Maybe a dumb question on standard error in equations

Click For Summary

Homework Help Overview

The discussion revolves around calculating velocity using the formula v = sqrt(2*g*change in y), where the change in y is given as 12.10 cm with an associated standard error of ±0.06 cm. Participants are exploring how to incorporate the standard error into their velocity calculation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Some participants suggest evaluating the velocity by plugging in the change in y value along with its standard error to determine the impact on the velocity calculation. Others question the validity of averaging the results from the upper and lower bounds of the change in y to find the error in velocity.

Discussion Status

The discussion is ongoing, with participants sharing different methods for incorporating standard error into the velocity calculation. There is no explicit consensus, but some guidance has been provided regarding the algebraic approximation for small errors.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the methods they can use to evaluate their answers. There is also uncertainty about the correct approach to handle the standard error in the context of the velocity formula.

JazzyJones
Messages
20
Reaction score
0

Homework Statement



I am using a value of change in y say 12.10 cm + or - .06cm.

I am trying to find velocity using the formula
v= sqrt(2*g*change in y)

how do I evaluate this equation with my standard error? because I can't just add or subtract the .06cm after since I will have a value for velocity now.

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
Can you just plug in 12.10 cm to get v and then plug in 12.10 cm + .06cm and 12.10 cm - .06cm to figure out the error in v?
 
i'm not sure if this was correct but, I plugged in the value with + then plugged in te value with -. Average the two values, and did + or - the difference between the two
 
JazzyJones said:
i'm not sure if this was correct but, I plugged in the value with + then plugged in te value with -. Average the two values, and did + or - the difference between the two
That'll work. The algebraic way is to approximate sqrt(x + dx) = sqrt(x)sqrt(1+dx/x) as sqrt(x)(1+dx/2x) for small dx.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 8 ·
Replies
8
Views
3K