# How much must the spring be compressed? helppp

#### ohheytai

how much must the spring be compressed?!??!?! helppp

A package of mass 9 kg sits at the equator of an airless asteroid of mass 3.0x10^20 kg and radius 2.1x 10^5 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 179 m/s. We have a large and powerful spring whose stiffness is 2.3x10^5 N/m. How much must we compress the spring?

i cant get this someone please help me this is my work
escape speed:
v = sqrt(2GM/R); Where:
G = 6.673 E-11 [m³ / (kg-s²)]; Gravitational Constant
M = 3.0 E+20 kg; Mass of asteroid
R = 2.1 E+5 m; Radius of asteroid

v = sqrt[ 2 * 6.673 E10^(-11) [m³ / (kg-s²)] * 3.0 E10^20 kg ÷ (2.1 E10^5 m) ]
v = 1.9066 E5 m²/s²
v = 437 m/s

E = 1/2 m v²
E = 1/2 (9 kg) (437 m/s + 179 m/s)²
E = 4.5 kg (379496 m²/s²)
E = 1,707,500 J

E = 1/2 kx²
1.708 E6 kg m²/s² = 1/2 (2.3 E5 kg/s²) x²
14.85 m² = x²
x = 3.85m

#### Redbelly98

Staff Emeritus
Homework Helper
Re: how much must the spring be compressed?!??!?! helppp

A package of mass 9 kg sits at the equator of an airless asteroid of mass 3.0x10^20 kg and radius 2.1x 10^5 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 179 m/s. We have a large and powerful spring whose stiffness is 2.3x10^5 N/m. How much must we compress the spring?

i cant get this someone please help me this is my work
escape speed:
v = sqrt(2GM/R); Where:
G = 6.673 E-11 [m³ / (kg-s²)]; Gravitational Constant
M = 3.0 E+20 kg; Mass of asteroid
R = 2.1 E+5 m; Radius of asteroid

v = sqrt[ 2 * 6.673 E10^(-11) [m³ / (kg-s²)] * 3.0 E10^20 kg ÷ (2.1 E10^5 m) ]
v = 1.9066 E5 m²/s²
v = 437 m/s

E = 1/2 m v²
E = 1/2 (9 kg) (437 m/s + 179 m/s)²
Your error starts here. It's incorrect to simply add the escape speed to the final desired speed.
E = 4.5 kg (379496 m²/s²)
E = 1,707,500 J

E = 1/2 kx²
1.708 E6 kg m²/s² = 1/2 (2.3 E5 kg/s²) x²
14.85 m² = x²
x = 3.85m
There are three forms of energy at play here: due to gravity, due to the spring, and kinetic energy. Using that, can you set up an equation from Einitial=Efinal?

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