Chapter 1, Problem 7P

(a)

To determine

The percentage of uncertainty of a hand-timed measurement of $5.5\text{ s}$ .

Answer to Problem 7P

Solution:4%

Explanation of Solution

Given:

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s due to human reaction time atthe start and stop moments.

Formula used:

Here, the formula used is

  $\text{Percent uncertainty = }\frac{\text{Absolute uncertainty}}{\text{Absolute length}}\text{ ×100 }$

  $\begin{array}{l}\text{Where, Absolute uncertainty = 0}\text{.2 s}\hfill \\ \text{ Absolute time = 5}\text{.5 s}\hfill \end{array}$

Calculation:

  $\begin{array}{l}\frac{0.2}{5.5}=0.03636\hfill \\ 0.03636\times 100\%=3.6\%\approx 4\%\hfill \end{array}$

Conclusion:

Percent uncertainty of a hand-timed measurement of 5.5 s is almost 4%.

(b)

To determine

The percentage of uncertainty of a hand-timed measurement of 55 s.

Answer to Problem 7P

Solution:0.4%

Explanation of Solution

Given:

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s due to human reaction time at the start and stop moments.

Formula used:

Here, the formula used is

  $\text{Percent uncertainty = }\frac{\text{Absolute uncertainty}}{\text{Absolute length}}\text{ ×100 }$

  $\begin{array}{l}\text{Where, Absolute uncertainty = 0}\text{.2 s}\hfill \\ \text{ Absolute time = 5}\text{.5 s}\hfill \end{array}$

Calculation:

  $\begin{array}{l}\frac{0.2}{55}=0.00363\hfill \\ 0.00363\times 100\%=0.36\%\approx 0.4\%\hfill \end{array}$

Conclusion: Percent uncertainty of a hand-timed measurement of 55 s is almost 0.4%.

(c)

To determine

The percentof uncertainty of a hand-timed measurement of 5.5 min.

Answer to Problem 7P

Solution:0.1%

Explanation of Solution

Given:

Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s due to human reaction time atthe start and stop moments.

Formula used:

Here, the formula used is −

  $\text{Percent uncertainty = }\frac{\text{Absolute uncertainty}}{\text{Absolute length}}\text{ ×100 }$

  $\begin{array}{l}\text{Where, Absolute uncertainty = 0}\text{.2}\hfill \\ \text{ Absolute time = 5}\text{.5 min}\hfill \end{array}$

Calculation:

  $\begin{array}{l}\frac{0.2}{5.5\times 60}=\frac{0.2}{330}=0.0006060\hfill \\ 0.0006060\times 100\%=0.06\%\approx 0.1\%\hfill \end{array}$

Conclusion:Percentof uncertainty of a hand-timed measurement of 5.5 min is almost 0.1%.