You\'re driving along at 50 miles per house. Your tiers are 24 inches in diamete

Question

You're driving along at 50 miles per house. Your tiers are 24 inches in diameter. You feel a vibration in your car at a frequency of 24 Hz. the slabs of concrete that form the road are 100 feet long, and there is a gap between slabs for summer time expansion. Grooves are cut in the shoulder of the road to wake up drivers who fall asleep while driving. The grooves are perpendicular to the direction of travel and spaced 3 inches apart.

Would it be reasonable to conclude that the vibration is from a single bubble on a tire, two diametrically opposed bubbles on a tire, the gaps in the concrete, the grooves in the should, or something else? Why?

Explanation / Answer

A 24 in diameter tire has a radius of 12 inch, and a circumference of 2r = 75.4 in.

This means that every 75.4 in the car's tire will repeat.

The 24 Hz means that 24 times a second, you feel a bump. That means the bumps are coming at you every .042 seconds.

If you are driving 50 miles/hour, we want to convert this inches/sec, so

50 mile/hour ( 1 hour / 3600 sec )( 5280 ft / 1 mile )( 12 inches / 1 ft ) = 880 in/sec

So how far, in inches, does the car go in .042 sec?

v=d/t

880 in/sec = d/.042 sec

d= 37 in.

This means every 37 inches a bump is felt.

Looking at the above choices, the one that makes the most sense is:

two diametrically oppoosed bubble.

If the tire has a circumference of 75.4, and it had two bubbles, then each bubble will be felt after 37.7 in of driving. This is incredibly close to our answer, so this is the correct choice. All other choices are nowehere near close.

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