Mechanical Energy Homework: Zero Planet w/ 10kg Probe Launch

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Homework Help Overview

The problem involves a hypothetical planet named Zero, with specified mass and radius, and a scenario where a 10 kg space probe is launched vertically from its surface. The main question focuses on determining the kinetic energy of the probe at a specific distance from the center of the planet after being launched with a given initial kinetic energy.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the equation related to kinetic energy and gravitational potential energy, questioning the values used for the radius and the distances involved. There is uncertainty about the correct interpretation of the radius in the context of the problem.

Discussion Status

Participants are actively engaging with the problem, raising questions about the values used in the equations and the interpretation of distances. Some guidance has been offered regarding the measurement of distances from the center of the planet, but no consensus has been reached on the correct approach or values.

Contextual Notes

There is a noted lack of clarity regarding the appropriate values for the radius in the equations, and participants are considering the implications of measuring distances from the center of the planet versus the surface.

norcal
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Homework Statement



Zero, a hypothetical planet, has a mass of 1.0x10^23 kg, a radius of 3.0x10^6 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial kinetic energy of 5.0x10^7 J, what will be its kinetic energy when it is 4.0x10^6 m from the center of Zero?

Homework Equations



(1/2)mv^2 - (GMm/R)=(1/2)mv^2 - (GMm)/(10R)

The Attempt at a Solution



5.0e7 - [(6.67e-11)(1e23)(10)]/(3e6)= KE - [(6.67e-11)(1e23)(10)]/(10(4e6)]

I don't think that I am using the right values for R though. Am I?
 
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(1/2)mv^2 - (GMm/R) = (1/2)mv^2 - (GMm)/(10R)

I can't see where the 10R comes from. Should be R as on the LHS.
 
ok, well do I have the correct values of R set up in the equation or do I need to take the difference of the distance of the satellite to the center or anything?
 
I think all your distances are measured from the centre of Zero.
 

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