Question

When you measure the distance between a series of spark marks to be 8.5 cm, a safe estimation of the uncertainty in this number due to the precision of the ruler is +/-0.1 cm (both due to the cheap construction of the measuring tool and due to reading errors).

As discussed in previous labs, uncertainties are propagated through calculations. Let us assume that this measurement of 8.5 cm, with the corresponding uncertainty, corresponds to a trail of 13 spark marks, or 12 time intervals of 1/60 s.

The speed is thus:

8.5 cm / (12/60 s) = 42.5 cm/s

For simplicity, we will assume that the rate of spark production is very precise (i.e., the uncertainty associated with the time intervals being 1/60 s introduces a negligible contribution to the total error). But the uncertainty associated with the use of a cheap plastic ruler should still be accounted for...

What is the uncertainty in the speed above, in cm/s?

Answer 1

Answer:

$0.5\frac{cm}{s}$

Explanation:

The resulting uncertainty when making a division of magnitudes with some uncertainty in the measurement is given by the following formula:

$\Delta C=\frac{A}{B}(\frac{\Delta A}{A}+\frac{\Delta B}{B})$

Here, $\Delta A$ and $\Delta B$ are the uncertainties associated with the magnitudes A and B respectively.

So, the uncertainty in the speed are given by:

$\Delta v=\frac{x}{t}(\frac{\Delta x}{x}+\frac{\Delta t}{t})\\\\\Delta v=\frac{8.5cm}{(12/60) s}(\frac{0.1cm}{8.5cm}+\frac{0}{(12/60) s})\\\\\Delta v=0.5\frac{cm}{s}$