# Chapter 1

Chapter thumbnail # Chapter 1 : Measurement and the scientific method. - all with Video Solutions

### Problem 3

Show that $1.0 \textrm{ m/s} = 3.6 \textrm{ km/h}$ . Hint: Show the explicitsteps involved in converting $1.0 \textrm{ m/s} = 3.6 \textrm{ km/h}$

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### Problem 9

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

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### Problem 13

(a) A car speedometer has a 5.0% uncertainty. What is the range of possible speeds when it reads $90\textrm{ km/h}$? (b) Convert this range to miles per hour. ($1 \textrm{ km} = 0.6214 \textrm{ mi}$)

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### Problem 17

State how many significant figures are proper in the results of the following calculations: (a) $\dfrac{(106.7)(98.2)}{(46.210)(1.01)}$ (b) $(18.7)^2$ (c) $\left( 1.60 \times 10^{-19} \right) (3712)$

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### Problem 18

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

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### Problem 19

(a) If your speedometer has an uncertainty of 2.0 km/h at a speed of 90 km/h , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h , what is the range of speeds you could be going?

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### Problem 20

(a) A person's blood pressure is measured to be $120 \pm 2 \textrm{ mm Hg}$ . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?

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### Problem 21

A person measures his or her heart rate by counting the number of beats in $30 \textrm{ s}$ . If $40 \pm 1$ beats are counted in

$30.0 \pm 0.5 \textrm{ s}$, what is the heart rate and its uncertainty in beats per minute?

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### Problem 24

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. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

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### Problem 25

The sides of a small rectangular box are measured to be $1.80 \pm 0.01 \textrm{ cm}$ $2.05 \pm 0.02 \textrm{ cm}$ $3.1 \pm 0.1 \textrm{ cm}$, long. Calculate its volume and uncertainty in cubic centimeters.

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### Problem 26

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0.4539 kg . (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (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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### Problem 27

The length and width of a rectangular room are measured to be $3.955 \pm 0.005 \textrm{ m}$ and $3.050 \pm 0.005 \textrm{ m}$. Calculate the area of the room and its uncertainty in square meters.

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### Problem 28

A car engine moves a piston with a circular cross section of $7.500 \pm 0.002 \textrm{ cm}$ diameter a distance of $3.250 \pm 0.001 \textrm{ cm}$ to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

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### Problem 31

How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of $10^{-22} \textrm{ s}$.)

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### Problem 32

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of $10\times 10^{-27}\textrm{ kg}$ and the mass of a bacterium is on the order of $10\times 10^{-15}\textrm{ kg}$)

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### Problem 35

(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

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