Inelastic collision of equal masses and velocities

In summary, after a completely inelastic collision between two objects of equal mass, each having initial speed v, the two objects move off in the same direction with a speed of v/5.5. To find the angle between their initial directions, the momentum equation is used and a triangle is formed to represent the motion of the particles. The total momentum is conserved, leading to an equation that can be solved for theta and the angle between the particles.
  • #1
Fanman22
42
0
After a completely inelastic collision between two objects of equal mass, each having initial speed, v, the two move off with speed v/5.5. What was the angle between their initial directions?

Well, inelastic collision so it looks like I'll be using the momentum equation in here. My professor loves these "ratio-type" problems and I believe that I'll have to use something of the sort on this.

Momentum in = Momentum out
mv + mv = m(v/5.5) + m(v/5.5)

Not sure where to go from there, and I don't see how I will find an angle out of all of this. Anyone have any sugestions as to where I should start?
 
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  • #2
No,no,conservation of momentum is a typical example of vector relation/equation...

Sides,in the final state,there's only one particle...:wink:

Daniel.
 
  • #3
Fanman22,

Have you tried drawing a picture showing the particles and their directions of travel before and after the collision? If not, it might help.
 
  • #4
Yeah,you'd see an isosceles triangle there.It would help you with the projection of the vector equation on some nicely chosen axis of coordinates.

Daniel.
 
  • #5
*****http://img.photobucket.com/albums/v225/Fanman22/c7f601bb.jpg *****

Is that even remotely correct? I'm not sure the isosceles triangle idea makes sense to me. I don't understand how it represents the motion of the 2 particles before the collision and how it represents the velocity of the total mass afterwards.
 
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  • #6
Nope.It should have been more like an Y.Actually exactly like an Y...

Daniel.
 
  • #7
I can see the "Y-shape" now...What I did was take the components (in the direction of the final velocity) of each V. So...

Vsin(theta) + Vsin(theta) = (v/5.5) = 2Vsin(theta)
Theta = 5.216

To find the angle between the particles...
180 - 5.216 - 5.216 = the middle angle = 169.6

But of course, I got it wrong again :grumpy:

Where did I go wrong?
 
  • #8
Fanman,

You almost have it. But what does your equation:

Vsin(theta) + Vsin(theta) = (v/5.5)

say is conserved? What's really conserved?
 
  • #9
yes what jdavel said
Edit* didn't look too closely myself
 
Last edited:

1. What is an inelastic collision?

An inelastic collision is a type of collision in which kinetic energy is not conserved. This means that the total energy of the system before and after the collision is not the same. In other words, some of the kinetic energy is lost during the collision, typically in the form of heat or deformation of the objects involved.

2. What are equal masses and velocities?

Equal masses and velocities refer to objects that have the same mass and are traveling at the same speed. In the context of an inelastic collision, this means that two objects with the same mass and velocity collide with each other.

3. How is momentum conserved in an inelastic collision of equal masses and velocities?

In an inelastic collision of equal masses and velocities, momentum is still conserved. This means that the total momentum of the system before and after the collision is the same. However, since kinetic energy is not conserved, the objects will have different velocities after the collision.

4. What happens to the kinetic energy in an inelastic collision of equal masses and velocities?

In an inelastic collision of equal masses and velocities, some of the kinetic energy is lost. This is because the objects involved stick together after the collision and some of the energy is dissipated as heat or used to deform the objects.

5. How is an inelastic collision of equal masses and velocities different from an elastic collision?

In an elastic collision, kinetic energy is conserved and both objects bounce off each other with no loss of energy. In an inelastic collision of equal masses and velocities, some of the kinetic energy is lost and the objects stick together after the collision. Additionally, in an elastic collision, the objects will have the same velocity after the collision, whereas in an inelastic collision, the objects will have different velocities.

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