A person who weighs 691 N is riding a 89-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 8.40 x 105 Pa, what is the area of contact between each tire and the ground?

F=691+89=780 N

p=(F/2)/A=F/2A =>
A=F/2p=780/2•8.4•10⁵=4.6 10⁻⁴m²

To find the area of contact between each tire and the ground, we can use the formula:

Pressure = Force/Area

In this case, we know the pressure (8.40 x 10^5 Pa) and the force (Weight of the rider plus bike, which is 691 N + 89 N = 780 N). We can rearrange the formula to solve for area:

Area = Force / Pressure

Plugging in the values, we get:

Area = 780 N / 8.40 x 10^5 Pa

To get the answer, we'll perform the calculation.

Area = 9.29 x 10^-4 m^2

Therefore, the area of contact between each tire and the ground is approximately 9.29 x 10^-4 square meters.