# Perfect inelastic collison

1. Jun 24, 2010

### Agent M27

1. The problem statement, all variables and given/known data
A 6 kg object moving with a speed of 9.9 m/s collides with a 19 kg object moving with a velocity of 7.2 m/s in a direction 24* from the initial direction of motion of the 6 kg object. What is speed of the two objects after the collision if they remain stuck together?

2. Relevant equations

Px = m1v1icos$$\theta$$+m2v2icos$$\theta$$ = m1v1fcos$$\theta$$ + m2v2fcos$$\theta$$

Py = m1v1isin$$\theta$$+m2v2isin$$\theta$$ = m1v1fsin$$\theta$$ + m2v2fsin$$\theta$$
3. The attempt at a solution

Edit I realized my original way was faulty in its logic.

So what I did was I began by finding the initial and final momenta components in both the x and y directions for the two particles. Being that they stick together their final velocity ought to be the same.

$$\Sigma$$Pxi = m1v1cos$$\theta$$ + m2v2cos$$\theta$$

=184.37302

$$\Sigma$$Pyi = m1v1sin$$\theta$$ + m2v2sin$$\theta$$

=55.641573

As I mentioned their final velocity should be equal since they are stuck together. Equating my initial momenta to my final momenta in the x direction I get the following:

Vf = $$\frac{(m1v1cos\theta + m2v2cos\theta}{(m1+m2)cos\theta}$$

=8.072856 m/s

When I checked it using the momenta of the y direction I come to a different value for the final velocity which doesn't make sense so I know I made a mistake somewhere... Thanks in advance.

Joe

Edit: I tried a new way, but

Last edited: Jun 24, 2010
2. Jun 24, 2010

### Staff: Mentor

Looks good to me.

3. Jun 24, 2010

### Agent M27

Thanks Doc Al, are you refering to the first way I solved the problem or refering to this edited version? The first way did not work, so thats why I tried a new method. Thanks for all your help in all of my posts.

Joe

4. Jun 24, 2010

### vela

Staff Emeritus
Actually, your first attempt was the correct solution. How do you know the answer you got is wrong?

5. Jun 24, 2010

### Staff: Mentor

I was referring to your original post, which looked fine to me. (I haven't looked at your revision.)

6. Jun 24, 2010

### Agent M27

It is an online homework module, and this is not the first question that I have been correct about and it kicked back my answer as incorrect...Thanks for your assistance.

Joe

7. Jun 24, 2010

### vela

Staff Emeritus
Thought so. Could be you're entering too many significant figures.

8. Jun 24, 2010

### inky

Do you know the direction (angle) after collision?

9. Jun 24, 2010

### Staff: Mentor

Why would that matter?

10. Jun 24, 2010

### inky

I mean after collision, two objects stuck together. So velocities are the same but problem didn't mention direction is angle theta. I think angles are not the same before and after collision.

11. Jun 25, 2010

### Staff: Mentor

True, but the direction of the final velocity doesn't matter for this problem. All they ask for is the speed.