# 2D Elastic Collision

1. Jun 20, 2012

### Zeeshan86

Hallo !
I am working on a problem.
The data of the problem is:
Two bodies are coming towards each other:
Body 1:
Mass = 3.5 Kg

Body 2:
Mass = 5 Kg
The velocity of body-2 before hitting was 3m/sec and angle was 45 degree.
The velocity of body-2 after hitting is 3.26197 m/sec and the angle is -40.565 degree.

I have to calculate the hitting velocity and angle of the Body-1.

By the conversation of momentum in the x-direction I have calculated the x-component of the body-1 before and after the hitting.

I am unable to calculate the y-component of the Body-1 before and after the collision.
I have get one equation that :
V_body1_y_component (before collision) = V_body1_y_component (after collision)

But I am not getting numerical value for the y-component of the body-1.

Can anybody help me ?
Regards,
Zeeshan

2. Jun 20, 2012

### jfy4

Remember that in an elastic collision kinetic energy is conserved. Make sure to use that also, you have
$$m_1 v_{1}^2 +m_2 v_{2}^2=m_1 v'_{1}^2+m_2 v'_{2}^2$$
in addition to the momentum equation. Furthermore, if you have figured out the velocity of $m_1$ before and after you can use trigonometry to solve for $m_2$.

P.S. this is a classic physics problem, perhaps before starting a new thread, give a quick search here and you will find this problem has been discussed before :)

3. Jun 21, 2012

### Zeeshan86

Dear Judah,

I have solved everything for mass-2. I know the velocity of Mass-2 before and after the collision in x and y-direction.

Using the law of conversation of momentum in x-direction I calculate the x-component of velocity of Mass-1 but when I am using the law of conversation of momentum in y-direction the it gives the following equation:

Mass-1 (y-component before collision) = Mass-1 (y-component after collision)

If I use the law of conversation of KE then I will get more than one value of the velocity of the Mass-1 before and after the hitting.

-----------------------------
PS : I have checked the other posts related to this topic, and I didn't get my answer.
I am not a Physicists, I am an engineer and I am using this in my some project.

4. Jun 21, 2012

### Infinitum

Hi Zeeshan86!

You cannot conserve momentum for only mass 1, as it experiences an impulsive force due to collision with mass 2. So, consider the initial and final y-momentum of mass 2 in this equation too.

5. Jun 21, 2012

### jfy4

Lets look at what you can say right off the bat. First, the collision is elastic, and there are no external forces, so kinetic energy is conserved, and momentum is conserved. One is a scalar, the other, a vector. Lets write these equations down.
$$p^i _1 +p^i _2 = p'^i _1 + p'^i _2$$
$$T_1 +T_2 =T'_1 +T'_2$$
with primed variables as after and un-primed as before. The $i=1,2$ for the two components of the vectors in the x=1, and y=2 directions, and the subscripts 1 and 2 denote the different bodies. All in all you actually have three equations:
$$p^x _1 +p^x _2=p'^x _1 +p'^x _2$$
$$p^y _1 + p^y _2 = p'^y _1 +p'^y _2$$
$$m_1 v_1 ^2 +m_2 v_2 ^2 = m_1 v'_1 ^2 + m_2 v'_2 ^2$$
This should help to get you back on track.

6. Jun 22, 2012

### Zeeshan86

Hi !

I am working on a table tennis playing robot. The picture of the robot is attached.

I have few questions.

1) Can I consider the collision between Ball and the plate as the two dimensional collision ? ? (At this time I am not considering z-axis)

2) If I am considering the 2-Dimensional collision (neglecting z-axis) and the mass of the Ball is considered as Mass-2, then should I consider the whole mass of the Robot as Mass-1 OR only the mass of the hitting plate is considered as Mass-1 ?

I am confused about the Mass-1 ... Either the whole robot is considered as Mass-1 or only the hitting plate is considered as Mass-1.

Can anyone help me in this ?

Regards,
Zeeshan

7. Jun 27, 2012

### Zeeshan86

Hi Judah !
I am still facing problem in calculating the hitting angle and velocity of Mass-1.
Can I have your email ID, so that I can send you my calculations.
Regards,
Zeeshan

8. Jun 27, 2012

### Zeeshan86

What would be the case, if the ball is collided with the plate. Just like the table tennis.
Can we also consider the collision between the table tennis racket and ball as the 2D collision like collision between two ball ? ?
Will the shape of the plate will effect the equations ?

9. Jun 27, 2012

### jfy4

if the ball is hitting a paddle being held stationary by someone, it's just like if a ball collides with a brick-wall, if the paddle is moving, it juts means the ball-wall relative velocity is larger. you can post your calculations on this thread if you want and I can take a look at some point.

10. Jun 27, 2012

### Zeeshan86

My calculations are in the attachment.
First I solve the problem in forward direction and then I try to solve it in the reverse direction to get the same result.
I have used all the conditions for conversation of momentum (x and y-direction) and the conversation of KE.
But I still required another equation.
I will be very thankful to you.

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