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slavikrds
2 months ago
6

A proposed space elevator would consist of a cable stretching from the earth's surface to a satellite, orbiting far in space, th

at would keep the cable taut. A motorized climber could slowly carry rockets to the top, where they could be launched away from the earth using much less energy.What would be the escape speed for a craft launched from a space elevator at a height of 56,000 km? Ignore the earth's rotation.
Physics
1 answer:
Ostrovityanka [3.2K]2 months ago
3 0

In tackling this issue, we will utilize principles associated with energy conservation. We will leverage the relationship between gravitational potential energy and kinetic energy to ascertain the escape velocity. The formula for gravitational potential energy is expressed as,

PE= \frac{GMm}{d}

The kinetic energy expression can be represented as,

KE= \frac{1}{2} mv^2

Where,

G = 6.67*10^{-11}m^3/kg\cdot s^2Gravitational Universal Constant

m = 5.972*10^{24}kg Mass of Earth

h = 56*10^6m  Height

r = 6.378*10^6m Radius of Earth

According to energy conservation principles:

\frac{1}{2} mv^2 = \frac{GMm}{d}

Rearranging this expression allows us to solve for the velocity,

v = \sqrt{\frac{2Gm}{d}} \rightarrow  The escape velocity from a specific height above the earth

If we define the height of the satellite above the earth as h, then the complete distance will be the earth's radius plus the height,

d = r+h

v = \sqrt{\frac{2Gm}{r+h}}

Substituting the values yields

v = \frac{2(6.67*10^{-11})(5.972*10^{24})}{6.378*10^6+56*10^6}

v = 3.6km/s

Thus, the escape velocity computes to 3.6 km/s

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A rocket is continuously firing its engines as it accelerates away from Earth. For the first kilometer of its ascent, the mass o
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Answer:

The correct response is:

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