Problem 1 B.27

[Melody Haratian 2J]

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]

To calculate the uncertainty in position, you firstly have to determine the uncertainty in momentum. The speed is 55m/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*m.

[Eliana Carney 3E]

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!