A person who weighs 869 N is riding a 98-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 7.80 x 105 Pa, what is the area of contact between each tire and the ground?
To find the area of contact between each tire and the ground, we can use the concept of pressure and force.
First, let's find the total force exerted on the ground by the rider and the bike. The entire weight of the rider plus the bike is supported equally by the two tires. The weight is given as 869 N, and since the weight is evenly distributed, each tire supports half of that weight, which is 869 N/2 = 434.5 N.
Next, let's calculate the force exerted by each tire. We know that force = pressure × area. In this case, the gauge pressure in each tire is given as 7.80 x 10^5 Pa. Let's assume that the area of contact between each tire and the ground is the same. We'll denote this area as A.
Hence, for each tire, the force exerted is 7.80 x 10^5 Pa × A.
Since the entire weight of the rider plus bike is supported equally by the two tires, the force exerted by each tire (7.80 x 10^5 Pa × A) is equal to half of the total force, which is 434.5 N.
Therefore, we can set up the equation:
7.80 x 10^5 Pa × A = 434.5 N
Now we can solve for the area of contact A:
A = (434.5 N) / (7.80 x 10^5 Pa)
Calculating this, we get:
A ≈ 5.57 x 10^(-4) m^2
Therefore, the area of contact between each tire and the ground is approximately 5.57 x 10^(-4) square meters.