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Chapter 1: Q5. (page 18)
What is the percent uncertainty in the measurement?
The percent uncertainty in the measurement is .
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(a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?
represents the dimensions for which of the following?
(a) cm2
(b) square feet
(c) m2
(d) All the above
What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius?
Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radiuswith an average total mass density of about. Only about 4% of total mass is due to 鈥渙rdinary鈥� matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light- year, see the Problem19.)
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.]
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