Make a hole through the earth from any two points in the surface connected by a cylindrical cavity. make sure to reinforce the boundaries of the cavity and then lubricate with superfluid butter or frictionless substance evacuate all the air from tunnel and insulate. By dropping yourself, or your sister, or a pizza box into the cavity it is possible to reach the otherside (wherever that may be) in exactly 42 minutes. It is not even necessary for the tunnel to go directly through the center of the earth. Maximum velocity will be achieved when the cart/train/sister/pizza is at the very middle of the path.
proof
d(Kinetic Energy + Potential Energy)/dt=0
KE + PE= c
1/2*mv^2 + PE= c
v=sqrt((c-2PE)/m) so velocity will be maximum when potential energy is minimum.
since gravitational potential energy has radial dependence inside a sphere it will be smallest at the point closest to the center. getting closer to the center increases an objects velocity while getting away from the center implies getting farther from another massive objects center of gravity and thus experience a deceleration. You better have someone catch you on the other side or you're coming right back.
even though the period of the oscillation is constant the maximum velocity isn't tunnels through the very middle of the earth will experience the most velocity since they cover the most distance and it can get pretty fast. relativistically it might even feel shorter to travel straight through the middle. id have to calculate that and get back to you.
so forget 30 minute free pizza and order yourself 42minute Chinese Food done right.
4 comments:
Where are you going to get all that butter II for the walls?
remind me of a movie... keep up the good work,lol
this is why i never see you at sbarros
Have you ever played portal? putting two portals next to each other on a floor and jumping into one provides a very similar motion to that you describe.
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