Why Does E=mc2?: (And Why Should We Care?) by Cox Brian & Forshaw Jeff

Author:Cox, Brian & Forshaw, Jeff [Cox, Brian]
Language: eng
Format: mobi
ISBN: 9780786752164
Publisher: Da Capo Press
Published: 2009-07-13T16:00:00+00:00

FIGURE 11

Let’s take a closer look at the three-dimensional momentum vector. Figure 11 shows an arrow in space. It might represent the amount by which a ball moves as it rolls across a table.6 To be more precise, suppose that at midday the ball is at one end of the arrow, then 2 seconds later it is at the other end, the tip. If the ball moves 1 centimeter each second, then the arrow is 2 centimeters long. The momentum vector is easy to obtain. It is an arrow pointing in exactly the same direction as the arrow in Figure 11 except that its length is different. The length is equal to the speed of our ball (in this case 1 centimeter per second) multiplied by the mass of the ball, which we might suppose to be 10 grams. Physicists would say that the momentum vector of the ball has a length of 10 gram-centimeters per second (which they would abbreviate to something like 10 g cm/s). It is again going to be well worth our while to be a little bit more abstract and introduce placeholders rather than commit to any particular mass or speed. As ever, we certainly do not wish to transmogrify into the school mathematics teachers of our youth. But . . . if Δx is a placeholder for the length of the arrow, Δt is the time interval, and m is the mass of the ball (Δx = 2 centimeters, Δt = 2 seconds, and m = 10 grams in the example), then the momentum vector has a length equal to mΔx/Δt. It is common in physics to use the Greek symbol Δ(pronounced “delta”) to represent “difference,” and in that spirit Δt stands for the difference in time or the time interval between two things, and Δx stands for the length of something, in this case the distance in space between the start and the end of our measurement of the ball’s position.

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