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Chapter 1: Q9. (page 18)
What, approximately, is the percent uncertainty for a measurement given as?
The correct answer of percent uncertainty is 0.6%.
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The smallest meaningful measure of length is called the Planck length, and it is defined in terms of three fundamental constants in nature: the speed of light , the gravitational constant , and Planck鈥檚 constant . The Planck length is given by the following combination of these three constants:
Show that the dimensions ofare length [L], and find the order of magnitude of. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are 鈥榮trings鈥� with lengths on the order of the Planck length,. These theories also suggest that the 鈥楤ig Bang鈥�, with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]
You are lying on a beach, with your eyes 20 cm above the sand. Just as the sun sets, fully disappearing over the horizon, you jump up. Your eyes are now 150 cm above the sand, and you can just see the top of the sun. If you count the number of seconds (= t) until the sun fully disappears again, you can estimate the earth鈥檚 radius. However, for this problem, use the known radius of the earth to calculate the time t.
Why is it incorrect to think that the more digits you include in your answer, the more accurate it is?
Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water鈥檚 edge, you can see its deck but none of the side of the sailboat. You then go to the sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1-16, where h = 1.5 m, estimate the radius R of the earth.
The sun, on average, is 93 million miles from the earth. How many meters is this? Express (a) using powers of 10, and (b) using a metric prefix (km).
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