Physics: Two neutron stars are separated by a distance of 1.0 x 1012 m. they each have a mass of 1.0 x 1028 kg and a radius of 1.0 x 103 m. they are initially at rest with respect to each other. as measured from that rest frame, how fast are they moving when (a) their separation has decreased to one-half its initial value and (b) they are about to collide?

Two neutron stars are separated by a distance of

Ответ:

SmokeyRN

10.01.2022

Physics

To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.

Gravitational potential energy can be defined as

$PE = -\frac{GMm}{R}$

As M=m, then

$PE = -\frac{Gm^2}{R}$

Where,

m = Mass

G =Gravitational Universal Constant

R = Distance /Radius

PART A) As half its initial value is u'=2u, then

$U = -\frac{2Gm^2}{R}$

$dU = -\frac{2Gm^2}{R}$

dKE = -dU

Therefore replacing we have that,

$\frac{1}{2}mv^2 =\frac{Gm^2}{2R}$

Re-arrange to find v,

$v= \sqrt{\frac{Gm}{R}}$

$v = \sqrt{\frac{6.67*10^{-11}*1*10^{28}}{1*10^{12}}}$

v = 816.7m/s

Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s

PART B) With a final separation distance of 2r, we have that

2r = 2*10^3m

Therefore

$dU = Gm^2(\frac{1}{R}-\frac{1}{2r})$

$v = \sqrt{Gm(\frac{1}{2r}-\frac{1}{R})}$

$v = \sqrt{6.67*10^{-11}*10^{28}(\frac{1}{2*10^3}-\frac{1}{10^{12}})}$

v = 1.83*10^7m/s

Therefore the velocity when they are about to collide is 1.83*10^7m/s

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Ответ:

ksa23

25.01.2022

Physics

Greenhouse gases in the air, mainly carbon dioxide, methane and water vapour, trap radiation from the Sun and act like a thermal blanket around the planet. Without the greenhouse effect, the Earth would have an average temperature of -18 °C and be covered in ice. Life as we know it would not be able to survive.

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