Physics, 27.10.2019 17:43 Jasten

According to the theory of relativity, the mass m of a particle depends on its velocity v. consider the following equation, where m0 is the mass when the particle is at rest and c is the speed of light.
m = m0 / [√1 – (v2/c2)]
find the limit of the mass as v approaches c – .

Answers: 2

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Yes. There we have it. That's why nothing with mass can keep
speeding up until it reaches the speed of light.

As 'v' approaches 'c',

-- the fraction (v²/c²) approaches ' 1 ' ,

-- the quantity inside the square root approaches (1 - 1) which is zero,

-- since the square root is in the denominator of the fraction,
the fraction gets bigger and bigger, approaching infinity,
and so does 'm' ... the mass of the object that's moving
faster and faster.

The closer the object comes to the speed of light, the greater
its mass becomes, and the more energy it takes to make it move
still faster. If the object has ANY mass when it's at rest, then it
takes an infinite amount of energy to push it to light speed.

By the way ... as unbelievable as it seems, this weird formula
has been tested and proved thousands of times, and there's no
doubt at all that it really happens. The faster something moves,
the bigger its mass gets. It's observed every day in experiments
where things move really fast ... like subatomic particles in an
accelerator. Their mass really does grow when they get going.

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Answer from: Quest

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According to the theory of relativity, the mass m of a particle depends on its velocity v. consider...