## Problem 1 B.27

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Melody Haratian 2J
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Joined: Wed Sep 30, 2020 9:48 pm
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### Problem 1 B.27

Hi everyone! I’m having trouble with problem 1 B.27 in the textbook. The problem is “ A bowling ball with a mass 8.00 kg is rolled down a bowling alley lane at 5.00 ± 5.0 m/s . What is the minimum uncertainty in its position?” Can someone help me with the first step of getting started with this problem?
Thank you!

Jiapeng Han 1C
Posts: 91
Joined: Wed Sep 30, 2020 9:50 pm

### Re: Problem 1 B.27

To calculate the uncertainty in position, you firstly have to determine the uncertainty in momentum. The speed is 5$\pm$5m/s, so the uncertainty in speed is 10-0=10m/s. We then calculate the uncertainty in momentum using p=mv. Finally, we plug the value of momentum into Heisenberg's equation, and the answer should be 6.59*$10^{-37}$m.

Eliana Carney 3E
Posts: 91
Joined: Wed Sep 30, 2020 9:31 pm

### Re: Problem 1 B.27

Hey Melody!

The first step to this problem is calculating the uncertainty of the bowling ball's momentum using the formula: Δp = (mass(m)) x Δv. The uncertainly of the velocity is going to be 5.0 m/s because as the problem states, the velocity is 5.00 ± 5.0 m/s. This shows that the uncertainly in velocity is ± 5.0 m/s.

Once you calculate the uncertainty of the bowling ball's momentum, you use this value in Heisenberg's indeterminacy equation, which is ΔpΔx ≥ (h/(4π)). By plugging in your known values and solving for Δx, you will be given the minimum uncertainty in the bowling ball's position.

Hope this helps!