Fractional Uncertainty in Total Mass fM: Taylor Expansion & Relation to fd

[leonne]

Homework Statement

If fd is the fractional uncertainty on the distance, what is the fractional uncertainty
on the total mass fM? Hint: use our Taylor expansion approximation that (1 +- x) ^a ~ 1 +- ax when x << 1.
The fractional uncertainty in the mass fM will be related to fd in a simple way.

Homework Equations

((f^(n) (a))/n!)(x-a)^n

The Attempt at a Solution

Don't really understand this question do i just do a taylor expansion or what

 

[mighty2000]

?

Hello there,

Yes, you are on the right track. The question is asking for the fractional uncertainty on the total mass fM, which is related to the fractional uncertainty on the distance fd. To solve this, you can use the Taylor expansion approximation, which states that (1 +- x)^a ≈ 1 +- ax when x << 1.

Using this approximation, we can write the total mass fM as (1 +- fd)^3, since the mass is directly proportional to the distance cubed. Using the Taylor expansion approximation, we can rewrite this as 1 +- 3fd. This means that the fractional uncertainty on the total mass is 3 times the fractional uncertainty on the distance, fd.

Therefore, the fractional uncertainty on the total mass fM is simply 3fd. I hope this helps. Let me know if you have any other questions.