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Chapter 1: Problem 42
How many Earths would fit inside the Sun?
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You're shopping for a new computer, and a salesperson claims the microprocessor chip in the model you're looking at contains 50 billion electronic components. The chip measures \(5 \mathrm{mm}\) on a side and uses 14 -nm technology, meaning each component is 14 nm across. Is the salesperson right?
Find the cube root of \(6.4 \times 10^{19}\) without a calculator.
The Moon barely covers the Sun during a solar eclipse. Given that Moon and Sun are, respectively, \(4 \times 10^{5} \mathrm{km}\) and \(1.5 \times 10^{8} \mathrm{km}\) from Earth, determine how much bigger the Sun's diameter is than the Moon's. If the Moon's radius is \(1800 \mathrm{km}\), how big is the Sun?
The volume of a sphere is given by \(V=\frac{4}{3} \pi r^{3},\) where \(r\) is the sphere's radius. For solid spheres with the same density-made, for example, from the same material-mass is proportional to volume. The table below lists measures of diameter and mass for different steel balls. (a) Determine a quantity which, when you plot mass against it, should yield a straight line. (b) Make your plot, establish a best-fit line, and determine its slope (which in this case is proportional to the spheres' density). $$\begin{array}{|l|c|c|c|c|c|} \hline \text { Diameter }(\mathrm{cm}) & 0.75 & 1.00 & 1.54 & 2.16 & 2.54 \\ \hline \text { Mass }(\mathrm{g}) & 1.81 & 3.95 & 15.8 & 38.6 & 68.2 \\ \hline \end{array}$$
In Chapter \(3,\) you'll learn that the range of a projectile launched -over level ground is given by \(x=v_{0}^{2} \sin 2 \theta / g,\) where \(v_{0}\) is the inimial speed, \(\theta\) is the launch angle, and \(g\) is the acceleration of gravIty. If you did an experiment that involved launching projectiles -with the same speed \(v_{0}\) but different launch angles, what quantity \- would you plot the range \(x\) against in order to get a straight line and thus verify this relationship?
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