A service station plans to install a single-stage hydraulic lift for lifting motorcycles. The lift must safely raise a maximum load of 3.0×103N (motorcycle plus rider). The large piston of the lift is to have a diameter of 30cm, while the operator can conveniently apply a force not exceeding 350N on the small piston.
(i) Starting from the definition of pressure, derive an expression that relates the output force on the large piston to the input force on the small piston in terms of their cross-sectional areas.
(ii) Using the data given, calculate the minimum diameter of the small piston that will just succeed in lifting the rated load in ideal conditions.
(iii) For safety, the design must include a factor of safety of 1.5 on the input effort. Compute the actual force the operator must be able to apply and comment on whether the specified limit of 350N is adequate.