1.B #27

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1.B #27

Postby 005343842 » Sun Oct 20, 2019 12:07 am

Don't really understand the concept behind this problem, could someone explain? A bowling ball of mass 8.00 kg is rolled down a bowling alley lane at 5.00 6 5.0 m/s-1. What is the minimum uncertainty in its position?

Angus Wu_4G
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Re: 1.B #27

Postby Angus Wu_4G » Sun Oct 20, 2019 2:30 am

Heisenberg's Uncertainty Equation is (deltaP)(deltaX) is greater than h/(4pi)
X in this case represents position, P represents momentum, and the delta represents the uncertainty.

Keep in mind that momentum is equal to mass times velocity, but since the mass is the same and does not vary in the problem, it is the velocity that changes.

Therefore we can rewrite the equation as (mass X deltaV)(deltaX) is greater than h/(4pi)

We are given the mass of the bowling ball, which is 8kg, and we are also given deltaV, which is the uncertainty in velocity, which is 5m/s. Plug in all the values and simply solve for deltaX.

Vincent Leong 2B
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Re: 1.B #27

Postby Vincent Leong 2B » Sun Oct 20, 2019 2:37 am

To solve the problem, just use the Δp Δx >= h/4pi and know that Δp = mv (mass in kg) * (velocity (m/s)) and isolate Δx to find the uncertainty of the position.

The concept behind using the uncertainty equation or applying Heisenberg's uncertainty principle here is to state that the equation itself naturally applies to everyday things; it's just that we don't use the equation because the larger the object, the more is known about them (or generally we assume so). In a quantum mechanics or quantum world perspective, the more uncertain the momentum and the position of a substance is.

The problem is a simple plug in values and generate a number type of problem but its significance is to resemble how values such as an objects position or momentum can fluctuate depending on the values given. You can see what to expect from a final answer (range of how large or small an answer is) based on given values.

Hope this helps!

chari_maya 3B
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Re: 1.B #27

Postby chari_maya 3B » Sun Oct 20, 2019 3:31 pm

Wouldn't the total uncertainty be 10 m/s, because the uncertainty is 5.00 m/s +/- 5.0 m/s?

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Re: 1.B #27

Postby Emily_4B » Sun Oct 20, 2019 3:33 pm

chari_maya 3B wrote:Wouldn't the total uncertainty be 10 m/s, because the uncertainty is 5.00 m/s +/- 5.0 m/s?

Do you always add the numbers to find the total uncertainty?

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