, the objects bounce off each other without any loss of kinetic energy.

## 3. Can the momentum of a system change during an elastic collision?

No, the total momentum of a system is always conserved in an elastic collision. This means that the momentum of an object before the collision is equal to the momentum of the object after the collision.

## 4. How is the speed of each train affected by an elastic collision?

The speed of each train is affected by the mass and velocity of the other train. In an elastic collision, the heavier train will experience a smaller change in speed compared to the lighter train.

## 5. Can an elastic collision occur between objects with different masses?

Yes, an elastic collision can occur between objects with different masses. In this case, the lighter object will experience a larger change in speed compared to the heavier object.

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