What is the optimal velocity for a bouncing ball to pass through a window?

[Oonej]

that is using your assumption that the angle doesn't change upon the first bounce.

 

[eczeno]

please see my post above. the assumption i make seems the only reasonable one to make.

 

[Oonej]

My understanding, not to discredit yours, is that the ball will encounter a rotation. I have had several people say that it does. I have researched it and can't find any proof.

So its all hearsay... can anyone provide information on this? If it is the case that the ball doesn't change trajectories after impact this problem becomes 10x's easier!

 

[eczeno]

i did say that i was making an assumption, and that there are many circumstances in which the law of reflection will not hold.

if there is friction, and the ball does begin to rotate, which is much more realistic, then the trajectory will probably be altered. But this will not, in my opinion, depend on e. and the equation theta_r = e * theta_i simply cannot be right; it predicts very strange things.

it is not immediately obvious to me how the angle of reflection would change with the introduction of friction, but it certainly depends on information like the coefficient of friction, which is not provided. and so, in order to be able to solve the problem, one must ignore friction and assume the law of reflection holds. i see no other way to solve the problem with the information provided.

cheers

 

[Oonej]

I will assume at this point that the law of reflection holds. and I can probably solve the whole project now :)

 

[cupid.callin]

i did say that i was making an assumption, and that there are many circumstances in which the law of reflection will not hold.

if there is friction, and the ball does begin to rotate, which is much more realistic, then the trajectory will probably be altered. But this will not, in my opinion, depend on e. and the equation theta_r = e * theta_i simply cannot be right; it predicts very strange things.

it is not immediately obvious to me how the angle of reflection would change with the introduction of friction, but it certainly depends on information like the coefficient of friction, which is not provided. and so, in order to be able to solve the problem, one must ignore friction and assume the law of reflection holds. i see no other way to solve the problem with the information provided.

cheers

you should always work with data given to you and ignore what's not

if e is given then that obvoiusly means that v_final is not equal to v_initial
so law of reflection is not followed

and it is possible that we can throw the ball through window if we change velocity

 

[Oonej]

you should always work with data given to you and ignore what's not

if e is given then that obvoiusly means that v_final is not equal to v_initial
so law of reflection is not followed

and it is possible that we can throw the ball through window if we change velocity

Is this ignoring my original assumption that the angle changes upon each bounce? If so, I was aware of that already ;) then someone told me it changes angles...

 

[eczeno]

if e is given then that obvoiusly means that v_final is not equal to v_initial
so law of reflection is not followed

I agree the speeds will be different, but they are speeds, they tell us nothing about direction. if we do not assume the law of reflection, how can we determine the angle of reflection? knowing e tells us nothing about direction, so that will not help us. I fail to see any other way to address the problem of direction than assuming the law of reflection. any deviation from the law of reflection will be due, in most part, to friction. since we don't know the friction, i ignored it.

 

[Oonej]

ah! I figured out why the angle changes!

the COR does not effect the X direction at all. Just the Y. so with the equation of Tan. it is Tan (theta) = y/x well if the y is affected by the COR, then the new angle is infact changed Tan^-1( y(COR) / x )

 

[eczeno]

yes, if that is the definition of COR, then you can use it to find the change in angle.

 

[cupid.callin]

i already told you that

during collision and falling X component will experience no change

 

[Oonej]

Well it just made sense to me when I thought about it :) Not stealing your thunder!

 

[Oonej]

you should always work with data given to you and ignore what's not

if e is given then that obvoiusly means that v_final is not equal to v_initial
so law of reflection is not followed

and it is possible that we can throw the ball through window if we change velocity

what velocity allows you to make the window? Because I tried a lot of different combination

 

[eczeno]

sorry cupid, i totally missed that as well. understanding the proper definition of a term is very helpful. :)

 

[Oonej]

I made a chart with a very HIGH velocity to see the impact. and with an extremely high velocity the ball was still landing under the window. The angle change is what screwed it up.

 

[Oonej]

Ok there was a correction to this problem. My TA assigned this project with an error.

We are to assume the ball does not change angle after each bounce, the COR only affects the Velocity.

If you guys could please shed some light...

I took Y₀ formula, combined it with the x₀ formula, and made a y9x) formula. after which I had a Y₁(x) and Y₂(x) and put in and x2 i replaced with 5 - x1 and had an enormously large equation that took forever to solve... and it gave me a number that was ALMOST correct... I got v1 to equal ~15.5 and then divided by my COR² and got 24.898 ... the correct answer is somewhere around that, between 23 and 24 for the min... the max is huge around 800-900ish ( i think ) but hoping there is a an easier solution to this problem ...

Thanks for any help guys! <3

 

[Oonej]

After brute forcing an excel sheet with numbers, i came to the conclusion that there are numerous min and max's ...

for instance, a min of 24

a max of ~191, ~780 etc seem to all work, unless i did something wrong in my formulas...
but like a velocity > 191 fails, but when its around 700ish, it works again...

how can this be?