An automobile tire is rated to last for 50000 miles. To an order of magnitude, through how many revolutions will it turn over its lifetime?
If L=2πR ∼ 2 m and s =50000 miles =80467361 m =>
N =s/L = 80467361/2 = 40233680 rev.
What is the estimate to the number of revolutions that a tire will make in 500000 miles?
33,613,524
Student
To calculate the approximate number of revolutions a tire will make over its lifetime, we need to consider the distance it covers in one revolution and then divide the total distance it will travel by that value.
To determine the distance covered in one revolution, we need to know the circumference of the tire. The circumference can be calculated using the formula: circumference = 2 * π * radius.
However, we are given the mileage (distance) rating of the tire, not its radius or diameter. So, to get an order of magnitude estimation, we can assume the average diameter of a tire to be around 30 inches. This is just an approximation and can vary depending on the size of the tire.
Using the diameter of 30 inches, we can calculate the radius by dividing the diameter by 2: radius = 30 inches / 2 = 15 inches.
Next, we calculate the circumference using the formula: circumference = 2 * π * radius.
Plugging in the values: circumference = 2 * π * 15 inches.
To get the value in miles, we need to convert inches to miles. There are 63,360 inches in a mile. So, one revolution of the tire covers: (2 * π * 15 inches) / 63,360 inches/mile ≈ 0.00942 miles.
Now, to find the number of revolutions, we divide the total distance the tire is rated for (50,000 miles) by the distance covered in one revolution:
Number of revolutions = 50,000 miles / 0.00942 miles/revolution.
Using a calculator, we divide 50,000 by 0.00942 to get an order of magnitude estimation of approximately 5,318,471 revolutions.
Therefore, an automobile tire rated to last for 50,000 miles will turn approximately 5 million revolutions over its lifetime.