An automobile with 0.300 m radius tires travels 75,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
75000km * 1000m/km * 1rev/.300*2π m = 3.98x10^7 rev
To determine the number of revolutions the tires make, we can use the formula:
Number of revolutions = Distance traveled / Circumference of the tire
First, let's find the circumference of the tire. The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
Given that the radius of the tire is 0.300 m, we can plug it into the formula to find the circumference:
Circumference = 2 * 3.14159 * 0.300
Circumference ≈ 1.88496 m
Now, we can calculate the number of revolutions:
Number of revolutions = Distance traveled / Circumference
Given that the distance traveled is 75,000 km, we need to convert it to meters:
75,000 km = 75,000 * 1,000 meters (1 km = 1,000 m)
75,000 km = 75,000,000 meters
Now, we can calculate the number of revolutions:
Number of revolutions = 75,000,000 m / 1.88496 m
Number of revolutions ≈ 39,745,705 revolutions
Therefore, the tires make approximately 39,745,705 revolutions when traveling a distance of 75,000 km, neglecting any backing up and any change in radius due to wear.