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        riddles >> medium >> A Brick and A Tennis Ball (Physics)
        
(Message started by: Barukh on Jan 12^th, 2004, 2:27am)

Title: A Brick and A Tennis Ball (Physics)
Post by Barukh on Jan 12^th, 2004, 2:27am

A brick falls from 1 meter height onto a tennis ball :o. After collision, the brick bounces up 0.5 meter. To what height will the tennis ball bounce ?

Title: Re: A Brick and A Tennis Ball (Physics)
Post by towr on Jan 12^th, 2004, 4:40am

that depends on a few things..
Is the tennisball secured to the ground? Does the brick bounce straight up, how much energy is lost in deformation of the tennisball, sound and heat (and perhaps even damage to the brick). What are the weights of the brick and the tennisball. What is the tennisball resting on. Was the tennisball even at rest when it was hit by the brick?

Supposing the brick falls straight down, and bounces straight up, is heavier than the tennisball, which also bounces straight up (and was at rest when hit), then the tennisball won't bounce higher than the brick since it'll bounce back down on hitting the brick above it, so 0.5 m
Of course this will give some very curious effects, seeying as when no energy leaves the system the tennisball and the brick will keep bouncing on each other and the floor (in which case momentum is kind of a problem since it need to be conserved, so energy must be lost through the floor, I think.. Unless the floor is infinitely heavy?! maybe.. )

Title: Re: A Brick and A Tennis Ball (Physics)
Post by Barukh on Jan 12^th, 2004, 5:36am

on 01/12/04 at 04:40:37, towr wrote:

that depends on a few things.

towr, I completely agree with you. What I have to say in my own defence is that - like usualy in such kind of questions - all abstractions/simplifications are assumed, if not stated differently.

So, the tennis ball is at rest on the the ground, there is no energy lost due to heat/deformation, the brick falls straight down and bounces straight up etc.

Quote:

...tennisball and the brick will keep bouncing on each other and the floor

The question is about the very first bounce.

Title: Re: A Brick and A Tennis Ball (Physics)
Post by towr on Jan 12^th, 2004, 7:02am

Well, I'm still hard pressed to answer without knowing the mass (or at least the ratio) between the brick and the tennis ball..
::[hide]The brick looses half it's energy to the ball (at the top it has half the potential energy compared to when it was dropped)
supposing m_brick=k*m_tennisball, I would say the tennisball bounces to k*1/2 m, if it wasn't for the brick being in the way. If it is in the way, some of the kinetic energy of the ball is transferred back to the brick, which goes higher than without it (unless the ball is heavier than the brick) so the ball won't bounce higher than somewhere below the 1/2 meter mark[/hide]::
Unless I'm missing something..

Title: Re: A Brick and A Tennis Ball (Physics)
Post by THUDandBLUNDER on Jan 12^th, 2004, 7:25am

Quote:

To what height will the tennis ball bounce ?

William of Ockham's answer:[hide]It won't because it cracked while the brick was bouncing off it.[/hide]
(But hang on, Bill has just noticed that this in in Medium!) :-/

If the brick is k times the weight of the tennis ball, off the top of his head he now gets [hide]k/2 metres.[/hide]

(Still don't see why it's in Medium.)

Title: Re: A Brick and A Tennis Ball (Physics)
Post by Barukh on Jan 16^th, 2004, 4:16am

on 01/12/04 at 07:25:19, THUDandBLUNDER wrote:

Still don't see why it's in Medium.

Where do you think it should be?

OK, let me present the solution I know – in hope it will initiate some discussion ;D
[smiley=blacksquare.gif]
[hide]When the brick starts bouncing after the collision, its speed equals the speed of the topmost point of the tennis ball – let denote it by v. Using the law of conservation of mechanical energy, we get that it will bounce to the height h_B = v²/2g.

After the collision and before leaving the ground, consider the tennis ball to be a perfect string. When it starts bouncing, the speed of its center of gravity is v/2, so it will reach the height h_T = h_B / 4.

Not only the answer is independent of mass, it doesn't depend on the original brick's height.[/hide]
[smiley=blacksquare.gif]

Title: Re: A Brick and A Tennis Ball (Physics)
Post by rmsgrey on Jan 22^nd, 2004, 8:44am

I'm not convinced by Barukh's analysis - it seems to assume that, at the time when the brick loses contact with the ball, it is the exact instant when the ball finishes decompressing, and that the ball is still in contact with the ground at that point. As the tennis ball has to account for half the energy in the system (since there's nowhere else for it to go by assumption, and the brick ends up with half) it must still be compressed when it loses contact with the brick. There's a contradiction looming, but I don't have time to explore it fully. Suffice to say that the problem statement describes an unphysical situation except for tennis balls ~~lighter~~ heavier than the brick ~~and h greater than two ball radii~~

Title: Re: A Brick and A Tennis Ball (Physics)
Post by Sameer on Jan 22^nd, 2004, 11:21am

Actually using law of conservation of energy I get

height of ball = (mass of brick)/(2 * mass of ball)

The flaw in your arguement is that you have assume that velocity of ball to be same as that of brick which would be false and that the velocity equivalent of energy would depend on ball's mass.

