By Benjamin Crowell

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When a rocket is launched into orbit, it goes up a little at first to get above almost all of the atmosphere, but then tips over horizontally to build up to orbital speed. Suppose the horizontal acceleration is limited to 3g to keep from damaging the cargo (or hurting the crew, for a crewed flight). (a) What is the minimum distance the rocket must travel downrange before it reaches orbital speed? How much does it matter whether you take into account the initial eastward velocity due to the rotation of the earth?

849 f / Example 1. 56 Chapter 1 Conservation of Mass How can we apply a conservation law, such as conservation of mass, in a situation where mass might be stored up somewhere? To use a crime analogy again, a prison could contain a certain number of prisoners, who are not allowed to flow in or out at will. In physics, this is known as a closed system. A guard might notice that a certain prisoner’s cell is empty, but that doesn’t mean he’s escaped. He could be sick in the infirmary, or hard at work in the shop earning cigarette money.

Of course, the unit of measurement symbolized by “cm” is not an algebra symbol standing for a number that can be literally multiplied by itself. But it is advantageous to write the units of area that way and treat the units as if they were algebra symbols. For instance, if you have a rectangle with an area of 6m2 and a width of 2 m, then calculating its length as (6 m2 )/(2 m) = 3 m gives a result that makes sense both numerically and in terms of units. This algebra-style treatment of the units also ensures that our methods of converting units work out correctly.

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