Solving Planck's Uncertainty Problem for Baseball Motion

[georgeh]

Imagine playing baseball in a universe where Planck's constant was 0.60 J-s. What would be the uncertainty in the position of a .50 kg baseball that is moving 20 m/s with an uncertainty of 1.0 m/s?
so i know, delta X*delta P=(plancks constant/2pi)/2
I solve for x. and it will tell me the uncertainty for position in the x,
my question is, how do i find out the percent uncertainity for this problem?
Do i do, 1/20 and that will give me % uncertainty? i know basic question..but any help is appreciated.

 

[big man]

You almost have it. When you divide the uncertainty by the actual value it is called the relative uncertainty. So 1/20 will give you the relative uncertainty and it isn't the percentage uncertainty. The percentage uncertainty is simply found by multiplying the relative uncertainty by 100.

ie $$\\frac{\Deltax}{x}(100)=% uncertainty$$

Edit: I still don't see the above latex properly so I will just put it in text here.

% unc = [delta(x)/x]*100

So obviously once you find the momentum ($$p=mv$$), multiply by the RELATIVE uncertainty (will be 1/20 in your case) to find the uncertainty in momentum. You then solve for x like you said, but remember this will give you the absolute uncertainty in the position...so unless you know the inital value for x you can't find the percentage uncertainty for the position.

That last paragraph was probably not necessary, but I thought it might explain a bit more ??

 

[kyle8921]

I would approach this problem by first using the formula you provided, Δx*Δp=(h/2π)/2, to calculate the uncertainty in position (Δx) for the given scenario. In this case, Δp can be calculated by multiplying the mass of the baseball (0.50 kg) by the uncertainty in velocity (1.0 m/s), giving us a value of 0.50 kg*m/s for Δp. Plugging in the given value of Planck's constant (0.60 J-s), we get:

Δx*0.50 kg*m/s = (0.60 J-s/2π)/2

Δx = (0.60 J-s/2π)/2 * (1/0.50 kg*m/s) = 0.19 m

Therefore, the uncertainty in position for a baseball moving at 20 m/s with an uncertainty of 1.0 m/s in a universe with a Planck's constant of 0.60 J-s is 0.19 m.

To find the percent uncertainty, we can divide the uncertainty in position (0.19 m) by the actual position (20 m) and multiply by 100 to get:

Percent uncertainty = (0.19 m/20 m) * 100 = 0.95%

This means that in this scenario, the position of the baseball could be off by 0.95% due to the uncertainty in velocity and the value of Planck's constant.

It's important to note that Planck's constant is a fundamental constant of nature and does not change in different universes. This exercise is simply a hypothetical scenario to illustrate the impact of Planck's constant on the uncertainty in position for a moving object.