# Momentum and kinetic energy of collision between two identical railroad cars

• dani123
In summary, a railroad car with a mass of 5.0x10^5kg collides with a stationary railroad car of equal mass, resulting in a total momentum of 4.0x10^6 kg*m/s and a loss of kinetic energy due to thermal energy and deformation of the cars.
dani123

## Homework Statement

A railroad car with a mass of 5.0x10^5kg collides with a stationary railroad car of equal mass. After the collision, the two cars lock together and move off at 4.0m/s.

a) Before the collision, the first railroad car was moving at 8.0 m/s. What was its momentum?

b) What is the total momentum of the two cars after the collision?

c) Find the kinetic energies of the two cars before and after the collision.

d) Account for the loss of kinetic energy.

## Homework Equations

Ma=Mb= 5.0x10^5 kg
Va1=8.0m/s
Va2=4.0 m/s=Vf

Vb1=0m/s
Vb2=4 m/s

## The Attempt at a Solution

a) momentum of railroad car A before collision=m*v=(5x10^5kg)*(8m/s)=4.0x10^6 kg*m/s

b) total momentum= (Ma+Mb)*Vf=[(5x10^5)*2]*(4m/s)= 4.0x10^6 kg*m/s

c) KE before= 1/2 (5.0x10^5kg) (8m/s)^2=1.6x10^7 J

KE after= 1/2 (10x10^5kg)(4m/s)^2= 8.0x10^6 J

d) There is thermal energy or deformation of cars created by the collision which results in a loss of total kinetic energy.

----> ok so, for all these questions I am just looking for someone to double check them for me and to verify that all my reasoning and work shown is correct and that I am not missing anything. Also to check and see that my significant figures are correct! Thank you so much in advance! :)

Everything looks good to me, including sig figs.

## 1. What is momentum in the context of a collision between two identical railroad cars?

Momentum is a physical quantity that describes the motion of an object. In the context of a collision between two identical railroad cars, momentum refers to the mass and velocity of the cars before and after the collision.

## 2. How is momentum conserved in a collision between two identical railroad cars?

Momentum is conserved in a collision between two identical railroad cars because the total momentum of the system remains constant before and after the collision. This means that the combined momentum of the two cars before the collision is equal to the combined momentum of the two cars after the collision.

## 3. What is kinetic energy and how does it relate to a collision between two identical railroad cars?

Kinetic energy is the energy an object possesses due to its motion. In a collision between two identical railroad cars, kinetic energy is transferred between the cars as they collide. The total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision, as long as there is no external force acting on the system.

## 4. Can the kinetic energy of the system change during a collision between two identical railroad cars?

Yes, the kinetic energy of the system can change during a collision between two identical railroad cars. This can happen if there is an external force acting on the system, such as friction or air resistance. In this case, some of the kinetic energy will be converted into other forms of energy, such as heat or sound.

## 5. How does the mass and velocity of the cars affect the momentum and kinetic energy in a collision between two identical railroad cars?

The mass and velocity of the cars play a significant role in determining the momentum and kinetic energy of a collision between two identical railroad cars. A higher mass or velocity will result in a higher momentum and kinetic energy, while a lower mass or velocity will result in a lower momentum and kinetic energy. This relationship is described by the equation p = mv, where p is momentum, m is mass, and v is velocity.

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