High School

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A car is traveling at 90.9 km/hr. The tires have a radius of [tex]r = 38.4 \, \text{cm}[/tex]. What is the centripetal acceleration of a piece of tire on the outer edge?

Answer :

Final answer:

To find the centripetal acceleration at the outer edge of a car tire, we need to convert the car's speed to m/s, convert the tire's radius to meters, and use the formula for centripetal acceleration. In this case, the acceleration is 1636.71 m/s².

Explanation:

The student is asking about the centripetal acceleration experienced by a piece of tire on the outer edge of a car's tire, given the car's speed and the tire's radius. To calculate this, first, we need to convert the car's speed from km/hr to m/s, which is the standard unit for such calculations in physics. The conversion factor is 1 km/hr = 0.27778 m/s. Therefore, we have:

90.9 km/hr × 0.27778 m/s per km/hr = 25.236 m/s

Now applying the formula for centripetal acceleration, ac = v2/r, where:

  • v is the velocity in m/s
  • r is the radius in meters

Before we can plug into the formula, we also need to convert the tire radius from cm to meters:

38.4 cm * 0.01 m/cm = 0.384 m

Now, using the formula we get:

ac = (25.236 m/s)2 / 0.384 m = 1636.71 m/s2

Therefore, the centripetal acceleration of a piece of tire on the outer edge is 1636.71 m/s2.

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