# 2d Inellastic collisions

• hhh79bigo
In summary, the angle "Theta" between the final line of motion and either of the initial velocities is cos-1(2).

#### hhh79bigo

Hi all,

I was wondering if someone can help me, its been a while since I did classical mechanics, I have a question I would appreciate a little help from anyone!

2 objects with the same mass m and same velocity v have an inelastic collision . After the collision the 2 object system of mass 2*m moves with speed v/2. What is the angle "Theta" between the final line of motion and either of the initial velocities?

All I need is a way to get started if anyone can help!

Thanks a lot guys

hhh79bigo

How about using conservation of momentum?

So should I use

2mv=2m(v/2)cos(x) where x is the angle described as theta.

in which case theta is cos-1(2) which cannot be done

or can it I am not sure

Thnx

hhh79bigo

HOW are to objects with the same VELOCITY going to collide? If they have the same velocity then they are both going at the same speed in the same direction and will always have a constant distance between them! Did you mean the same speed?

"What is the angle "Theta" between the final line of motion and either of the initial velocities?"
You need to make it clear which of the initial velocities theta is measured with respect to- and the angle between the initial velocities has to come into this somewhere. I would be inclined to set up a coordinate system with the x-axis along the initial line of motion of one of the bodies.

The initial velocities are the same, the problem I have been given has said so. The only thought in my mind is that the 2 bodies collide from an angle but the question doesn't specify that.

The first question was copied word for word from my script. The only other thought is that the 1st body is set off at an earlier time than that of the 2nd body. But again my question doesn't specify.

The two ball are moving with velocities of same magnitude v. This must be the sense of the question. The total momentum of the two balls will not be 2mv (in magnitude) then.

hhhhhm i don't fully understand if the masses are the same and the velocity is the same and they are moving linearly, then surely the total momentum before the collision is 2mv

correct me if I am wrong

Im just trying to understand, because this part of mechanics has always confused me

They are not moving linearly. If you and your friend driving with same velocities on a straight track how one can catch the other, the distance between you two will remain constant, as Hallsofivy has already posted. For collision if they have same speed they must move at an angle.

Ok its just that it doesn't specify that in my question from my proffessor it says that the "Velocities" are the same in which case both the direction and magnitude maybe its a type error. I appreciate your help though. I understand that the velocities can't be the same I am just confused :)

and with the symmetry we can immediatly guess that the final line of motion must bisect the angle between the initial velocities. Is it?

I presume so however there is no specifications to the initial angles.

thanks

## 1. What is a 2d Inellastic collision?

A 2d Inellastic collision is a type of collision in which kinetic energy is not conserved. This means that some of the kinetic energy of the colliding objects is lost in the form of heat, sound, or deformation. In contrast, in an elastic collision, kinetic energy is conserved.

## 2. How is momentum conserved in a 2d Inellastic collision?

In a 2d Inellastic collision, even though kinetic energy is not conserved, momentum is still conserved. This means that the total momentum of the colliding objects before and after the collision will be the same. However, the direction and speed of the objects may change.

## 3. What factors affect the outcome of a 2d Inellastic collision?

The outcome of a 2d Inellastic collision can be affected by several factors, such as the mass and velocity of the colliding objects, the angle at which they collide, and the nature of the objects (e.g. whether they can deform or not).

## 4. How is a 2d Inellastic collision different from a 1d Inellastic collision?

A 2d Inellastic collision occurs in two dimensions, meaning that the objects involved have motion in both the x and y directions. In contrast, a 1d Inellastic collision occurs in one dimension, with motion only in the x direction. This can affect the outcome of the collision as the objects may have different velocities and angles of collision in 2d compared to 1d.

## 5. What are some real-life examples of 2d Inellastic collisions?

Some examples of 2d Inellastic collisions in everyday life include a car crash, a ball bouncing and losing some of its kinetic energy, and a bat hitting a baseball. In these situations, kinetic energy is not conserved as it is lost in the form of sound, heat, and deformation.