How is mass related to speed?

Question

Does the mass of an object change if it's speed also changes? EXPLAIN????

Answer 1

Mass does not change. My mass on the Earth is the same as my mass on the moon; though my weight is approx 1/6 of what it is here.

However, the FORCE it takes to change the speed depends on the speed you are trying to get it to/from; and the mass.

Newton's 2nd law: Force=Mass*Acceleration

Now this is at normal speeds; Einstein postulates that as a mass approaches the speed of light; time dilates and takes longer to pass that at a normal speed. But I don't get how he figures that one.....

Answer 2

In classical physics, mass is invariant. It's a constant assuming one does not destroy it somehow (like burning and ejecting the fuel mass in a rocket).

But, and this is a big BUT, in relativistic physics mass varies according to m = M/L(v); where L(v) = sqrt(1 - (v/c)^2), which is called the Lorentz transform. v is the object's velocity and c is the speed of light (300,000 kps in a vacuum). M is the rest mass, which is the mass when v = 0 and m is the observed mass when v > 0.

Now check out L(v). When L(v = c) = 0, m ---> infinity because m = M/0 approaches infinity since anything divided by zero does that. That is, at the speed of light, mass behaves as though it were infinite in value.

Understand, the size of the mass (its dimensions) does not get bigger, but how it reacts to force, as in F = ma, changes since m in the force equation is the same m = M/L(v). Thus, at v = c, we have F = (infinite mass) a or F/(infinite mass) = 0 = a. And, lo and behold, at the speed of light, we can go no faster because acceleration must be zero, no more, no less.

And there you have it, the speed of light barrier. Mass can go no faster than the speed of light because it behaves as though it were infinite and no amount of force applied to it can make it accelerate. This is exactly why we say nothing with mass can go faster than the speed of light.

In fact, if you crunch the numbers in the L(v) factor, we find that the energy required to get real close to, but not at, the speed of light is greater than all the energy in our known universe. That is, from a technical point of view, we can't even get real close to light speed because there just isn't enough energy (or force) to do that.

[NB: If you have Excel, try writting =1/SQRT(1 - (A1^2)) in a cell and putting v into the A1 cell in terms of speed of light. For example, v = .5 means 50% the speed of light. Then see what happens to the 1/L(v) value for a variety of v values. You will see that 1/L(v) gets really really big as v --> 1.00 or the speed of light. This shows how mass M grows with its speed.)

Answer 3

You kind of have it backwards. If a objects mass changes while its moving, it's velocity will be affected. Newton's 2nd law is:

Force on an object is equal to the net change in momentum (m*v) of the object.

Almost all physics class problems assume that mass is constant. A perfect example of changing mass is jet propulsion of a rocket. As the rocket loses mass thru chemical reaction, that mass is accelerated down and the reacting force pushes the rocket up.

Answer 4

According the Special Theory of Relativity, the momentum of an object increases as it moves at any speed. The momentum, in turn depends on the velocity and mass of the object.

The momentum increase is by a factor of

1/{sqrt (1-[v^2/c^2])}.

So as you increase speed, you increase momentum (and therefore mass).

Since c is large, this factor is significant only when v is also large. In ordinary speeds, the factor has a value extremely close to 1, and so has a negligible effect.

Hope this helps... :)

Answer 5

To change a mass's speed there must be a change in momentum

Force = d(m*v)/dt = m * dv/dt + v * dm/dt

If the mass is changing we cannot ignore the 2nd term. A good example is that of a rocket where the gas is expelled from the rocket and produces thrust.