A person who weighs 717 N is riding a 80-N mountain bike. Suppose the entire weight of the rider plus bike is supported equally by the two tires. If the gauge pressure in each tire is 8.10 x 105 Pa, what is the area of contact between each tire and the ground?
pressure * one tire area = (717+80)/2
To find the area of contact between each tire and the ground, we need to use the equation for pressure:
Pressure = Force / Area
In this case, the force we are interested in is the weight of the rider and the bike, which is equal to 717 N + 80 N = 797 N.
Let's denote the area of contact for each tire as A. Since the weight is equally supported by the two tires, each tire supports half the weight, so the force on each tire is 797 N / 2 = 398.5 N.
Now we can use the equation for pressure to find the area:
Pressure = 8.10 x 10^5 Pa
Force = 398.5 N
We can rearrange the equation for pressure and solve for the area:
Area = Force / Pressure
Area = 398.5 N / 8.10 x 10^5 Pa
Calculating this would give us the area of contact between each tire and the ground.