A man weighing 100kg on the earth is found to weigh 101kg when on the space ship .What is the velocity of the space ship ?

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A man weighing 100kg on the earth is found to weigh 101kg when on the space ship .What is the velocity of the space ship ?

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Answer 1 · 2018-05-19T22:04:34

$v = 0.14 c$ $v=0.14c$

Explanation:

An object moving at a speed $v$ $v$ relative to an observer will seem to be heavier than normal. This happens all the time but the speeds are always too slow to have any noticeable effect, only being noticeable at relativistic speeds.

Formula for mass increase is $M = \frac{M_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$ $M=M_0/sqrt(1-v^2/c^2)$ , where:

$M$ $M$ = new mass ( $k g$ $kg$ )
$M_{0}$ $M_0$ = original mass ( $k g$ $kg$ )
$v$ $v$ = speed of object ( $m s^{- 1}$ $ms^-1$ )
$c$ $c$ = speed of light ( $~ 3.00 \cdot 10^{8} m s^{- 1}$ $~3.00*10^8ms^-1$ )

So,
$101 = \frac{100}{\sqrt{1 - \frac{{(a c)}^{2}}{c^{2}}}}$ $101=100/sqrt(1-(ac)^2/c^2)$

$1.01 = \frac{1}{\sqrt{1 - a^{2}}}$ $1.01=1/sqrt(1-a^2)$

$\sqrt{1 - a^{2}} = \frac{1}{1.01}$ $sqrt(1-a^2)=1/1.01$

$a^{1} = 1 - \frac{1}{1.0201}$ $a^1=1-1/1.0201$

$a = \sqrt{1 - \frac{1}{1.0201}} \approx 0.14$ $a=sqrt(1-1/1.0201)~~0.14$

$v = 0.14 c$ $v=0.14c$

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A man weighing 100kg on the earth is found to weigh 101kg when on the space ship .What is the velocity of the space ship ?

1 Answer

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