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Well you'd be incinerated as you pass through the hot and molten core! But imagine if the core wasn't there or you had a special suit that protected you from the heat—what would happen then? Would you suddenly stop when you got to Oz?
The scenario is an example of a simple harmonic oscillator—other examples being a swinging pendulum and a weight bobbing up down, suspended from a spring. Both of the latter rely on interchange of energy and its change in form, from kinetic energy due to motion of an object, to stored potential energy. In the example of a weight suspended from a spring, the potential energy is manifested as tension in the spring. Energy in physics is defined as "the ability to do work". And "work" in physics also has a specific meaning: work is done when a force moves a body through a distance. The stored potential energy in a spring can do work, which is how a clock spring can move the hands of the clock.
Simple harmonic oscillators as the name suggests oscillate or move backwards and forwards indefinitely. For an ideal spring-mass system in a vacuum, with a perfect spring and no friction, the mass will bounce up and down forever, with energy being interchanged as described above. Simple harmonic oscillators have a natural frequency that depends on the magnitude of the mass and the stiffness of the spring (how hard it is to stretch or compress it). In real life, systems are lossy and due to mechanical friction in a spring and drag from air, oscillations eventually die out. Technically this is known as damping. Dampers are actually used as components in your washing machine's drum suspension and also vehicle suspension systems to smooth out oscillations.
Back to the hole in the Earth that goes all the way to Australia—if you jumped in and there was no air in the hole, you would fall and accelerate, your velocity increasing as you drop downwards. In fact, you'd free fall under the influence of gravity, being continually accelerated. This differs from the situation where you're falling in air, because in that scenario, you eventually reach a constant velocity, known as terminal velocity, when the force of gravity acting downwards is equalled by drag acting upwards, and there's no net accelerating force. As you continue to fall closer to the centre of the Earth, your velocity increases until you reach maximum velocity at the centre. Due to inertia however you overshoot and pass through the centre. However, from now on, there's "less Earth" in front of you and more behind you. So now you're being decelerated and the gravitational force of the Earth is having a braking effect. Your velocity decreases after you pass through the centre, and it keeps decreasing until it falls to zero as you emerge from the hole on the other side, just like the way a ball kicked up into the air pauses momentarily when it reaches the apex of its trajectory. Once your velocity reaches zero, you start to fall back down the hole and the process is repeated as you fall back to where you started from. Without any losses due to friction, you would keep moving from one side of the planet to the other indefinitely, and it works out that the transit time would be 42 minutes. In reality, if such a hole was a civil engineering possibility, which is highly unlikely and it was filled with air, your oscillations back and forth would be damped and you'd eventually settle and float at the centre of the Earth, weightless.
























