1. A clever physics student wishes to design an advanced suction cup in the shape of a light downwardepainting cane (the mass of the cone can be neglected), whose pressure can be controlled through a valve (see Figure l). A mass can be attached at the tip of the cane and the cane~mass system is held to the ceiling by the pressure force, which is related to gauge pressure inside the cone. The cane's height is H and its radius is R. in the diagram, the z-axis is set to be the cane axis withz = l) at the tip of the cane and z :+ H at the base of the cone. The radial distance from the side of the cone to the axis is then r : R{z/H),f0r0 5 z 5 H. cmlina Radius 0" tone base: R Val-ut- to ' mama! ; 2 pressurr Figure 1: For Question 1. (a) Show that the net pressure force on an small section of the cone between and z + dz [4] is upward, with magnitude Zipgauge MR/HPZG'Z :2 Triirngauge |TdT'. (b) Then find an expression for|pgauge | if the suction cup is designed to hold a given mass [3] m. (c) Does ipgauge | depend on H ? Can you roughly explain why or why not? What does this [3] suggest about the best way to design the suction cup