A person who weighs 506 N is riding a 94-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 6.70 x 105 Pa, what is the area of contact between each tire and the ground?
(total Contact area)x(Gauge pressure)
= 2*(single tire Contact Area)x6.70*10^5 N/m^2
= Total wt.
= 600 N
Contact area = 4.48*10^-4 m^2
= 4.48 cm^2
P = F/A
But there are two tires. So the weight will be supported by the two tires, thus two areas.
So P=F/2A, solving this,
A = F/2P
A = 600/2*6.7*10^5
To find the area of contact between each tire and the ground, we need to use the formula:
Pressure = Force / Area
Given that the gauge pressure in each tire is 6.70 x 10^5 Pa and the weight of the rider plus bike is supported equally by the two tires, the total force exerted by the rider and bike is (506 N + 94 N) = 600 N.
We can now rearrange the formula to solve for the area:
Area = Force / Pressure
Area = 600 N / (6.70 x 10^5 Pa)
Area = 0.000895 m^2
So, the area of contact between each tire and the ground is 0.000895 square meters.