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

Question

Quizplus · Accepted Answer

The weight of the person and the bicycle is given by:
W = (m_person + m_bicycle)g = (100+5)kg × 9.8m/s^2 = 1043 N

The force that each wheel must support is half of the weight, or 521.5 N. The pressure on the ground is given by:
P = F/A
where A is the area of contact of both tires with the ground. Since the area of contact is the sum of the lengths of the two tire patches times the width of each tire, we have:
A = (2xL) x 0.02 m
where L is the length of each tire patch. Substituting the given values, we get:
8.0x10^5 Pa = 521.5 N / (2L x 0.02m)
L = 0.032 m = 3.2 cm

Therefore, the length of each tire patch in contact with the ground is 3.2 cm, or answer choice C.

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