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much more massive particles and acquire some of the properties of x-rays or gamma rays such as are emitted by radioactive substances There is a name for high-speed electrons that act this way: beta particles Physicists take advantage of the relativistic effects on the masses of protons, helium nuclei, neutrons, and other subatomic particles When these particles are subjected to powerful electrical and magnetic fields in a device called a particle accelerator, they get moving so fast that their mass increases because of relativistic effects When the particles strike atoms of matter, the nuclei of those target atoms are fractured It takes quite a wallop to break up the nucleus of an atom! When this happens, energy can be released in the form of infrared, visible light, ultraviolet, x-rays, and gamma rays, as well as a potpourri of exotic particles If astronauts ever travel long distances through space in ships moving at speeds near the speed of light, relativistic mass increase will be a dire concern While the astronaut s own bodies won t seem unnaturally massive, and the objects inside the ship will appear to have normal mass too, the particles whizzing by outside will gain real mass It is scary enough to think about what will happen when a 1-kg meteoroid strikes a space ship traveling at 999 percent of the speed of light But that 1-kg stone will mass more than 22 kg when u 0999, that is, at 999 percent of the speed of light As if this is not bad enough, every atomic nucleus outside the ship will strike the vessel s shell at relativistic speed, producing deadly radiation

The objective of this section is to describe the basic operation of an ideal accelerometer Readers interested in more detailed discussion of real accelerometer designs should consult references such as [37, 73, 126] Consider an accelerometer constructed via a spring-mass-damper system as depicted in Figure 111 The position vector of the mass m is p The position of the accelerometer case is pc The case relative position of the mass is pc = p pc For this discussion, we assume that pc can be perfectly measured The equilibrium position of mass m is pc = 0 The following discussion distinguishes between inertial (ie, physically applied) and kinematic forces (eg, gravity) In Figure 111, FI represents a force physically applied to the accelerometer case In an inertial reference frames (ie, the frame is not accelerating, not rotating, and has no gravitational eld) by Newton s laws, the dynamic

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Figure 111: Basic accelerometer equation for the inertial acceleration of the mass m is p= b k pc pc m m (117)

Relativistic time dilation and mass increase have been measured under controlled conditions, and the results concur with Einstein s formulas stated earlier Thus these effects are more than mere tricks of the imagination To measure time dilation, a superaccurate atomic clock was placed on board an aircraft, and the aircraft was sent up in flight to cruise around for a while at several hundred kilometers per hour Another atomic clock was kept at the place where the aircraft took off and landed Although the aircraft s speed was only a tiny fraction of the speed of light and the resulting time dilation was exceedingly small, the accumulated discrepancy was large enough to measure When the aircraft arrived back at the terminal, the clocks, which had been synchronized (when placed right next to each other, of course!) before the trip began, were compared The clock that had been on the aircraft was a little behind the clock that had been resting comfortably on Earth

2 Select one of the two options: Member-Oriented Tree Creates a simplified view of data This option is selected by default and is an ideal option if you are not a technical report author Custom Tree Constructs the meta-data available to be displayed in the report This option is useful for more technical report authors who have a good understanding of the dimensional structures 3 Below the Custom Tree option, you can select several checkboxes to choose the metadata that displays in the report A preview of the updated tree is shown as the options are changed in this screen 4 Click OK to save the settings

where k is the spring constant and b is the viscous damping constant De nk ing the accelerometer output as f = m pc , then eqn (117) can be rewritten as f = f + p (118)

You have several options to insert data in an Express Authoring Mode report Two buttons in the Actions bar can be used to determine how data is inserted: Set Selection and Insert Member Also, options for inserting child members when the parent member is already present on the report are available

b where the parameter = k is the time constant of the sensor The bandwidth of the accelerometer is determined by the parameter When the bandwidth of the acceleration signal p(t) is less that the sensor bandwidth, then f (t) is small and the sensor maintains the condition

To measure mass increase, particle accelerators are used It is possible to determine the mass of a moving particle based on its known rest mass and the kinetic energy it possesses as it moves When the mathematics is done, Einstein s formula is always shown to be correct

Part III:

f (t) = p(t)

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