Determining Uncertainty in Position using Heinsburg's Uncertainty Principle

[aquella7]

Homework Statement

A 52.9 g ball moves at 12.2 m/s.
If its speed is measured to an accuracy of
0.04%, what is the minimum uncertainty in
its position? Answer in units of m.

Homework Equations

delta x times delta p = 1/2 (h/2pi)

The Attempt at a Solution

I used the uncertainty of the speed to determine the minimum and maximum momentums for the ball. I used these to determine what delta p is equal to (0.6195648) and then substituted that number into the equation to solve for delta x. I used kilograms for the mass, which I believe are the correct units as opposed to just grams. If you could help me determine what I am doing wrong, that would be great! Thanks!

Homework Statement

 

[LowlyPion]

Homework Statement

A 52.9 g ball moves at 12.2 m/s.
If its speed is measured to an accuracy of
0.04%, what is the minimum uncertainty in
its position? Answer in units of m.

Homework Equations

delta x times delta p = 1/2 (h/2pi)

The Attempt at a Solution

I used the uncertainty of the speed to determine the minimum and maximum momentums for the ball. I used these to determine what delta p is equal to (0.6195648) and then substituted that number into the equation to solve for delta x. I used kilograms for the mass, which I believe are the correct units as opposed to just grams. If you could help me determine what I am doing wrong, that would be great! Thanks!

Homework Statement

Welcome to PF.

Δp*Δx ≥ ℏ/2

Planck's constant is pretty small, so I'd think you should get a very small number here.

h = 6.6*10⁻³⁴

And at that you are using ℏ which is h/2π.

Your Δp = .0004*.6344 already, so Δx must be quite small as far as the minimum allowed uncertainty in Δx

 

[nlightner]

The Heinsburg's Uncertainty Principle states that the product of the uncertainty in position (delta x) and the uncertainty in momentum (delta p) is equal to or greater than 1/2(h/2pi), where h is Planck's constant.

Using this principle, we can determine the minimum uncertainty in position for the given scenario.

First, we need to convert the mass of the ball from grams to kilograms. 52.9 g is equal to 0.0529 kg.

Next, we can calculate the minimum and maximum momentums for the ball using the given speed and uncertainty.

Minimum momentum (p_min) = m*v - (0.04% of m*v)

= (0.0529 kg)*(12.2 m/s) - (0.04%)*(0.0529 kg)*(12.2 m/s)

= 0.6195 kg*m/s

Maximum momentum (p_max) = m*v + (0.04% of m*v)

= (0.0529 kg)*(12.2 m/s) + (0.04%)*(0.0529 kg)*(12.2 m/s)

= 0.6196 kg*m/s

Now, we can use these values to calculate delta p.

delta p = p_max - p_min

= 0.6196 kg*m/s - 0.6195 kg*m/s

= 0.0001 kg*m/s

Finally, we can use the Heinsburg's Uncertainty Principle to calculate the minimum uncertainty in position.

delta x = (1/2(h/2pi)) / delta p

= (1/2(6.626 x 10^-34 J*s / 2*pi)) / (0.0001 kg*m/s)

= 3.98 x 10^-34 m

Therefore, the minimum uncertainty in position is 3.98 x 10^-34 m.