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Say you're walking by the highway and you can feel the vibrations of cars moving along. How would you approximate the force that the ground is exerting on your feet due to these vibrations?

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Just put some weight on a very sensitive scale before the car passes by. When the car passes by, note the maximum reading on the scale. If there is any upward force exerted, then the maximum scale change will give you the maximum upward force per (base area of the scale).

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3  
"a very sensitive scale" - aka a seismograph. These are usually set up to indicate distance moved rather than force exerted, but of course you can calculate between the two. And note that the force exerted will depend on the mass of the object resting on the vibrating ground, since to a close approximation the ground moves as it pleases and relatively light objects resting on top of it are moved correspondingly. – Steve Jessop Feb 21 at 2:16

During the Christchurch earthquake in 2011, there was a peak ground acceleration of 2.2g - enough to throw people, vehicles and buildings into the air.

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