Title: Re: A Brick and A Tennis Ball (Physics)
Post by rmsgrey on Jan 23^rd, 2004, 7:14am

the brick only accelerates upwards while in contact with the top of the ball, so when they separate, the brick and the top of the ball must have the same velocity...

Title: Re: A Brick and A Tennis Ball (Physics)
Post by aero_guy on Jan 23^rd, 2004, 12:01pm

Barukh's reasoning seems correct (with a lot of assumptions). It has the interesting effect that you can identify the mass of the tennis ball. From conservation of energy we see that m_brickh_b=m_ballh_ball so that the final energy equals the energy of the brick inititally.

This tells us that the tennis ball weighs four times as much as the brick, or the assumptions in the problem are false. That is one hell of a tennis ball.

Title: Re: A Brick and A Tennis Ball (Physics)
Post by Sameer on Jan 23^rd, 2004, 4:07pm

on 01/23/04 at 12:01:26, aero_guy wrote:

Barukh's reasoning seems correct (with a lot of assumptions). .

Please Explain!!! :-/

Title: Re: A Brick and A Tennis Ball (Physics)
Post by KarmaBandit on Jan 23^rd, 2004, 6:48pm

My two cents:

I would put towr's original response of "k * (1/2) meters" on a Freshman physics test, though I would expect to see something more like Barukh's analysis in real life.

Barukh's analysis takes into account the loss of energy during the collision in a neat way, though the "perfect string" approximation will probably only give you a rough estimate of real life.

Also:

> "From conservation of energy we see that m_brickh_b=m_ballh_ball "

I don't see any reason for that to be true. Why do they have the same final energy?

Title: Re: A Brick and A Tennis Ball (Physics)
Post by rmsgrey on Jan 24^th, 2004, 4:33am

Barukh's second post explicitly rules out energy loss to heat/deformation, so, unless a significant amount ends up as sound or something, the kinetic + gravitational potential energy of ball and brick after collision must equal the intial g.p.e. or the brick.

Since the brick bounces to half its initial height, it ends up with half the energy. so the tennis ball must have the other half. Bouncing to a quarter the height of the brick, it must therefore have four times the mass.

Title: Re: A Brick and A Tennis Ball (Physics)
Post by Sameer on Jan 29^th, 2004, 9:47am

on 01/24/04 at 04:33:31, rmsgrey wrote:

Bouncing to a quarter the height of the brick, it must therefore have four times the mass.

According to Barukh's post, a ball of any mass will bounce to quarter the height!!!!

According to rmsgrey, since it bounces to quarter the height, its mass is 4 times.

:-/

Still waiting for towr's explanation!!!!

Title: Re: A Brick and A Tennis Ball (Physics)
Post by towr on Jan 29^th, 2004, 2:25pm

on 01/29/04 at 09:47:01, Sameer wrote:

Still waiting for towr's explanation!!!!

I don't really have a differing view..

aero_guy and rmsgrey have explaned it well enough imo.
The constraints of the problem make it so you needn't know the mass of the ball, as there is only one possibility for it.

Title: Re: A Brick and A Tennis Ball (Physics)
Post by lucierty on Apr 26^th, 2004, 2:12am

:-X :-[ :P ::) ??? 8) :o :( >:( ;D :D ;) :)HOW WOULD I KNOW IM TRYING TO DO A PROJECT ON WETHER HEAT AFFECTS THE HEIGHT OF THE BOUNCE OF THE TENNIS BALL. :o :'( :-* :-/

Title: Re: A Brick and A Tennis Ball (Physics)
Post by Icarus on Apr 26^th, 2004, 4:20pm

lucierty:

1) Please stop screaming and punching everything in sight! Perhaps it's time for your medications?

2) Theoretically, there are small changes in the overall velocity of the ball due to heat exchange between it and the floor that it bounces from. These exchanges can go either way, sometimes increasing the velocity of ball, sometimes decreasing it - on average not changing it, assuming the ball and floor at the same temperature. However, for a large object like a ball, these effects are below our ability to measure. For molecules they are substantial.

There is another affect of temperature, though. As the temperature increases, the material properties of both ball and floor change. My guess is that as temperature rises, hardness of both will decrease, resulting in more inelastic collisions, and thus as temperature rises, the ball will not bounce as high.