Minimum Indeterminacy [ENDORSED]

[Jasleen Kaur 1J]

Your bowling ball of mass 4.02kg rolls down a lane with a speed of 2.35+/- 0.1 m.s^-1. What is the minimum indeterminacy of its position? Can you blame the Heisenberg Uncertainty Principle when your ball misses the pins?

I had trouble solving this?

[Lyndon_Bui_3J]

So you want to use the equation ΔpΔx=h/4pi. The equation is normally with a greater than or equal to sign, but since it says minimum, just use equal sign. The minimum indeterminacy of position is Δx, so you just solve for Δx using plancks constant (h) and plugging in the rest. Δp=mΔv, because momentum (p) is defined as m (mass) times v (velocity). Mass is given, so you just have to figure out what the indeterminacy of velocity (Δv) is. hint: use the margin of error given. Hope that helps!

[Jenny_Thompson_3I]

Another note to this when you are imputing the velocity into the equation you need to multiply it by 2 due to the fact that there is a +/- sign in front of it. This will account for both the positive and negative uncertainty of the velocity.

[Jazmin Martin 1D]

But we multiply the 2 to 2.35+/-0.1 m/s or just multiply 2 to 0.1m/s. I'm still a little confused on that part.

Cuz like how Is that done on a step by step mathematical basis.

Thank you,
Jazmin

[Jimmy Zhou 3D]

In regards to why it's multiplied by 2. +-0.1 is only one arm of the indeterminancy factor. delta V refers to the both arms or sides of the indeterminancy so we must use 0.2 instead of 0.1 as velocity can either be =0.1 or -0.1.

[Drake_Everlove_1K]

In regards to why it's multiplied by 2. +-0.1 is only one arm of the indeterminancy factor. delta V refers to the both arms or sides of the indeterminancy so we must use 0.2 instead of 0.1 as velocity can either be =0.1 or -0.1.

So do you mean that any value in the delta V must be multiplied by 2, always? What if the indeterminancy is something like +0.3 to -0.2, would that number then be 0.5 delta V?

[Joseph Nguyen 3L]

So do you mean that any value in the delta V must be multiplied by 2, always? What if the indeterminancy is something like +0.3 to -0.2, would that number then be 0.5 delta V?

No, he does not mean that. V itself is velocity. delta V is UNCERTAINTY in velocity. For this problem, the uncertainty is + or - .1, for which the total uncertainty is the range of how far away in values the velocity can be, which is .1 * 2 = .2. If the uncertainty was from .3 to -.2, then the range would be .5, and therefore delta V would be 0.5. That just means that in a the lowest velocity possible and the highest velocity possible (or the uncertainty) can be .5 m/s apart.