1. Intro to Physics Units
Introduction to Units
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The earth's circumference is approximately 40.1 Mm (megameters). What is this circumference in kilometers?
Astronomers often detect radio waves with wavelengths of 3,000,000,000 nm. What is this wavelength expressed in decameters (dam)?
The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds.
(a) What are the units of A and B?
Write the following numbers in powers of 10 notation:
Write out the following numbers in full with the correct number of zeros:
(c) 2.5 x 10⁻¹
Time intervals measured with a physical stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of 4.5 min?
A watch manufacturer claims that its watches gain or lose no more than 9 seconds in a year. How accurate are these watches, expressed as a percentage?
Write the following as full (decimal) numbers without prefixes on the units:
(e) 22.5 nm
Express the following using the prefixes of Table 1–4: 18 x 10² bucks and
The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in :
The Sun, on average, is 93 million miles from Earth. How many meters is this? Express
(b) using a metric prefix (km).
"(I) Estimate the order of magnitude (power of 10) of: (b) 86.30 x 10³"
"(II) Use Table 1–3 to estimate the total number of protons or neutrons in :(c) the human body"
"(II) A typical atom has a diameter of about 1.0 x 10⁻¹⁰ m. (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch?"
(III) 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's edge, you can just see its deck but none of the side of the sailboat. You then go to that 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. 1–14, where h = 1.5 m , estimate the radius R of the Earth. <IMAGE>
Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to ±2 m, what percent uncertainty in the distance is required? How many significant figures are needed in the distance?
If you walked north along one of Earth's lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile (page 7).
Determine the percent uncertainty in θ, and in sin θ, when θ = 75.0° ± 0.5°.
Dimensional analysis. Waves on the surface of the ocean do not depend significantly on the properties of water such as density or surface tension. The primary 'return force' for water piled up in the wave crests is due to the gravitational attraction of the Earth. Thus the speed v (m/s) of ocean waves depends on the acceleration due to gravity g. It is reasonable to expect that υ might also depend on water depth h and the wave's wavelength λ. Assume the wave speed is given by the functional form v = Cgᵅ hᵝ λᵞ, where α , β , c and C are numbers without dimension.
(a) In deep water, the water deep below the surface does not affect the motion of waves at the surface. Thus υ should be independent of depth h (i.e., β = 0). Using only dimensional analysis (Section 1–7 and Appendix D), determine the formula for the speed of surface ocean waves in deep water.
(II) Estimate how many books can be shelved in a college library with 6500 m² of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are about the size of this one, on average.
(II) Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 1–12). (State your assumptions, such as the mower moves with a 1-km/h speed, and has a 0.5-m width.) <IMAGE>
(II) A hiking trail is 270 km long through varying terrain. A group of hikers cover the first 49 km in two and a half days. Estimate how much time they should allow for the rest of the trip.
(II) Estimate the number of jelly beans in the jar of Fig. 1–13.
Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius R = 13.7 x 10⁹ light-years = 13.0 x 10²⁵ m with an average total mass density of about 1 x 10⁻²⁶ kg/m³. Only about 4% of total mass is due to 'ordinary' 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 Problem 25.)
(II) The diameter of the planet Mercury is 4879 km.
(a) What is the surface area of Mercury?
One mole of atoms consists of 6.02 x 10²³ individual atoms. If a mole of atoms were spread uniformly over the Earth's surface, how many atoms would there be per square meter?