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Chapter 1: Problem 51
A solution consisting of \(8.50 \%\) acetone and \(91.5 \%\) water by mass has a density of \(0.9867 \mathrm{g} / \mathrm{mL} .\) What mass of acetone, in kilograms, is present in 7.50 L of the solution?
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As mentioned on page \(13,\) the MCO was lost because of a mix-up in the units used to calculate the force needed to correct its trajectory. Ground-based computers generated the force correction file. On September \(29,1999,\) it was discovered that the forces reported by the ground-based computer for use in MCO navigation software were low by a factor of \(4.45 .\) The erroneous trajectory brought the MCO \(56 \mathrm{km}\) above the surface of Mars; the correct trajectory would have brought the MCO approximately \(250 \mathrm{km}\) above the surface. At \(250 \mathrm{km},\) the MCO would have successfully entered the desired elliptic orbit. The data contained in the force correction file were delivered in lb-sec instead of the required SI units of newton-sec for the MCO navigation software. The newton is the SI unit of force and is described in Appendix B. The British Engineering (gravitational) system uses a pound (lb) as a unit of force and \(\mathrm{ft} / \mathrm{s}^{2}\) as a unit of acceleration. In turn, the pound is defined as the pull of Earth on a unit of mass at a location where the acceleration due to gravity is \(32.174 \mathrm{ft} / \mathrm{s}^{2} .\) The unit of mass in this case is the slug, which is \(14.59 \mathrm{kg}\). Thus, BE unit of force \(=1\) pound \(=(\text { slug })\left(\mathrm{ft} / \mathrm{s}^{2}\right)\) Use this information to confirm that BE unit of force \(=4.45 \times\) SI unit of force 1 pound \(=4.45\) newton
Describe the necessary characteristics of an experiment that is suitable to test a theory.
Indicate whether each of the following is an exact number or a measured quantity subject to uncertainty. (a) the number of sheets of paper in a ream of paper (b) the volume of milk in a liter bottle (c) the distance between Earth and the sun (d) the distance between the centers of the two oxygen atoms in the oxygen molecule
In the third century \(\mathrm{BC}\), the Greek mathematician Archimedes is said to have discovered an important principle that is useful in density determinations. The story told is that King Hiero of Syracuse (in Sicily) asked Archimedes to verify that an ornate crown made for him by a goldsmith consisted of pure gold and not a gold-silver alloy. Archimedes had to do this, of course, without damaging the crown in any way. Describe how Archimedes did this, or if you don't know the rest of the story, rediscover Archimedes's principle and explain how it can be used to settle the question.
The reported value for the volume of a rectangular piece of cardboard with the dimensions \(36 \mathrm{cm} \times\) \(20.2 \mathrm{cm} \times 9 \mathrm{mm}\) should be \((\mathrm{a}) \quad 6.5 \times 10^{3} \mathrm{cm}^{3};\) (b) \(7 \times 10^{2} \mathrm{cm}^{3} ;\) (c) \(655 \mathrm{cm}^{3} ;\) (d) \(6.5 \times 10^{2} \mathrm{cm}^{3}\).
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