How does mass depend on speed?


In order to answer this question, we have to consider two situations:

a) The object could be at rest in our reference frame.

b) The "object" is never at rest in any (physically realizable) frame of reference.

An electron and a tennis ball belong to situation (a), where as a photon belongs to situation (b)

Let us assume that two masses exist, the mass when object has zero speed 'm0' and mass 'm' when object has speed 'V' as observed in our frame of reference.

When the object has zero speed, it is at rest (as observed by us or by someone accompanying the object), and so 'm0' is called the object's rest mass. It is an intrinsic property of the object.

For instance every electron has rest mass m0=9.11 x 10^-31 Kg.

If we set into motion a tennis ball that is initially at rest, the ball acquires kinetic energy, the energy associated with motion.Its energy increases.

From the equation  E=mC2; it implies that increase in energy will correspond to increase in mass too. We deduce that ball's inertia increases. Thus the mass 'm' of moving ball is greater than the rest mass 'm0'. Hence m>m0 holds for any object with kinetic energy.

In 1905, Einstein summarized his theoretical discovery with sentence,

" The mass (i.e. the inertia) of a body is a measure of its energy content.  

 

What is wave motion?

Wave motion, in general refers to transfer of energy from one point to other point of medium.

For transfer of energy through a medium, the medium must possess the properties of
i) Elasticity ii) Inertia & iii) Negligible frictional resistance

and now the question is what propagates in wave motion?

It is not the matter that is propagated but it is only state of motion of matter that is propagated.
It may be said that in wave motion momentum and energy are transferred or propagated.


What is grounding?

Grounding is one of primary ways to minimize unwanted noise and pickup.

There are two basic objectives involved in designing good grounding systems.

i) To minimize noise voltage generated by currents from two or more circuits flowing thorugh a common ground impedance.

ii) To avoid creating ground loops which are susceptible to magnetic fields and differences in ground potential.

Grounding, if done improperly however, can become a primary means of noise coupling.

In most general sense a ground can be defined as equipotential point or plane which serves as a reference voltage for a circuit or system. By equipotential point we mean the point where voltage does not change regardless of the amount of current supplied to it or drawn from it. 

If the ground is connected to earth through a low impedance path, it can then be called an earth ground.

There are two common reasons for grounding a circuit:

i) For safety

ii) To provide an equipotential reference for signal voltages

Safety grounds are always at earth potential where as signal grounds are usually but not necessarily at earth potential.

In many cases, a safety ground is required at a point which is unsuitable for a signal ground, and this may complicate noise problem.