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CHAPTER 2 Mechanical Forces
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Fig. 2-5.
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Center of mass.
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The current de nition of kilogram is de ned by a carefully protected bar of platinum iridium metal in France. Scientists would like to replace this bar of metal with a more universally accurate de nition but haven t been able to come up with a good one yet. An object has mass spread all over and through it. Since objects can be in all sorts of awkward shapes, it can be di cult to calculate how they will behave when pushed, unless we simplify them. For every object, there is a single point in space where the mass of the object is balanced in every direction. This is called its center of mass. In the presence of gravity, this is also known as the center of gravity, or COG. For a sphere, square, box, or other well-behaved and symmetrical object, this point is in the very center of the object. For more unusual shapes, such as the letter C, it takes a bit more math to nd the center of gravity (Fig. 2-5). Once found, however, the object can be treated as a single mathematical point for many calculations.
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VELOCITY: v
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Feet per second: ft/s Meters per second: m/s Velocity is a derived unit. This means it doesn t represent anything new, but combines base units to come up with a new concept. Time, length (or distance), and mass are base units. Velocity describes the change in position of something over time (Fig. 2-6). To describe velocity you need both a distance, in meters or feet, and the time measurement in seconds. Velocity is also known as speed. A velocity of 3 m/s means the object has traveled three meters in one second. It could also mean it moved six meters in two seconds, nine meters in
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CHAPTER 2 Mechanical Forces
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Fig. 2-6.
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Velocity.
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Single axis.
six seconds, and so on. You assume the measurement is made across one second unless otherwise speci ed. Once an object is moving, it stays moving until another force acts on the object to make it stop moving. This is Newton s rst law of motion:
A body must continue in its state of rest or of uniform motion in a straight line, unless acted on by some external force.
Note that an object doesn t just move, but it moves in a direction. If you are pushing beads on a wire, there is only one direction they can move, along the wire. Technically, there are two directions, back and forth along the wire. This wire, with its constrained direction of motion, can be thought of as one-dimensional, since there is just one dimension or direction of motion, along the wire. The wire itself is an axis (Fig. 2-7). When you are pushing blocks on your desk there are two parts to the direction it can move: left/right, also called the X-axis, and toward/away from you, the Y-axis. This is a two-dimensional space, and the axes are directions along the desktop (Fig. 2-8). Each axis is perpendicular to the other axes. Distance along a wire is described by a single number, the distance from the start. Distance on a desktop, however, needs two numbers to describe, the distance between two positions along the X-axis and the Y-axis (Fig. 2-9). These are considered part of one measurement, a two-dimensional vector. If this distance describes two positions of the same object, it describes the two-dimensional motion ( x, y). The Greek , called delta, represents a change or di erence in some value. Therefore x represents the change in position along the X-axis. Another way _ to represent a change in position is to put a single dot over the value, x.