Minimum position uncertainty for a 50g ball using Heisenberg principle

[jaidon]

A ball of mass 50g moves with a speed of 30 m/s. If its speed is measured to an accuracy of 0.1%, what is the minimum uncertainty in its position? What does this answer indicate about the relevance of quantum mechanics to macroscopic objects?

I am completely confused. My prof just gave us HUP but didn't explain how to use it.

I know: (delta p)(delta x) > h /2, where h is actually h bar i just don't know how to type it.

I think i need to sove for delta x, but i have tried similar problems that i have the answers to and I'm not even close.

please, if anyone can help me understand this i would greatly appreciate it.
Thanks.

 

[Data]

Indeed solving for $\Delta x$ is correct. Why don't you show us the work you've done.

 

[jaidon]

honestly i haven't figured out where to start.
i can get momentum by multiplying the mass and the speed. i wanted to multilpy that by 0.1% to get a delta p value and then solve for delta x. this is the method i used for other questions, and i did not get the right answer.

also i am not sure what is significant about the fact that it asks for the minimum uncertainty.

 

[Data]

That sounds right. Post your calculations.

Since you know the uncertainty in momentum, and $\Delta p \Delta x \geq \frac{\hbar}{2}$, the minimum uncertainty in position is achieved when there is equality.

 

[jaidon]

p=0.05kg * 30 m/s = 1.5 kgm/s.

1.5 kgm/s * 0.1% =0.0015 kgm/s

(delta x) > h/(2Delta p) where h is h bar ie) h/2pi

delta x > 6.626*10^-34/ (4 *pi* 0.0015)

delta x > 3.52*10^-32

like i said, i tried this method with another question, but i gave the kinetic energy and a 5% accuracy in the momentum. for that, i calculated the velocity from 1/2mv^2 and then multiplied by the mass. then i multiplied that value by the 5% and used the same method above for determining delta x, and i was way off. I'm not too sure about this whole HUP thing.

thanks

 

[Data]

Yes, that looks right.

Can you post the other question (that your answer was wrong for) in its entirety (preferably verbatim)?

 

[jaidon]

i just realized that i kept repeatedly using the same wrong number to figure out the other question. now i get it exactly right. thanks for your input on the my original question. guess I'm not as lost as i thought.
thanks.

 

[Data]

Good :)

I really would like to be able to make one word replies. asdf