Can You Calculate Individual Energy Absorption in a Partially Plastic Collision?

[Karol]

Homework Statement

Is there a way to know how much kinetic energy has lost and transferred into internal energy for each of the members in a partially plastic collision?
I can only know how much kinetic energy has lost in total, i don't know how much of it each member got.
When a car collided with a parking car, i want to know what's the amount of energy that the parking car absorbed. this energy deformed the parking car

Homework Equations

Conservation of momentum: $m_1v_1+m_2v_2=m_1u_1+m_2u_2$

 

[BiGyElLoWhAt]

wut

Do you mean partially elastic collision?

Using conservation of momentum and your initial conditions, you can firstly calculate the initial energy, then apply COM to get your final conditions, and use those to calculate the final energy. The problem is that not all of the energy goes into internal energy. There's soundwaves, there's deformation (which may or may not be considered internal), and just a whole range of stuff. You can most definitely calculate the difference in energy between states and determine how much energy was lost via the collision, but not necessarily the amount of internal energy that resulted from that loss.

 

[nasu]

No, conservation of momentum alone is not enough to find the final velocities and how much kinetic energy is converted into other forms. You cannot even find the total amount unless you know some details about the mechanism of the collision, properties of the bodies, etc. Even for two bodies.
For simple objects you may find a parameter called "coefficient of restitution" which provide this missing information in a global way.

 

[BiGyElLoWhAt]

Ahh yes nasu is correct. I assumed that you had some piece of information, like the final velocity of one of the objects or something to that effect.

 

[Karol]

Yes, i have the final velocity of both bodies, and in a car collision i am not interested in sound waves etc. i assume all the lost kinetic energy in transformed into deformation. so, how much of the lost energy each body gets?

 

[nasu]

Well, if you have initial and final velocities then I don't see what is the problem. Just take the difference between the kinetic energies.
However if you don't know the initial velocities, the difficulties are still there.

 

[Karol]

If i take the difference between the initial and final kinetic energies i only get the total amount of difference, but i want to know how much of it was "consumed" by each member. in the case of the car crash, what's the amount of kinetic energy that caused the deformation in one of the cars, not both

 

[nasu]

If you do it for each car you will get the energy for each car.
When you say you know the "final velocity of both bodies" you mean two values or just one?
Do they move together after collision?

 

[haruspex]

If i take the difference between the initial and final kinetic energies i only get the total amount of difference, but i want to know how much of it was "consumed" by each member. in the case of the car crash, what's the amount of kinetic energy that caused the deformation in one of the cars, not both

There's no way to know in general. You need to know something about the materials involved. If one body is highly elastic and the other much less so, most of the lost work will probably go into the less elastic body. But it can be more complicated. Two materials may have the same coefficient of restitution but different stiffness. Less work will be done in deforming the stiffer material, so less will be lost there.
To be exact, if the moduli are k₁, k₂ and the coefficients r₁, r₂ then the deformations x₁, x₂, will be in the inverse ratio of the moduli, so the work done will also be in that inverse ratio (x_i²k_i ~ 1/k_i), and the losses will be proportional to (1-r_i²)/k_i. Or something like that.

 

[Chestermiller]

In your original post, you asked "is there any way to know..." The answer is yes, but it isn't simple. As haruspex was alluding to, one would have to do a complicated deformational stress strain analysis of the collision, and one would have to include the geometry of the deforming bumpers (etc), and the deformational properties of the metals involved (beyond the elastic range, with yield and failure). The analysis would involve the solution of a complicated set of partial differential equations. Finite element stress analysis would be the tool of choice. It would take a huge amount of work and expertise to set up the model. The $$ cost of getting the answer would be very high.

Chet