How to Calculate Uncertainty in Complex Equations with Trigonometric Functions

  • Thread starter Thread starter questions
  • Start date Start date
  • Tags Tags
    Uncertainty
AI Thread Summary
To calculate the uncertainty in the theoretical value of R using the given equation involving trigonometric functions, one must apply the method of partial derivatives. Since basic uncertainty rules are insufficient for this complex equation, the discussion emphasizes the need to understand how to compute partial derivatives to assess the uncertainty accurately. The conversation also highlights the use of Excel for calculations, suggesting that learning to calculate derivatives can be done quickly. Participants express a need for guidance on applying these concepts effectively. Understanding partial derivatives is crucial for solving the uncertainty problem in this context.
questions
Messages
6
Reaction score
0
calculating uncertainty
I have a lab where I have to calculate the theoretical value of R using the following equation and then find the uncertainty in R.

R=(xCOS(y))*((-xSIN(y)-SQRT((xSIN(y))^2-2*-9.8*z))/-9.8)
*I know the values of x,y,z and their respective uncertainties.

The problem is that we have only learned basic uncertainty rules (i.e. for multiplication/division you add the %uncertainty, for addition/subtraction you add the absolute uncertainties). This is much more complicated since I have to deal with SIN/COS and square roots. I was searching around and it seems that I have to calculate the partial derivative or differentials. I am not familiar with differentials and I have no idea how to solve this problem. If anyone can offer any help whatsoever it would be greatly appreciated or anywhere where I can find this information.

i'm using excel if that makes any difference.
 
Physics news on Phys.org
Do you know how to calculate a derivative? If so, it shouldn't take more than a minute to learn how to take a partial derivative.
 
take extremes!
simple and perfect
 
i know how do to partial derivatives but is the uncertainty just the partial derivative of the equation.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Understanding the Proper Uncertainty Formula to Use
Replies
4
Views
939
How can I calculate the uncertainty of the mean with Gaussian error propagation?
Replies
15
Views
924
Calculating Numerical Uncertainties in an Equation
Replies
20
Views
2K
Solving Uncertainty in Data Analysis with Spectrophotometry
Replies
3
Views
1K
Uncertainty of Speed of Sound in water, using Mackenzie's Equation
Replies
9
Views
2K
Determining uncertainty in an experimental value of g
Replies
9
Views
3K
Propagation of uncertainty with tangent function?
Replies
5
Views
6K
How to calculate the uncertainty for weight?
Replies
4
Views
5K
Calculating Uncertainty when Converting Time
Replies
3
Views
4K
How do I find the uncertainty in this specific scenario?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top