Is Quantum Behavior Observable in a Tennis Ball?

[samjohnny]

Homework Statement

Attached.

The Attempt at a Solution

I've attached it. I'm not sure if I've gone wrong somewhere; I've got an extremely high quantum number, but I guess that should be expected considering we're dealing with macroscopic objects. Could someone kindly check to see if I've got it right so far. And if so, how do I carry out the last part of the question? The part about estimating the smallest fractional change QM allows and are these effects perceptible to us. I'm not quite sure how to tackle that part.

 

[berkeman]

The image of your work is pretty dark and hard to read. Can you try taking a better photo? Or else scan it. Or maybe do some image processing on the image to lighten it and increase the contrast.

or else just type it into the forum -- that is usually the best.

 

[Goddar]

Hi.
I didn't check the final numerical result but your reasoning and equations are correct and, indeed, n should be very big given the mass and energy involved.
You don't need to mention gravity since the quantum system is one-dimensional, along the direction where the ball is kicked (clearly this whole problem is not rigorous, it's just a way to make you see the scale at which quantum behaviors become noticeable).

For the last part, what would be the change in energy if n change by one unit? how does it compare to the total energy?

 

[samjohnny]

Hi.
I didn't check the final numerical result but your reasoning and equations are correct and, indeed, n should be very big given the mass and energy involved.
You don't need to mention gravity since the quantum system is one-dimensional, along the direction where the ball is kicked (clearly this whole problem is not rigorous, it's just a way to make you see the scale at which quantum behaviors become noticeable).

For the last part, what would be the change in energy if n change by one unit? how does it compare to the total energy?

I let n=1.22*10^35 from n=1.21*10^35. The change in energy is rather miniscule; only out by a few joules. Am I understanding you correctly?

 

[samjohnny]

The image of your work is pretty dark and hard to read. Can you try taking a better photo? Or else scan it. Or maybe do some image processing on the image to lighten it and increase the contrast.

or else just type it into the forum -- that is usually the best.

I apologise for that, how's it now?

 

[Goddar]

I let n=1.22*10^35 from n=1.21*10^35. The change in energy is rather miniscule; only out by a few joules. Am I understanding you correctly?

Let n = 1, so that ΔE = h²/8mL
The change is completely negligible indeed (as 1<<10^35, in fact), so how does the tennis player feel about the difference?

 

[samjohnny]

Let n = 1, so that ΔE = h²/8mL
The change is completely negligible indeed (as 1<<10^35, in fact), so how does the tennis player feel about the difference?

Aha now I get it! Thanks a lot :)