## College Physics Problem 1.28

#### (b) Find the uncertainty in this volume.

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## College Physics Problem 1.27

#### The length and width of a rectangular room are measured to be 3.955 ±0.005 m and 3.050 ± 0.005 m . Calculate the area of the room and its uncertainty in square meters.

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## College Physics Problem 1.26

#### (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

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## College Physics Problem 1.25

#### The sides of a small rectangular box are measured to be 1.80±0.01 cm, 2.05±0.02 cm, and 3.1±0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

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## College Physics Problem 1.24

#### (d) What is the uncertainty in the average speed?

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## Solution:

The area of a circle can be computed using the formula below when radius is given.

$\displaystyle A=\pi r^2$

We also know that the radius is half the diameter, so the area can be calculated using the formula,

$\displaystyle A=\pi \left(\frac{d}{2}\right)^2$

So, by direct substitution

$\displaystyle A=\pi \left(\frac{3.102\:cm}{2}\right)^2=7.557\:cm^2$          ☚

The area of the circle is 7.557 square centimetre.

## Solution:

In order to compute for the heart rate in beats per minute, we need to solve for the base. The base is

$\displaystyle \frac{40\:beats}{30\:sec\:}\times \frac{60\:sec}{1\:min}=80\:beats/min$

Then we compute for the percent uncertainty by combining the uncertainties of the number of beats and time. That is

$\displaystyle \%\:uncertainty=\frac{1\:beat}{40\:beats}\times 100\%+\frac{0.5\:s}{30.0\:s}\times 100\%$

$\displaystyle \%\:uncertainty=2.5\%+1.7\%$

$\displaystyle \%\:uncertainty=4.2\%$

Based on this percent uncertainty, we compute for the tolerance

$\displaystyle \delta _A=\frac{\%\:uncertainty}{100\:\%}\times A$

$\displaystyle \delta _A=3.3\:beats/min$

Therefore, the heart rate is

$\displaystyle 80\pm 3\:beats/min$          ☚

## Solution:

### Part a

The percent uncertainty is computed as

$\displaystyle \%\:uncertainty=\frac{2\:mmHg}{120\:mmHg}\times 100\%=1.7\%$

### Part b

The uncertainty in the blood pressure is

$\displaystyle \delta _{bp}=\frac{1.7\:\%}{100\:\%}\times 80\:mmHg=1.3\:mmHg$

## Solution:

#### Part a

The percent uncertainty is computed as

$\displaystyle \%\:uncertainty=\frac{2.0\:km/hr}{90\:km/hr}\times 100\%=2.2\%$

### Part b

The tolerance of the velocity is

$\displaystyle \delta _v=\frac{2.2\:\%}{100\:\%}\times 60\:km/hr=1\:km/hr$

Therefore, the range of the velocity is 60±1km/h, or that is 59 to 61 km/h.