Example 1.7

[Gabi Landes 1-H]

Hello!
In text example 1.7 (p. 18) -

Estimate the minimum uncertainty in:
(a) the position of an object as heavy as a marble of mass 1.0 g given that its speed is known within +1.0mm/s and
(b) the speed of an electron confined to within the diameter of a typical atom (200. pm).

Why is v = 2 x (1.0x10^-3 m/s)?

I would think this would simply be 1.0x10^-3 m/s because the "speed is known within +1.0mm/s" not +2.0mm/s?

[annie_finneran_1K]

because its +or- 1 it is really 2 because it is either plus 1 or minus 1 so the overall range is actually 2. does that make sense? like if a dog's weight fluctuated around 50 lbs with +-1, then its weight is either 49,50,or 51 lbs, but the overall range in the uncertainty of its weight at a time is actually 2 lbs.

[Daniel Cho Section 1H]

A better way to look at the indeterminacy of the velocity is to find the values of whatever speed you are given plus and minus a random number. For example, plus minus 1 is doubled because you are subtracting the range which would lead to 1 and -1 mm/s. When you subtract 1 and -1 you would get 2 which is double your given velocity.

Another example is 133[+][/u] .5. 133+.5 is 133.5 as 133-.5 is 132.5. When you subtract 133.5-132.5, the difference is 1.

I hope this helps as a good way to figure out why we double the velocity as a good shortcut to finding the indeterminate velocity.