Hydraulic brake systems are increasingly common on bicycles, especially those
using disc brakes. The Magura MT4 brake system, widely used on mountain bikes,
has a small piston and cylinder of diameter \(1.04 \mathrm{~cm}\) connected to
the brake actuation lever on the handlebars, and a larger
\(2.10-\mathrm{cm}\)-diameter piston/cylinder that pushes the brake pads against
the rotating brake disc. (a) What force must be applied to the smaller piston
to produce a force of \(3.25 \mathrm{kN}\) on the larger piston? (b) If the
smaller piston moves a maximum of \(8.80 \mathrm{~mm}\), what's the
corresponding motion of the larger piston? (c) How much work is done on each
piston as they undergo the motions of part (b)?