A 100-kg person sits on a 5-kg bicycle. The weight is borne equally by the two wheels of the bicycle. The tires are inflated to a gauge pressure of 8.0 x 10⁵ Pa and are 2.0 cm wide. What length of each tire is in contact with the ground?

Question

Quizplus · Accepted Answer

The weight of the person and the bicycle is 105 kg, which is 1030 N. Each wheel supports half of this weight, or 515 N. The area of contact of each tire with the ground is:$$A = \frac{F}{P} = \frac{515 	ext{ N}}{8.0 	imes 10^5 	ext{ Pa}} = 6.44 	imes 10^{-3} 	ext{ m}^2$$The length of each tire in contact with the ground is:$$L = \frac{A}{w} = \frac{6.44 	imes 10^{-3} 	ext{ m}^2}{2.0 	imes 10^{-2} 	ext{ m}} = 0.322 	ext{ m} = 32.2 	ext{ cm}$$

A 100-Kg Person Sits on a 5-Kg Bicycle