Problem 1
Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.
Problem 2
According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 (L) = 1000 cm\(^3\) and 1 in. = 2.54 cm, express this volume in cubic inches.
Problem 3
How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)
Problem 4
The density of gold is 19.3 g/cm\(^3\). What is this value in kilograms per cubic meter?
Problem 5
The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by using only the conversions 1 L = 1000 cm\(^3\) and 1 in. = 2.54 cm.
Problem 6
A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ft\(^2\). If a lot has an area of 12.0 acres, what is its area in hectares?
Problem 7
How many years older will you be 1.00 gigasecond from now? (Assume a 365-day year.)
Problem 8
While driving in an exotic foreign land, you see a speed limit sign that reads 180,000 furlongs per fortnight. How many miles per hour is this? (One furlong is \\(\frac{1}{8}\\) mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed furrow.)
Problem 10
The following conversions occur frequently in physics and are very useful. (a) Use 1 mi = 5280 ft and 1 h = 3600 s to convert 60 mph to units of ft/s. (b) The acceleration of a freely falling object is 32 ft/s\(^2\). Use 1 ft = 30.48 cm to express this acceleration in units of m/s\(^2\). (c) The density of water is 1.0 g/cm\(^3\). Convert this density to units of kg/m\(^3\).
Problem 11
In the fall of 2002, scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a nuclear chain reaction. Neptunium-237 has a density of 19.5 g/cm\(^3\). What would be the radius of a sphere of this material that has a critical mass?
