Calculating Kinetic & Potential Energy of Rama's Impact

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Homework Help Overview

The discussion revolves around calculating the kinetic and potential energy of an object, specifically Rama, as it impacts Earth. The context is drawn from a scenario in "Rendezvous With Rama" by Arthur C. Clarke, where the object's mass and speed are provided, prompting questions about energy calculations just before impact.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of equations for gravitational force and kinetic energy, questioning how to incorporate potential energy in the calculations. There is an exploration of calculating potential energy at different heights and how it relates to kinetic energy during descent. Some participants express confusion about the steps needed to arrive at the final equation for energy at impact.

Discussion Status

The discussion is ongoing, with participants providing insights into the relationship between kinetic and potential energy. There is a recognition of the need to clarify the definitions of energy terms and the equations involved. Some guidance has been offered regarding the formulation of energy equations, but no consensus has been reached on the final approach.

Contextual Notes

Participants are grappling with the definitions of kinetic and potential energy, as well as the necessary information, such as altitude, to complete their calculations. There is an acknowledgment of the complexity involved in transitioning from potential energy to kinetic energy as the object descends.

Mecia22
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Homework Statement


-- This is out of Rendezvous With Rama by Arthur C. Clarke
You know it is 907184 kg and is going 50,000 m/s
So how much energy does it have right before it hits the earth?

Homework Equations



Do I use Fg= Gm1m2/r^2 ?
Ek=1/2mv^2?
I have ΔE=1/2mv^2 written down as an equation to use as well.

The Attempt at a Solution


I think I'm supposed to calculate the potential energy at 2 different spots and find the ΔE, but I'm not sure.

E=Gm1m2/r+1/2mv^2 would that work?
 
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At any particular point it has both KE and PE. As it descends, PE decreases and KE increases by the same amount. At the point you describe the KE is given by Ek=1/2mv^2, but to know what the energy will be when it strikes Earth you also need to know how much PE it will lose in the remaining descent. So you need the altitude at the point where the speed is known.
 


haruspex said:
At any particular point it has both KE and PE. As it descends, PE decreases and KE increases by the same amount. At the point you describe the KE is given by Ek=1/2mv^2, but to know what the energy will be when it strikes Earth you also need to know how much PE it will lose in the remaining descent. So you need the altitude at the point where the speed is known.


Okay, so then the equation would be E=EK+EP?
 


Depends what you mean by EP there. Write the equation in terms of four entities: Eki = KE at known initial point, Epi = PE at known initial point, Ekf = KE on collision, Epf = PE on collision.
 


Yikes... you're confusing me.
I guess what I'm asking is what steps would I do to get to my final equation?Would it be Efinal=Ekinetic+change of Epotential ?
 
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Mecia22 said:
Yikes... you're confusing me.
I guess what I'm asking is what steps would I do to get to my final equation?


Would it be Efinal=Ekinetic+change of Epotential ?

Yes, provided (i) Efinal means the KE on impact, and (ii) you get the sign right on the change in potential.
 

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