Problem 15
The Star of Africa, a diamond in the royal scepter of the British crown jewels, has a mass of \(530.2\) carats, where 1 carat \(=0.20 \mathrm{~g}\). Given that \(1 \mathrm{~kg}\) has a weight of \(2.21 \mathrm{lb}\), what is the weight of the Star of Africa in pounds?
Problem 16
What are the SI base units for mass, length, and time?
Problem 17
What does the prefix kilo (k) mean? How can this prefix be used to modify the description of an obstacle course that is \(1450 \mathrm{~m}\) long?
Problem 18
Why must all terms in a physics equation have the same dimensions?
Problem 19
What is the difference between a unit and a dimension? Give an example of each to illustrate your point.
Problem 20
The speed of light in a vacuum is approximately \(0.3 \mathrm{Gm} / \mathrm{s}\). What is the speed of light in meters per second?
Problem 21
Many highways in the United States have a speed limit of \(65 \mathrm{mi} / \mathrm{h}\). (a) Is this speed greater than, less than, or equal to \(65 \mathrm{~km} / \mathrm{h}\) ? Explain. (b) Find the speed limit in kilometers per hour that corresponds to \(65 \mathrm{mi} / \mathrm{h}\).
Problem 22
Show that the equation \(v_{\mathrm{f}}=v_{\mathrm{i}}+a t\) is dimensionally consistent. In this equation, \(v_{\mathrm{f}}\) and \(v_{\mathrm{i}}\) are velocities, \(a\) is an acceleration, and \(t\) is time.
Problem 24
What is the area of a circle with a radius of \(12.77 \mathrm{~m}\) ? Recall that the area of a circle is given by area \(=\pi\) (radius) \(^{2}\).
Problem 25
The triangular sail on a boat has a height of \(4.1 \mathrm{~m}\) and a base of \(6.15 \mathrm{~m}\). What is the area of the sail? Recall that the area of a triangle is given by area \(=\frac{1}{2}\) (base)(height).
