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Juku is on a bicycle hike and wants to pump a little more air into his bike’s rear wheel. To make things easier, Juku packs his heavy hike equipment off the rack and turns the bike upside down (wheels are directed towards the sky). Estimate by how many percent smaller force he needs to apply while pumping as compared to the situation where the equipment was still on. The radius of the wheel is R=\SI33.0cm, radius of the tire r=\SI2.5cm, the mass resting on the rear wheel (the wheel together with the hike equipment) m=\SI30kg, the gauge pressure in the wheel under the load p=\SI150kPa, air pressure p0=\SI100kPa and gravitational acceleration g=\SI9.8m/s2.
Hint. The mass of the wheel without the load is given by an equation V=2π2(R−r)r2 and with loading it decreases by ΔV≈S⋅ΔR/2, where S≈2πΔRRr is the area of contact between the tire and the ground and ΔR≪r is the range of tire’s deformation (see figure).