I have to do a lab with uncertainties, I have worked out that the uncertainty of the weight of Newton weights is (±0.48g)and the time uncertainty is (±0.0005s)but how do you find the uncertainty of acceleration? (using (v^2-u^2)/ (2s) ) just theoretically how would you go about doing this? and the distance was measured by a normal ruler so I guess the uncertainty of distance would be something like 0.0005m?

Question

I have to do a lab with uncertainties, I have worked out that the uncertainty of the weight of Newton weights is (±0.48g)and the time uncertainty is (±0.0005s)but how do you find the uncertainty of acceleration? (using (v^2-u^2)/ (2s) ) just theoretically how would you go about doing this? and the distance was measured by a normal ruler so I guess the uncertainty of distance would be something like 0.0005m?

thanks for helping!

Answer 1

Good question. It is not something I can answer here, for lack of time. Examples are in the first link, and if you want to check your calcualtions, see any of the uncertainity calculators in this.

http://www.google.com/search?hl=en&client=firefox-a&rls=org.mozilla:en-US:official&hs=0bp&ei=LwmKSdk_hPoyzKWgzgc&sa=X&oi=spell&resnum=0&ct=result&cd=1&q=uncertainty+in+calculations&spell=1

Few master understanding the importance of this subject, thanks for asking.

Answer 2

To calculate the uncertainty of acceleration, you need to consider the propagation of uncertainties through the given formula. Here are the steps to calculate the uncertainty of acceleration using the formula (v^2 - u^2) / (2s):

1. Write down the formula for acceleration: a = (v^2 - u^2) / (2s), where 'v' is the final velocity, 'u' is the initial velocity, and 's' is the distance.

2. Calculate the first derivative of the formula with respect to each variable on the right-hand side. The derivative with respect to 'v' is (2v), the derivative with respect to 'u' is (-2u), and the derivative with respect to 's' is (-1/2s^2).

3. Once you have the derivatives, multiply each by the respective uncertainties associated with the variables. Let's assume the uncertainties are denoted with a symbol delta (Δ). Therefore, the uncertainty of 'v' would be Δv, the uncertainty of 'u' would be Δu, and the uncertainty of 's' would be Δs.

4. Plug in the values you have into the derivatives multiplied by their respective uncertainties:

Δa = | (2v)Δv | + | (-2u)Δu | + | (-1/2s^2)Δs |

Note: The vertical bars represent absolute values.

5. Simplify the equation by evaluating the derivatives at specific values for 'v', 'u', and 's'. As you have not provided specific values, you can leave the equation as it is without numerical evaluation.

6. The resulting expression, Δa, will give you the uncertainty in acceleration.

Regarding the uncertainty in distance, you mentioned that it was measured using a normal ruler, and you assume the uncertainty to be around 0.0005m. It's worth mentioning that the uncertainty for distance measurement depends on the precision of the ruler and the skill of the person making the measurement. It is best to consult the ruler's specifications or refer to any uncertainty data provided with it to determine a more accurate value for uncertainty.

Remember that these calculations assume that the uncertainties of the measurements and equipment used in your lab are the only significant sources of uncertainty.