Calculating Speed & Time of Message Packet Through Earth's Center

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To calculate the speed of a message packet passing through a tube bored through a planet, one must first determine the gravitational acceleration at a given radius, which can be derived from the planet's density and radius. The equation of motion for the packet can be expressed as d2r/dt2 = -g(r), where g(r) is the gravitational acceleration at radius r. The speed of the packet at a distance of 0.480R from the center can be calculated using principles of physics related to gravitational forces and energy conservation. Additionally, to find the total time for a message to travel from one side of the planet to the other, one would integrate the speed over the distance traveled. Understanding these concepts is crucial for solving the problem effectively.
zhenyazh
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Hi,
i am preparing for a test and i really have no idea how to solve the following question.
i would appreciate if some one could give me the direction of solution explaining why things should be done the way the should. i am really clueless here.

The residents of a small planet have bored a hole straight through its center as part of a communications system. The hole has been filled with a tube and the air has been pumped out of the tube to virtually eliminate friction. Messages are passed back and forth by dropping packets through the tube. The planet has a density of 3820 kg/m3, and it has a radius of R=5.31E+6 m.

What is the speed of the message packet as it passes a point a distance of 0.480R from the center of the planet?

How long does it take for a message to pass from one side of the planet to the other?

thanks
 
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Hi zhenyazh! :smile:

What is the gravitational acceleration at radius r inside the planet?

If it's g(r), then d2r/dt2 = -g(r). :wink:
 
thanks for your response but i still don't get it.
can u give a more detailed explanantion?
 

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