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## Homework Statement

Russian aviator Vsevolod Mikhailovich Abramovich invented the Abramovich Flyer based on the design of the Wright brothers' first plane. After this first success, Abramovich became obsessed with deep space travel designing a spring based launcher to fire a probe of mass 90kg from Earth (mass 6.00×10^24kg, radius 6.40×10^6m) into deep space.

Determine the minimum speed to launch this probe into deep space such that it never returns.

vesc=

**11183.1346 m/s**

Determine the compression of the spring, having spring constant 5.50×105N[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngm, [Broken] needed to launch this probe using Abramovich's design.

s=___________________

## Homework Equations

vesc=sqrt(2GM/R)

F⃗ spring=−kŝ

Us=∫(dUs/ds)ds=∫ksds=1/2ks^2−Es[/B]

## The Attempt at a Solution

First part I just plugged it into the V escape equation.

Second part attempt: 5.50×10^5N[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngm [Broken] * 6.40×10^6m = 3.52E12 Newtons

3.52E12 =

U = mc^2

U = 6E24*(3E8)^2 = 5.41E41

Integrate (1/2)(

**5.50×10^5N[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngm [Broken])^2 -**[/B]

**5.41E41**

Maybe use Youngs Module to find compression?

I think I'm somewhere on the right track but I'm kinda lost..Maybe use Youngs Module to find compression?

I think I'm somewhere on the right track but I'm kinda lost..

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