Heisenburg Uncertainty Principle - Seems like an easy question?

[tnbstudent]

Heisenburg Uncertainty Principle - Seems like an easy question??

Homework Statement

The position of a 900 kg boulder's center of mass has been determined to within an uncertainty of 1.0 nm. (a) What is the minimum uncertainty in the boulder's velocity? (b) Repeat the calculation, but for a proton with the same uncertainty in position. (c) Repeat the calculation, but for an electron with the same uncertainty in position.

Homework Equations

Δx*Δp ~ h
Assuming that there is no uncertainty in the measurement of mass,
Δx*mΔv = h
where Δv is the uncertainty in the measurement of velocity.
Δv = h / Δx *m

h = 6.6256 *10^-34 J-s
m = 900 kg for boulder
mp = 1.6725*10^-27 kg for proton
me = 9.1*10^-31 kg for electron.
Δx = 1.0*10^-9 m

The Attempt at a Solution

I did each of these the same way. Plugged in the variables using this equation:
Δv = h / (Δx *m)
The answers I got are:
a. 7.36*10^-28 m/s
b. 396.7 m/s
c. 7.28*10^5 m/s

I'm hoping I've made a silly error somewhere, but I've been unable to find it.

 

[jambaugh]

The more precise form of the HUP is:
[tex] \Delta x \Delta p \ge \frac{\hbar}{2}[/tex]
(wikipedia:Plank's Constant)
That will give you a factor of 1/4 pi in your answers.

 

[Steely Dan]

What makes you think you've made an error?

 

[tnbstudent]

Thanks for the help.
I used the link from jambaugh and that equation helped. I got a, but it still won't accept b&c. It is really picky about significant digits.

 

[asteriatic]

I'm not sure why the uncertainty in velocity for the electron is so much larger than the other two.
I would like to point out that the Heisenburg Uncertainty Principle is a fundamental principle of quantum mechanics and is not related to the uncertainty in measurements of macroscopic objects. The principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle. Therefore, trying to apply this principle to the measurements of a boulder or a proton may not be appropriate.

That being said, the answers you have calculated seem to be reasonable based on the given information and the equations you have used. However, it is important to note that the uncertainty in velocity for the electron is larger because it has a much smaller mass compared to the boulder and the proton. The uncertainty in velocity is inversely proportional to the mass, so a smaller mass will result in a larger uncertainty in velocity.

In conclusion, while the calculations you have done are correct, it is important to understand the limitations of the Heisenburg Uncertainty Principle and its applicability to different scales of objects.