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In this lesson, we will learn how to convert between the absolute uncertainty and percent uncertainty in measured values.

Q1:

Suppose your bathroom scale reads your mass as 65 kg with a 3 % uncertainty. What is the uncertainty in your mass (in kilograms)?

Q2:

What is the percent error of thinking the melting point of tungsten is 3 6 9 5 ∘ C instead of the correct value of 3 6 9 5 K?

Q3:

A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time.

Calculate the percent uncertainty in the distance.

Calculate the percent uncertainty in the elapsed time.

What is the average speed in meters per second?

What is the uncertainty in the average speed?

Q4:

A car engine moves a piston with a circular crosssection of 7 . 5 0 0 ± 0 . 0 0 2 cm in diameter a distance of 3 . 2 5 0 ± 0 . 0 0 1 cm to compress the gas in the cylinder.

By what amount is the gas decreased in volume in cubic centimeters?

Find the uncertainty in the decrease in the volume of the gas when the gas is compressed.

Q5:

An infant’s pulse rate is measured to be 1 3 0 ± 5 beats/min. What is the percent uncertainty in this measurement?

Q6:

A good-quality measuring tape can make an error in length measurement of 0.40 cm when measuring a distance of 24 m. What is its percent uncertainty?

Q7:

A car speedometer has a 3 % uncertainty.

What is the range of possible speeds when the speedometer reads 85 km/h?

What is the possible range of speeds when the speedometer reads 85 km/h, stating this speed range in miles per hour, where 1 km = 0.6214 mi.

Q8:

A grocery store sells 5 lb bags of apples. The weights of some bags of apples sold by the store are 4.8 lb, 5.3 lb, 4.9 lb, and 5.4 lb. The average weight of these bags of apples is 5 . 1 ± 0 . 2 lb. What is the percent uncertainty in the weight of a bag of apples?

Q9:

A set of seismographs record the arrival times of seismic waves from earthquakes, measuring these times to 0.100 s precision. To determine the distance to the epicenter of an earthquake, geologists compare the arrival times of S-waves and P-waves from the epicenter. If the S-waves and P-waves travel at 4.00 km/s and 7.20 km/s respectively, how precisely can the distance to the source of the earthquake be determined?

Q10:

Mass can be measured using a non-metric unit called the pound-mass. 1 = 0 . 4 5 3 9 l b k g .

If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty?

Suppose that there is a 0 . 1 % uncertainty in the pound-mass unit. What mass in pounds would have an uncertainty in mass of 1 kg?

Q11:

The volume of gasoline dispensed at a commercial gas station for a nominal volume of 10 L was measured on five separate trials. The measured values were 9.89 L, 10.02 L, 10.30 L, 9.48 L, and 9.91 L. What is the mean volume 𝑉 m e a n and the standard deviation 𝜎 of the values?

Q12:

The length of a pipe is measured with a meter stick. This measurement requires three uses of the stick since the pipe is more than 2 metres long. The first measured value is 1.00 m, the second measured value is also 1.00 m, and the third measured value is 0.76 m. The length of the pipe is the sum of the three measured values and each measured value has a measurement uncertainty ± 0 . 1 5 cm. Find the length of the pipe and find the estimated uncertainty in the length by summing the fractional measurement uncertainties in quadrature.

Q13:

Two gauge pressures 𝑃 1 and 𝑃 2 are measured in order to determine the difference in pressure Δ 𝑃 across an opening. Several measurements are made of each and it is found that 𝑃 = 2 5 ± 1 . 8 1 mmHg and 𝑃 = 1 2 ± 0 . 6 2 mmHg. What is the estimate of Δ 𝑃 and the standard deviation 𝜎 of Δ 𝑃 ?

Q14:

The legs of a right triangle are measured to have lengths of 1 2 . 2 ± 0 . 1 mm and 2 . 8 ± 0 . 1 mm. Find the area of the triangle and the uncertainty in its area by summing the fractional measurement errors in quadrature.

Q15:

The masses of eight nominally identical items were determined to be 4.23 g, 4.37 g, 3.98 g, 4.75 g, 4.12 g, 4.45 g, 4.71 g, and 3.35 g. What is the mean mass 𝑚 m e a n and the standard deviation 𝜎 of the masses?

Q16:

Compute the standard deviation of the following measures of bearing diameter: 5.80 mm, 5.83 mm, 5.82 mm, 6.11 mm, 5.80 mm.

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