Calculating Error from an Experiment

[Scholesy]

Homework Statement

From v = s×√(g/2h), where s is distance, g is gravity, and h is height, what would the expression of error for v?

Homework Equations

My physics lab manual gives the following equations to help out-

multiplication rule- z= xy
limit error for the above: δz= |z| (δx/|x| + δy/|y|)

division rule- z = x/y
limit error for the above: same as multiplication rule

exact power- z=x^n
limit error for the above: δz= |z|[|n| (δx/|x|)]

The Attempt at a Solution

What I did was try and use those equations and fit them to the equation I'm trying to solve for, the v= ... one.

So my attempts are:

δv= |v|(δs/|s| +(δ√(g/2h))/|√(g/2h)| )

Then I would need to use the exact power rule for the square root portion but that's where I get stuck because the format calls for z = x^n. In terms of (sqrt) g/2h, x is g/2h, n is 1/2, but what would z be?

Thanks for any help

 

[anathema]

!

I would first clarify the question and ask for more information. What is the context of this equation? What are the units for each variable? Is this a theoretical equation or one that has been experimentally derived? Without this information, it is difficult to determine the appropriate error expression for v.

Assuming that this is a theoretical equation, I would approach the problem by first identifying the independent and dependent variables. In this case, the independent variables are s, g, and h, and the dependent variable is v. I would then use the multiplication rule to determine the error expression for v.

δv = |v| (δs/|s| + δ√(g/2h)/|√(g/2h)|)

To find the error for √(g/2h), I would use the exact power rule, with z = √(g/2h), x = g/2h, and n = 1/2.

δ√(g/2h) = |√(g/2h)| [|1/2| (δ(g/2h)/|g/2h|)]

To find δ(g/2h), I would use the division rule, with z = g/2h, x = g, and y = 2h.

δ(g/2h) = |g/2h| (δg/|g| + δ2h/|2h|)

Finally, I would substitute this expression into the original equation to get the final error expression for v:

δv = |v| (δs/|s| + |√(g/2h)| [|1/2| (δg/|g| + δ2h/|2h|)] / |√(g/2h)|)

This may seem complicated, but it is important to accurately account for the errors in each variable in order to obtain a reliable error expression for v. It would also be helpful to double check the units for each variable to make sure they are consistent with the units for v.

 

[tomcue]

!



Calculating error in an experiment is an important step in ensuring the accuracy and reliability of your results. From the given equation, we can see that the velocity (v) is dependent on the distance (s), gravity (g), and height (h). Therefore, the error in v will be affected by the errors in these variables.

Using the multiplication rule, we can write the expression for the error in v as:

δv = |v| (δs/|s| + δ√(g/2h)/|√(g/2h)|)

As you have correctly identified, we need to use the exact power rule for the square root portion. In this case, z would be the square root of g/2h, which can be written as z = (g/2h)^(1/2). Therefore, the error in v can be expressed as:

δv = |v| (δs/|s| + |(g/2h)^(1/2)| (δ(g/2h)/|(g/2h)|))

I would also recommend using the division rule to simplify the expression further. This would give you:

δv = |v| (δs/|s| + (1/2) δ(g/2h)/|(g/2h)|)

I hope this helps you in calculating the error in v. Remember to always consider the errors in all the variables when calculating the error in your final result.