The residents of a small planet have bored a hole straight through its center as
ID: 1699408 • Letter: T
Question
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 4000 kg/m3, and it has a radius of R=6.05E+6 m.=> What is the speed of the message packet as it passes a point a distance of 0.260R 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?
Explanation / Answer
the gravity force. F=G*M*m/r^2 where M=D*4*pi*r^3/3. so F=G*D*4pi*r*m/3 so F=G*D*m4pi*l/3 where l be distance of the packet to the middle point of the tube. so that a=G*D*4pi*l/3. this have the same equation as a harmonic motion (spring, etc...). where k=G*D*m4pi/3. so that w=sqrt(G*D*4pi/3)=1.06e-3(rad/s). ----------------------------------------- we have that A=R. so (R*w)^2=(0.26Rw)^2+v^2. so v=6200(m/s). --------------- It is T/2=pi/1.06e-3=3000(s)