# Solving an Impact Problem: Elastic Collision of Two Wagons with Bumpers

• Alec
In summary, the conversation discusses a collision between two wagons with elastic bumpers. After the collision, wagon A with a mass of 0.1 kg has a speed of 0.5 meters/second while wagon B remains still. The conversation focuses on finding the velocity of each wagon before the collision by using the principles of conservation of energy and conservation of momentum. The equations used to solve for the unknowns are discussed, as well as the steps needed to solve the set of equations.
Alec
Hi,
two wagons with elastic bumpers colide without any friction. Wagon A has the mass 0.1 kg while wagon B has 0.4 kg. After the collision wagon A has the speed 0.5 meters / second and wagon B lies still. Taken in consideration that the collision was elastic, what velocity does each wagon have before the collision?

I've came to the conclusion that Wk before = Wk after since it's elastic.
And that you can calculate the Wk after since you have all the information, yet this leaves me with two unknown constants, V1 and V2.

What else besides the energy has to be conserved?

The momentum: P before = P after.
But still, I have V1 and V2 unknown.

You have only two unknowns, right? (V1 and V2).

you have decided on two equations:

Conservation of energy (NOT work!)
Conservation of momentum.

With two equations and two unknowns, you can solve the set of equations

Ok, how?
I seriously have no idea.
Could it be that Wk = p^2/2m ?

ENERGY is p^2/2m (I'm a bit disturbed by your use of the variable Wk -- is that how your book denotes it? I'd say the kinetic energy KE or E_k is p^2/2m).

Calculate the total energy of the two objects before the collision.
Write an expression for the total energy after the collision (using variables for the unknowns).
Set these two equal to each other.
THAT means that energy is conserved -- since energy before the collision equals the energy after the collision -- which is the case in an elastic collision (no energy is used in heating or deforming the objects.

Do the same for the momentum.

Then you have two equations to solve for the unknowns. (look up how to solve a set of equations).

Sorry, yeah my book says Energy is Wk, although Ek is much more logical in English (I'm european if that explains it).

Well I've tried figuring it out but I have no idea how to solve for two unknown s. Physics is really not my cup of tea.

Alec said:
Well I've tried figuring it out but I have no idea how to solve for two unknown s. Physics is really not my cup of tea.
Perhaps you could show us what you have written?

yes, sorry.
I wrote:
Ek = (0.1^2 * V(1)^2) / 0.2 + (0.4^2 * V(2)^2 / 0.8) = 0.0125.
Momentum = V1 * 0.1 + V2 * 0.4 = 0.0125.

This was before the collision.
After the collision it's the same but V(2) = 0 and V(1) = 0.5. So:
Ek = (0.1^2 * 0.5^2) / 0.2 + (0.4^2 * 0^2 / 0.8) = 0.0125.
Momentum = 0.5 * 0.1 + 0 * 0.4 = 0.0125.

Alec said:
yes, sorry.
I wrote:
Ek = (0.1^2 * V(1)^2) / 0.2 + (0.4^2 * V(2)^2 / 0.8) = 0.0125.
Momentum = V1 * 0.1 + V2 * 0.4 = 0.0125.
In these two equations you have used the results you found from the following equations

This was before the collision.
After the collision it's the same but V(2) = 0 and V(1) = 0.5. So:
Ek = (0.1^2 * 0.5^2) / 0.2 + (0.4^2 * 0^2 / 0.8) = 0.0125.
Momentum = 0.5 * 0.1 + 0 * 0.4 = 0.0125. <== You need to look at this again
See the annotations in the quote

## 1. What is an elastic collision?

An elastic collision is a type of collision where there is no loss of kinetic energy. This means that the total kinetic energy of the system before and after the collision remains the same.

## 2. How do you solve for the final velocities of two wagons in an elastic collision?

To solve for the final velocities, you need to use the conservation of momentum and the conservation of kinetic energy equations. This involves setting the initial and final momenta and kinetic energies equal to each other and solving for the final velocities.

## 3. Can two objects with different masses have the same final velocities after an elastic collision?

Yes, it is possible for two objects with different masses to have the same final velocities after an elastic collision. This can happen if the initial velocities and masses of the objects are carefully chosen.

## 4. How do bumpers affect the outcome of an elastic collision between two wagons?

Bumpers can affect the outcome of an elastic collision by changing the duration of the collision. If the bumpers are compressible, they can increase the duration of the collision and decrease the impact force, resulting in less damage to the wagons.

## 5. What are some real-life applications of understanding elastic collisions?

Understanding elastic collisions is important in various fields such as engineering, physics, and sports. It can be used to design safer cars with better bumpers, predict the outcome of collisions in particle accelerators, and optimize equipment used in sports like billiards and pool.

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