1.3 Unit Conversion

Light travels about 9 Pm in a year. Given that a year is about $3 \times 10^{7} \text{s} ,$ what is the speed of light in meters per second?

We know from the reference that the diameter of Earth is on the order of 10⁷ m, so the order of magnitude of its surface area is 10¹⁴ m². What is that in square kilometers (that is, km²)? (Try doing this both by converting 10⁷ m to km and then squaring it and then by converting 10¹⁴ m² directly to square kilometers. You should get the same answer both ways.)

Given that 1 lbf (pound-force) is 4.45 N, were the numbers being output by SM_FORCES too big or too small?

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

In SI units, speeds are measured in meters per second (m/s). But, depending on where you live, you’re probably more comfortable of thinking of speeds in terms of either kilometers per hour (km/h) or miles per hour (mi/h). In this problem, you will see that 1 m/s is roughly 4 km/h or 2 mi/h, which is handy to use when developing your physical intuition. More precisely, show that (a) $1.0 \text{m}/\text{s} = 3.6 \text{km}/\text{h}$ and (b) $1.0 \text{m}/\text{s} = 2.2 \text{mi}/\text{h} .$

Soccer fields vary in size. A large soccer field is 115 m long and 85.0 m wide. What is its area in square feet? (Assume that 1 m = 3.281 ft.)

Mount Everest, at 29,028 ft, is the tallest mountain on Earth. What is its height in kilometers? (Assume that 1 m = 3.281 ft.)

Tectonic plates are large segments of Earth’s crust that move slowly. Suppose one such plate has an average speed of 4.0 cm/yr. (a) What distance does it move in 1.0 s at this speed? (b) What is its speed in kilometers per million years?

The density of nuclear matter is about 10¹⁸ kg/m³. Given that 1 mL is equal in volume to cm³, what is the density of nuclear matter in megagrams per microliter (that is, $\text{Mg}/ \mu \text{L}$)?

A commonly used unit of mass in the English system is the pound-mass, abbreviated lbm, where 1 lbm = 0.454 kg. What is the density of water in pound-mass per cubic foot?

It takes $2 \pi$ radians (rad) to get around a circle, which is the same as 360°. How many radians are in 1°?

A light-nanosecond is the distance light travels in 1 ns. Convert 1 ft to light-nanoseconds.

A fluid ounce is about 30 mL. What is the volume of a 12 fl-oz can of soda pop in cubic meters?