How do I find uncertainty (math/physics)?

Question

the problem is:

find v=d/t and its uncertainty if d=5.10 +/- 0.01 and t=6.02 +/- 0.02

I know v is 0.847 but I can't figure out how to find the uncertainty.

there is a similar problem too:

Find P=IV if I=2.10 +/- 0.02 and V=1.02 +/- 0.01

Please help. I just need to know where to start with these problems...

Answer 1

When you multiply or divide two numbers, the percentage error in the result is the sum of the percentage errors in the numbers.

When you add or subtract, the magnitude of the error in the result is the sum of the magnitudes of the errors in the numbers.


(a +- da)*(b +- db) = a*b(1 +- (da/a + db/b)
(a +- da)/(b +- db) = (a/b)(1 +- (da/a + db/b)
(a +- da)+(b +- db)=a + b +_(da+db)
(a +- da)-(b +- db)=a - b +_(da+db)

Answer 2

You need maths to come up with the uncertainty principle. It's not something that you experience on your daily life. The purpose of Schrodinger's thought experiment isn't to show that a macroscopic object can be in two states simultaneously, but rather to show that our perception doesn't apply to microscopic objects. The predictions of quantum mechanics are validated by experiments, it's our perception of small large objects that can't be extended to small objects.

Answer 3

Well, if you multiply a number carrying a 1% possible error with another number (or its inverse) carrying a 2% possible error, the resulting possible error e = 1.01 * 1.02 = 1.03 or 3%. Note it is close to additive at these small values for error.

As Cirric says, don't look for errors to cancel each other out. They always accumulate.

Answer 4

Hi. The uncertainty is the '+/-" number. It is always additive.

Answer 5

p=(2.1+.02)(1.02+.01)=2.1x1.02+error
error may be either + or -