Physics I For Dummies. Steven Holzner
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Название: Physics I For Dummies

Автор: Steven Holzner

Издательство: John Wiley & Sons Limited

Жанр: Физика

Серия:

isbn: 9781119872245

isbn:

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      FIGURE 3-1: Examining displacement with a golf ball.

      

In physics terms, you often see displacement referred to as the variable s (don’t ask me why).

      Scientists, being who they are, like to go into even more detail. You often see the term si, which describes initial position, (the i stands for initial). And you may see the term sf used to describe final position.

      In these terms, moving from diagram A to diagram B in Figure 3-1, si is at the 0-meter mark and sf is at +3 meters. The displacement, s, equals the final position minus the initial position:

      

Displacements don’t have to be positive; they can be zero or negative as well. If the positive direction is to the right, then a negative displacement means that the object has moved to the left.

      In diagram C, the restless golf ball has moved to a new location, which is measured as –4 meters on the measuring stick. The displacement is given by the difference between the initial and final position. If you want to know the displacement of the ball from its position in diagram B, take the initial position of the ball to be

; then the displacement is given by

      

When working on physics problems, you can choose to place the origin of your position-measuring system wherever is convenient. The measurement of the position of an object depends on where you choose to place your origin; however, displacement from an initial position si to a final position sf does not depend on the position of the origin because the displacement depends only on the difference between the positions, not the positions themselves.

      Examining axes

      Finding the distance

      Take a look at Figure 3-2, where a golf ball moves around in two dimensions. The ball starts at the center of the graph and moves up to the right. In terms of the axes, the golf ball moves to +4 meters on the x-axis and +3 meters on the y-axis, which is represented as the point (4, 3); the x measurement comes first, followed by the y measurement: (x, y).

      FIGURE 3-2: A ball moving in two dimensions.

      So what does this mean in terms of displacement? The change in the x position,

(
, the Greek letter delta, means “change in”), is equal to the final x position minus the initial x position. If the golf ball starts at the center of the graph — the origin of the graph, location (0, 0) — you have a change in the x location of

      The change in the y location is

      

Using the distance formula — which is just the Pythagorean theorem solved for the hypotenuse — you can find the magnitude of the displacement of the golf ball, which is the distance it travels from start to finish. The Pythagorean theorem states that the sum of the squares of the legs of a right triangle
is equal to the square on the hypotenuse
. Here, the legs of the triangle are
and
, and the hypotenuse is s. Here’s how to work the equation:

      So in this case, the magnitude of the ball’s displacement is exactly 5 meters.

      Determining direction

      

You can find the direction of an object’s movement from the values of
and
. Because these are just the legs of a right triangle, you can use basic trigonometry to find the angle of the ball’s displacement from the x-axis. The tangent of this angle is simply given by

      Therefore, the angle itself is just the inverse tangent of that:

      The ball (refer to Figure 3-2) has moved at an angle of 37° from the x-axis.

      There’s more to the story of motion than just the actual movement. When displacement takes place, it happens in a certain amount of time. You may already know that speed is distance traveled per a certain amount of time:

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