# Elastic and inelastic collisions

• mystreet123
In summary, the angle between the paths of two particles after a collision can vary depending on the energy and mass of the particles. A high-energy proton colliding with a stationary proton will not result in a 90 degree angle due to the increase in mass of the moving proton. In general, a collision is considered elastic if the colliding particles remain the same, while an inelastic collision can result in a change in the identities of the particles involved. The equation ½ mu2 = ½ mv2 + ½ ms2 is used to calculate the kinetic energy of particles after a collision, where ms is the kinetic energy of the center of mass of the two colliding particles.
mystreet123

## Homework Statement

A low-energy particle collides elastically with a stationary particle of the same mass. The angle between the subsequent paths of both particles are 90 degrees.
But when a high-energy proton collides with a stationary proton, the angle between the two paths is not 90 degrees. Why is it so?

## Homework Equations

½ mu2 = ½ mv2 + ½ ms2

## The Attempt at a Solution

I answered that it's because the collision was not elastic so the above equation couldn't apply. But the answer is that because the proton is moving near speed of light so it's mass is greater than rest mass. So is this collision between the two protons still an elastic one? How to know whether a collision is an elastic or an inelastic one by its nature? I saw on some websites they say subatomic collisions are elastic but from another past paper it says the scattering between electrons and hydrogen nuclei is an inelastic collision...

mystreet123 said:

## Homework Statement

A low-energy particle collides elastically with a stationary particle of the same mass. The angle between the subsequent paths of both particles are 90 degrees.
But when a high-energy proton collides with a stationary proton, the angle between the two paths is not 90 degrees. Why is it so?

## Homework Equations

½ mu2 = ½ mv2 + ½ ms2

## The Attempt at a Solution

I answered that it's because the collision was not elastic so the above equation couldn't apply. But the answer is that because the proton is moving near speed of light so it's mass is greater than rest mass. So is this collision between the two protons still an elastic one? How to know whether a collision is an elastic or an inelastic one by its nature? I saw on some websites they say subatomic collisions are elastic but from another past paper it says the scattering between electrons and hydrogen nuclei is an inelastic collision...
The collision is elastic if the colliding parties remain the same. If two protons collide, both of them remain the same protons. If an electron collides with a proton, you can get a neutron and a neutrino , for example; or you can get a hydrogen atom - these are inelastic collisions.

mystreet123
ehild said:
The collision is elastic if the colliding parties remain the same. If two protons collide, both of them remain the same protons. If an electron collides with a proton, you can get a neutron and a neutrino , for example; or you can get a hydrogen atom - these are inelastic collisions.
Thank you so much!

I never understood why the equation was ½ mu2 = ½ mv2 + ½ ms2 in the first place. I understand the mu and mv portion, but I don't quite understand the ms part of the equation. What is it derived from?

Disputationem said:
I never understood why the equation was ½ mu2 = ½ mv2 + ½ ms2 in the first place. I understand the mu and mv portion, but I don't quite understand the ms part of the equation. What is it derived from?
Note that you are responding to a five year old thread to ask a peripherally related question.

My response moved to https://www.physicsforums.com/threa...sions-between-particles.1006366/#post-6531530

Last edited:

## 1. What is the difference between elastic and inelastic collisions?

Elastic collisions occur when the total kinetic energy of the colliding objects remains constant. In inelastic collisions, some kinetic energy is lost and converted into other forms of energy, such as heat or sound.

## 2. How do you calculate the coefficient of restitution for an elastic collision?

The coefficient of restitution is equal to the ratio of the relative velocities of the objects after the collision to their relative velocities before the collision. Mathematically, it is represented as e = (v2 - v1) / (u1 - u2), where v1 and v2 are the final velocities and u1 and u2 are the initial velocities.

## 3. Can momentum be conserved in an inelastic collision?

Yes, momentum is always conserved in any type of collision. In inelastic collisions, some of the kinetic energy is lost, but the total momentum of the system remains constant.

## 4. What is an example of an inelastic collision?

A common example of an inelastic collision is a car crash. When two cars collide, some of the kinetic energy is converted into sound and heat, making it an inelastic collision. The cars also stick together after the collision, reducing their relative velocities.

## 5. How does the mass of an object affect the outcome of a collision?

The mass of an object affects the outcome of a collision by determining how much momentum and kinetic energy it has. In a collision between two objects of different masses, the heavier object will experience less change in velocity compared to the lighter object. This is because the heavier object has more inertia and is more resistant to changes in motion.

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