A Ford Focus goes about 2 meters down the road for each revolution of its tires, which, when new, have treads about 1 centimeter thick. If it goes 80,000 km (50,000 mi) before its tread is gone, find the average thickness of tire lost durin each revolution. Compare this thickness to the diameter of the smallest of atoms, and discuss.
To find the average thickness of tire lost during each revolution, we need to calculate the number of revolutions the Ford Focus tires make over a distance of 80,000 km (50,000 miles).
First, let's convert the distance to meters. Since 1 km is equal to 1,000 meters, 80,000 km is equal to 80,000,000 meters.
Next, we divide the total distance covered by the car (80,000,000 meters) by the distance covered per revolution (2 meters) to find the number of revolutions:
Number of revolutions = Total distance / Distance per revolution
Number of revolutions = 80,000,000 meters / 2 meters
Now, let's calculate the number of revolutions:
Number of revolutions = 40,000,000 revolutions
Since the average thickness of tread lost during each revolution is equal to the initial tread thickness minus the final tread thickness, we need to find the final tread thickness.
Given that the tire has new treads that are 1 centimeter (0.01 meters) thick, we subtract the distance covered by the car (in meters) from the initial tread thickness to find the final tread thickness.
Final tread thickness = Initial tread thickness - (Number of revolutions * Distance per revolution)
Final tread thickness = 0.01 meters - (40,000,000 revolutions * 2 meters)
Now, let's calculate the final tread thickness:
Final tread thickness = 0.01 meters - 80,000,000 meters
Final tread thickness = -79,999,999.99 meters
From our calculation, we find that the final tread thickness is a negative value. This indicates that the tread will be completely worn out after the Ford Focus travels 80,000 km (50,000 miles).
Moving on to the comparison with the diameter of the smallest atoms, the average thickness of the tire lost during each revolution is much larger than the diameter of an atom. Atoms typically have diameters on the order of picometers (10^-12 meters), whereas the tire loss is in the range of meters. This shows the significant difference in scales between the thickness of the tire loss and the size of atoms, highlighting how minuscule and precise atomic scales are compared to macroscopic measurements.