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- Thread starter blader324
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when two objects of the same mass collide (in an elastic collision) the angles that they bounce off from should combine to 90 degrees. right?

i couldnt understand. could you show a diagram or something

if the velocities of two objects after the collision multiplied to equal zero...

this too

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i don't know how to draw a diagram on this thing.

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Hi everyone, i was just wondering, when two objects of the same mass collide (in an elastic collision) the angles that they bounce off from should combine to 90 degrees. right?

Really? Let's say two the two objects (of same mass) head for each other. After an elastic collision, they retrace their paths. How would you calculate the angles and what do they add up to in my example?

Do you have a more general problem at hand? If so, post that question, we will try to help.

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if it was so as you said, people wouldnt be playing a game called snooker. try watching a game and see if the combined angle is 90

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assuming that the path of approach of object a passes through the centre of object b, object b will go in the direction of motion of object a and object a will retrace its path(provided the masses of the objects allow this condition), change in the direction of object a is 180 degrees and object b is... duh what was the initial direction of motion of b???

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It's an elastic collision. What is its definition? With the given information can you arrive at a simple relation between initial and final velocities of the objects?

Next, use the conservation of momentum and the above result to show what you have been asked for. (It's just algebra)

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i did all that already...and then i get the final velocity of A and B equal to zero

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thanks so much again!!!! THANK YOU THANK YOU THANK YOU THANK YOU!

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Doc Al

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I presume you mean that you get that the dot (scalar) product of the final velocity vectors equal zero: [itex]\vec{V}_a \cdot \vec{V}_b = 0[/itex]. If so, you're done since that implies that the angle between the vectors is 90 degrees.i did all that already...and then i get the final velocity of A and B equal to zero

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Are You Serious!!!!

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but how does that work?

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Doc Al

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That's a fact, jack.

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Doc Al

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The scalar product of the vectors [itex]\vec{A} \cdot \vec{B} = AB\cos\theta[/itex]. That can only be zero if theta = 90 (or A or B equals zero, which is not the case here).but how does that work?

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Doc Al

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My pleasure. (Next time, stick to one thread! )

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Psst,doc... theta = pi/2. ;)

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Doc Al

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D'oh! Thanks, neutrino. I'll fix that! (I left out the 9 in 90.)Psst,doc... theta = pi/2. ;)

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First all, I think this result applies only if one of the balls is initially at rest, right? You can then prove the result by applying the conservation laws of energy - since it's an elastic collision - and of momentum.

Conserving energy gives you one equation in terms of the magnitudes of the three velocities (initial velocity of the one moving ball and two final velocities), and conserving momentum gives you a vector equation relating the three velocities. Combine the two equations and do a little algebra and you get the result you're looking for, i.e. the dot product of the two final velocities is zero.

And by the way, for those posters who were wondering about the collision headed directly for the center of the stationary ball, you can work out what final velocities must be in that case, and you'll see that the ball that was initially moving will be at rest and the initially stationary ball will move with the initial velocity. The dot product is still zero, so this result is consistent with the statement that the velocities are perpendicular.

Conserving energy gives you one equation in terms of the magnitudes of the three velocities (initial velocity of the one moving ball and two final velocities), and conserving momentum gives you a vector equation relating the three velocities. Combine the two equations and do a little algebra and you get the result you're looking for, i.e. the dot product of the two final velocities is zero.

And by the way, for those posters who were wondering about the collision headed directly for the center of the stationary ball, you can work out what final velocities must be in that case, and you'll see that the ball that was initially moving will be at rest and the initially stationary ball will move with the initial velocity. The dot product is still zero, so this result is consistent with the statement that the velocities are perpendicular.

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