When to Use Mass in Uncertainty Equation

[Caitlin_Tang_Dis3H]

During discussion, I could not understand why my TA suddenly added mass into the equation.

The TA gave us this problem --- A bowling ball of mass 6.0 kg is rolled down a bowling alley lane at 4.00+3.5m/s. What is the minimum uncertainty in its position?
The way she used uncertainty equation is that (mass)(delta momentum)(delta position) > h/4pi. Why would she add mass to the left side of the equation?

[JacksonWissing2G]

Momentum is equal to mass times acceleration, so in this case you’d multiply the mass (6 kg) by the uncertainty in the velocity (7 m/s because it’s plus or minus 3.5) to find the uncertainty in momentum. If you know the uncertainty in momentum you can then plug everything else in and solve just for uncertainty in position.

[VeronicaShepherd3B]

When we try to find momentum the equation for position uses mass and velocity! By switching around the formula, it helps us solve it.

[Caden Ciraulo 1J]

If you replace what you wrote as delta momentum with delta velocity, that would make sense. the equation can substitute out delta momentum for mass(delta velocity) and therefore it would be mass(delta velocity)(delta position) ≥h/4π

[marisakuriyama1D]

Hi - Jackson answered this perfectly - just wanted to add that pretty much every time we are asked to solve for uncertainty position, we must use the mass to calculate the answer (unless we are explicitly given uncertainty momentum). This is because in order to calculate uncertainty position we must know uncertainty momentum, and we usually have to first calculate uncertainty momentum using equation delta momentum = mass x delta velocity.

[Samir Panwar]

In this case the uncertainty in momentum, p, is equivalent to the mass times the uncertainty in the velocity, m x delta (v). Given the mass and the uncertainty in velocity which is simply 3.5(2)=7, we can simply plug in the numbers into the equation to find the uncertainty in position.

[305597516]

Hello! So Heisenberg's Indeterminacy Equation is mostly known as (delta p)(delta x) = h/4pi, with p being momentum and x being position. However, in problems where the mass is given, we can alternatively use another formula that is essentially the same, but with momentum broken down a little bit. Momentum is essentially the mass of an object times its velocity (p = mv), and delta p is also equal to this mass times velocity. Therefore, this equation is (delta p) = mv. If we substitute mv for delta p in the equation, we get:

(mv)(delta x) = h/4pi

In this given problem, you would then use 6.0 kg for m (as we use kg for the units here) and 4.00 - 3.5 m/s as the velocity, since the question asks for the minimum. From there, you can find the uncertainty of the position. I hope this helped! :)

[Celine Khuu 2F]

Remember that momentum is equal to mass x velocity (p=mv). In the question you mentioned, the mass and velocity are given, and you are asked to find the uncertainty in position. What you must do with the given information is multiply the mass and uncertainty in velocity of the bowling ball to get the uncertainty in momentum. From there, you can proceed with the Heisenberg equation as normal!

[Arden Napoli 1E]

Hi,

It is important to remember that the variable (delta)p is included in the Heisenberg equation, which is equal to momentum, which is the same as mass *the change in velocity.

[davis sandberg 2H]

Momentum (p) = mass*velocity

[Mya_Chiarappa_2C]

Instead of having momentum in the denominator of the right side of the equation, your TA multiplied both sides by delta momentum to move it to the left side. And then they just expanded it, as delta momentum = mass * delta velocity.