Calculating Uncertainties of Measured quantities (Physics)

In summary, when calculating the value of d3 using the measured quantities d1, d2, v1, and 0, the uncertainty for d3 is determined using the formula: \frac{\Delta z}{z} = \sqrt{ \left ( \frac{\Delta x}{x} \right ) ^2 + \left ( \frac{\Delta y}{y} \right ) ^2}. This formula takes into account the errors in each individual measurement to determine the overall uncertainty for d3.
  • #1
Joystar77
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d1 = 2.53 cm +/- .05 cm

d2 = 1.753 m +/- .001 m

0 = 23.5 degrees +/- .5 degrees

v1 = 1.55 m/s +/- .15 m/s

Using the measured quantities above, calculate the following. Express the uncertainty calculated value.

a = 4 v1^2 / d2

a = 4 (1.55 m/s +/-.15 m/s)^2 / 1.753 m +/- .001 m

a = 6.8 m/s ^2 / 1.754 m

a = 13.6 m/s / 1.754 m

a = 7.753705815

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d3 = 4 (d1 + d2)d3 = 4 (2.53 cm +/- .05 cm) + (1.753 m +/- .001 m)d3 = 10.12 cm +/- .2 cm + 7.012 m +/- .004 md3 = 10.32 cm + 7.016 m

I tried to work this problem out, but I don't understand it and think it's not right. Someone please help me with this problem.
 
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  • #2
Joystar1977 said:
d1 = 2.53 cm +/- .05 cm

d2 = 1.753 m +/- .001 m

0 = 23.5 degrees +/- .5 degrees

v1 = 1.55 m/s +/- .15 m/s

Using the measured quantities above, calculate the following. Express the uncertainty calculated value.

d3 = 4 (d1 + d2)

d3 = 4 (2.53 cm +/- .05 cm) + (1.753 m +/- .001 m)

d3 = 10.12 cm +/- .2 cm + 7.012 m +/- .004 m

d3 = 10.32 cm + 7.016 m

I tried to work this out, but I don't think it's right so someone please help me.
There is no single formula that you can use to get errors. Which you use depends on what kind of experiment you are doing and what data you have. One of the typical ones in use is this:

Given x, y and their respective errors \(\displaystyle \Delta x,~\Delta y\) and the equation z = x + y you can calculate
\(\displaystyle \frac{\Delta z}{z} = \sqrt{ \left ( \frac{\Delta x}{x} \right ) ^2 + \left ( \frac{\Delta y}{y} \right ) ^2}\)

You can use the same formula for z = xy or z = x/y as well. If you have more variables, such as z = x + y + w just add a term for w under the square root.

-Dan
 

FAQ: Calculating Uncertainties of Measured quantities (Physics)

What is the purpose of calculating the uncertainties of measured quantities in physics?

The purpose of calculating uncertainties is to determine the range of possible values for a measured quantity. This helps to evaluate the reliability and accuracy of experimental results, and allows for better comparison and analysis of data.

How do you calculate uncertainties in physics?

Uncertainties are typically calculated using the formula: uncertainty = (highest value - lowest value) / 2. This takes into account the range of possible values for a measured quantity and provides a reasonable estimate of its uncertainty.

Can uncertainties be eliminated completely?

No, uncertainties are an inherent part of any measurement. They can be minimized by using precise instruments and techniques, but they can never be eliminated entirely.

How do different sources of error affect uncertainties?

Different sources of error, such as random errors or systematic errors, can have varying effects on uncertainties. Random errors can increase the overall uncertainty, while systematic errors can lead to a consistent bias in the measurement and a lower uncertainty.

How can uncertainties be reduced in physics experiments?

Uncertainties can be reduced by using more precise instruments, taking multiple measurements and averaging them, and minimizing sources of error. It is also important to follow proper experimental procedures and record data accurately to minimize uncertainties.

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