Calculating Kinetic Energy of an Object Falling from Space

AI Thread Summary
To calculate the kinetic energy of an object falling from space, one must consider both its initial velocity and the gravitational potential energy as it descends. For a 4-tonne metal rod ejected from 10,000 kilometers with an initial velocity of 10 m/s, the kinetic energy upon impact can be determined using the formulas for gravitational potential energy (U = -GMm/r) and kinetic energy (KE = 0.5mv²). The impact force can be calculated using the change in momentum divided by the impact time (F = -dp/dt). Understanding these equations allows for adjustments in future calculations with different parameters. This discussion highlights the importance of gravitational effects on falling objects and the necessary formulas for accurate energy calculations.
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First of all, I apologize if this is the wrong forum... I couldn't tell real well where I should post it, so I just did it in general... If it's the wrong place, I apologize and request it be moved to where it should go. (I don't think it's qualifies as Homework", as it's not homework... I'd just like to know XD)

Second of all, my question:

I'd like to know with how much kinetic energy an object falling from space would hit with, assuming the object doesn't disintegrate in the atmosphere.

If a 4 tonne metal rod was ejected from 10,000 kilometers in the atmosphere, towards earth, with an initial velocity of 10 m/s, what would it's KE be as it hits?

And, if possible, could I be given a formula which would calculate it for me? I'd like to mess with the numbers in the future...

Please and thank you!
 
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Use the equation for gravitational potential energy. U=-GMm/r if its closer to Earth you can use mgh , And the impact force would be F=-dp/dt
the change in momentum divided by the impact time.
 
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