A person who weighs 539 N is riding a 77-N mountain bike. Suppose the entire weight of the rider plus the bike is supported equally by the two tires. If the gauge pressure in each tire is 8.10 x 10^5 Pa, what is the area of contact between each tire and the ground?
To solve this problem, we can use the formula:
pressure = force/area
We know the total weight on the two tires is:
539 N + 77 N = 616 N
Since each tire supports an equal weight, the weight on each tire is:
616 N / 2 = 308 N
Now we can use the formula to find the area of contact for each tire:
8.10 x 10^5 Pa = 308 N / area
Solving for area, we get:
area = 308 N / (8.10 x 10^5 Pa) = 0.00038025 m^2
Therefore, the area of contact between each tire and the ground is 0.00038025 m^2.