Problems & Exercises

A car is traveling at a speed of $\text{33 m/s}$. (a) What is its speed in kilometers per hour? (b) Is it exceeding the $\text{90 km/h}$ speed limit?

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

The speed of sound is measured to be $\text{342 m/s}$ on a certain day. What is this in km/h?

(a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

An infant’s pulse rate is measured to be $\text{130}\pm 5$ beats/min. What is the percent uncertainty in this measurement?

A can contains 375 mL of soda. How much is left after 308 mL is removed?

(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?

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

What is the area of a circle $3\text{.}\text{102}\text{cm}$ in diameter?

A marathon runner completes a $\text{42}\text{.}\text{188}\text{-km}$ course in $2\text{h}$, 30 min, and $\text{12}\text{s}$. There is an uncertainty of $\text{25}\text{m}$ 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?

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where $1\text{lbm}=0\text{.}\text{4539}\text{kg}$. (a) If there is an uncertainty of $0\text{.}\text{0001}\text{kg}$ 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?

A car engine moves a piston with a circular cross section of $7\text{.}\text{500}\pm 0\text{.}\text{002}\text{cm}$ diameter a distance of $3\text{.}\text{250}\pm 0\text{.}\text{001}\text{cm}$ 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.

A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

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 ${\text{10}}^{-\text{27}}\text{ kg}$ and the mass of a bacterium is on the order of ${\text{10}}^{-\text{15}}\text{ kg.}$)

(a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?