Edits to “Statement”, “Solution”, “Answer”

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en/2.6.53.md +43 −25
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### Statement
−$2.6.53.$ [Insert problem description here]
+$2.6.53.$ The famous physicist F. Dyson suggested that it would be possible to fully utilize the energy of stars if space civilizations could surround stars with spherical shells. Find the stress in the material of a stationary homogeneous shell that would surround the Sun according to this assumption, with its radius equal to the radius of the Earth’s orbit. The density of the shell material $ρ =4·10^3 kg/m^3$ .
−__Example Statement__:
−$1.1.1.$ Determine the coordinate $x(t)$ of a body as a function of time $t$, given that its acceleration is defined as $a(t) = bt$, where $b$ is a constant.
−
−
### Solution
−[Your solution should be placed here]
+$$
+σdS=dF
+$$
−__Example Solution__:
−The acceleration of the body defined by
+$$
+S=R²Ω
+$$
−$$a(t) = bt$$
+$$
+dS=2RdRΩ
+$$
−We know that acceleration is the time derivative of velocity:
+$$
+dR=\frac{dS}{2RΩ}
+$$
−$$a(t) = \frac{d v(t)}{d t}$$
+$$
+dF=g*dm
+$$
−To find the velocity $v(t)$, we integrate $a(t)$ with respect to time:
+$$
+\oint gdS=-4πGM
+$$
−$$v(t) = \int a(t) \, dt = \int b t \, dt$$
+$$
+-4πR²g=-4πGM
+$$
−If the initial velocity is $v(0) = 0$, then the velocity becomes:
+$$
+g=\frac{GM}{R²}
+$$
−$$v(t) = \frac{b t^2}{2}$$
+$$
+dm=ρdV
+$$
−Likewise, integrate $v(t)$ with respect to time:
+$$
+dV=4πR²dR=\frac{RdS}{2}
+$$
−$$x(t)= \int v(t) \, dt = \frac{b}{2} \int t^2 \, dt$$
+$$
+σdS=\frac{GM}{R²}ρ\frac{RdS}{2}
+$$
−From where the coordinate from time, considering the initial conditions:
+$$
+σ=\frac{GMρ}{2R}
+$$
−$$\boxed{x(t)=\frac{bt^3}{6}}$$
+$$
+\boxed{σ=1.8*10¹²Pa}
+$$
#### Answer
−
−[Insert a concise answer or boxed result, like this:]
−
−
−__Example Answer__:
−$$ x(t)=\frac{bt^3}{6} $$
+$$
+σ=1.8*10¹²Pa
+$$