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Levi Tate
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id be very impressed if anyone could build a tunnel through the earth, but if it was perfectly through the center of the earth id imagine one would get stuck in the middle
Homework Statement
A tunnel is drilled straight through the earth from Detroit to Zxxiuw. At the middle of the tunnel it is at 1/2 earth radius from the center. Assuming that a mass m placed in the tunnel will slide without friction, show that it experiences a force that is directly proportional to its distance from the center of the tunnel. Give an expression for this force in terms of the distance and the weight mg at the surface. Assume the earth is not rotating, a bad approximation, but hey, you're not going to drill this tunnel anyhow.
Homework Statement
A tunnel is drilled straight through the earth from Detroit to Zxxiuw. At the middle of the tunnel it is at 1/2 earth radius from the center. Assuming that a mass m placed in the tunnel will slide without friction, show that it experiences a force that is directly proportional to its distance from the center of the tunnel. Give an expression for this force in terms of the distance and the weight mg at the surface. Assume the earth is not rotating, a bad approximation, but hey, you're not going to drill this tunnel anyhow.
I am thinking I need to use energy and then take the derivative to get the force, but I am having trouble finding out the right assumptions to make such that I can do that.
That there is the problem, I am on an iPad so in the attachment is a picture of the problem as well as what I've been able to work out.
Thank you in advance
its acceleration towards the opposite direction its in is equal to its distance from the center of the earth divided by earths radius times 9.8m/s/s
sorry should have explained this more, before i was explaining the end result. The reason for the acceleration is because the force of gravity is based on the amount of mass on the other side of the object. From the surface of the earth there is an acceleration of 9.8 m/s/s as it moves closer to the center of the earth it decreases. then becomes zero at the center of the tunnel. then as it is at the other end of the tunnel it has an acceleration of 9.8 m/s/s in the other directionNothing you've said proves that, now does it?
Right xirow that's the general idea of what's going on but the hard part is solving the problem.
I have that expression and tried to integrate using the second law, but I got a pretty ridiculous solution to the differential equation
Cos I have to write v=dv/dt in one dimension don't i?