drop_a_slinky

Highway Seismograph

Bumpin over the logs

Introduction

As you drive down a highway, you can use an extended arm and hand to model the operation of a seismograph.

Material

A car, a driver, and a bumpy highway.
A felt tip pen
A pad of lined paper.

To Do and Notice

While driving down the highway as a passenger in a car, hold your arm straight out in front of you. Hold it near the dashboard without touching the dash.

Notice that as you hit bumps your hand moves up and down relative to the dashboard.

To record the motion, use one hand to hold a pad of paper vertically against the dashboard.
Hold the felt tip pen in the other hand stretched out to arms length.
As you drive along, use the pen to trace the line from left to right across the paper. Move the pen slowly.

Notice that when you hit a bump the pen moves up and down making a seismogram-like recording.

What’s Going On?

When the car hits a bump it accelerates up. You are firmly attached to the car and accelerate with it. Your hand and arm are less firmly attached to the car and so their mass and inertia cause them to lag behind the motion of your body and the car.

This is why your arm moves down relative to the car.

In actuality your arm stays the same height above the earth, but the dashboard moves up.

Math Root

Earthquakes are measured on a logarithmic scale.

Let's create a logarithmic car bump scale called the Pothole scale.

Measure the maximum amplitude of each recorded bump.
Convert your measurement to micrometers.
Take the base 10 logarithm of the amplitude in micrometers.
This is the bump rating on the pothole scale.

For example a 1 cm amplitude bump is 10⁴ micrometers or a 4 on the Pothole scale.

A Pothole 5 bump is 10 times larger than a Pothole 4.
So the pen motion for a pothole 5 is 10 cm.

A Pothole 6 bump is big enough to destroy your car!

So What ?

The Richter scale measures earthquakes. The Richter magnitude takes the amplitude in micrometers of the pen motion on a Wood-Anderson seismograph and takes the base 10 logarithm of this amplitude. (The magnitude is adjusted to make it what it would have been if the earthquake were 100 km away.)

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