Suppose that when you ride on your 7.90-kg bike the weight of you and the bike is supported equally by the two tires. If the gauge pressure in the tires is 72.5 lb/in2 and the area of contact between each tire and the road is 7.13 cm2, what is your weight?
To find your weight, we can use the concept of pressure.
First, let's convert the given pressure from pounds per square inch (lb/in²) to Pascal (Pa).
1 lb/in² = 6894.76 Pa
So, the pressure in Pascal is:
72.5 lb/in² = 72.5 * 6894.76 Pa ≈ 500763.7 Pa
Now, we can calculate the force on each tire. The force can be calculated using the formula:
Force = Pressure * Area
The area of contact between each tire and the road is given as 7.13 cm². However, it's easier to work with square meters for the calculations, so let's convert it to square meters.
1 cm² = (1/100)² m² = 0.0001 m²
Therefore, the area in square meters is:
7.13 cm² = 7.13 * 0.0001 m² = 0.000713 m²
Now we can calculate the force on each tire:
Force = 500763.7 Pa * 0.000713 m² ≈ 357.73 N
Since the weight of you and the bike is supported equally by the two tires, the total force acting on the tires is twice the force calculated above.
Total Force = 2 * 357.73 N = 715.46 N
Hence, your weight is approximately 715.46 N.