Calc Error in Centripetal Force | Physics Lab

[sunshine88]

Homework Statement

Determine the error in the calculated centripetal force, F (dynamic), for each value of r from the estimated error in the quantities m, r, and from the standard deviation from the mean of your three measurements of f. Derive the equation for the error using Rule # 2 for the combination of errors.

Rule #2 = When you multiply or divide two or more measurements, you add the absolute value of the fractional or percentage errors to find the fractional or percentage error in the result.

Homework Equations

FD = 4pi(squared) m f(squared)r

The Attempt at a Solution

Δ FD = Δm/ m + Δ f/ f + Δr/ r

Am I on the right track?

 

[emailanmol]

if a quantity y depends as

y=[(k^a)* (x^b)*(z^c)]/(t^d) where k is a fixed constant like ∏ or e or let's say 4/

Δy/y = b*(Δx/x) + c*(Δz/z) + d*(Δt/t) (Why?)


(its simply taking sum of all Δ(measured variable)/variable and mu;tiplying it by the power it was raised to in the formula)
here Δy means maximum possible error in y.

Now calculate your answer again

 

[sunshine88]

So would it be

ΔFd = Δm/m + 2 Δf/f + Δr/r ?

Thank you for replying!

 

[emailanmol]

Yes now the equation is correct.

Also part of the problem suggests you calculate Δf using the mean values.

What we actually assume in these cases is that the mean value you calculate after repeating the experiment n times is equal to the real vale of f.

Suppose you repeat the experiment 3 times and get value of f as 3.10,3.20, 3.20.
The mean of all this will be (3.10+3.20+3.36)/3=3.22

Now we assume the the real value of f is 3.22

so Δf in case one is |3.10-3.22|(where || is for absolute value) and similarly for other cases.
We take || to calculate maximum possible error.


I hope you understood

 

[asteriatic]

As a scientist, it is important to accurately calculate and account for errors in our measurements and calculations. In this case, the error in the calculated centripetal force can be determined by using Rule #2 for the combination of errors. This rule states that when multiplying or dividing two or more measurements, we add the absolute value of the fractional or percentage errors to find the fractional or percentage error in the result.

In order to determine the error in the calculated centripetal force (FD), we can use the equation Δ FD = Δm/ m + Δ f/ f + Δr/ r, where Δm, Δf, and Δr represent the errors in the quantities m, f, and r, respectively. This equation follows Rule #2 as we are multiplying the quantities m, f, and r to calculate the centripetal force.

To derive this equation, we can use the chain rule for combining errors. This rule states that when a quantity is calculated using multiple measurements, the error in the final result is the square root of the sum of the squares of the individual errors. In this case, we are multiplying m, f, and r, so the equation becomes:

Δ FD = √(Δm/m)^2 + (√Δf/f)^2 + (√Δr/r)^2

Simplifying this equation, we get:

Δ FD = Δm/ m + Δ f/ f + Δr/ r

Therefore, you are on the right track in using this equation to determine the error in the calculated centripetal force. However, it is important to note that this equation assumes the errors in the individual quantities are independent of each other. If there is any correlation between the errors, a more complex formula may be needed to accurately calculate the error in the final result.