Pascal's Law & Hydraulic Lift Practice Problems

A nurse uses a hydraulic lift to transfer a patient from a bed to a chair. The hydraulic piston has an area of 0.02 m². If the patient has a mass of 80 kg, determine the gauge pressure of the hydraulic fluid

A mechanic standing on a hydraulic lift supports three 120 kg motorcycles at a height of 1.2 m above the mechanic's piston. The hydraulic lift is filled with oil, and the mechanic's piston has a radius of 6 cm. Calculate the radius of the piston lifting the motorcycles if the mechanic's mass is 72 kg. Assume that oil has a density of 900 kg/m³.

An 85 kg mechanic balances a 1450 kg car on the hydraulic lift shown below. When a second person joins the mechanic,  the mechanic's piston goes down, creating a 38 cm height difference between the two pistons. Determine the mass of the second person. Take incompressible fluid density as 930 kg/m³.

What is the area of the input piston if a hydraulic press is used to lift a heavy crate with a mass of 970 kg to a height of 40 cm, with an output piston diameter of 44 cm and an input force of 420 N?

A lab technician applies a force of 4.2 N on a pipette plunger with a diameter of 1.6 cm while dispensing a solution through a nozzle with a diameter of 0.30 mm into a container where the gauge pressure is approximately 85 mm-Hg. What would be the required amount of force just before the solution starts flowing?

A heavy toolbox that has a bottom surface area of 20.0 cm² is accidentally pressed inside of an automotive garage using a hydraulic lift. The hydraulic lift consists of a large piston that has a diameter of 30.0 cm and a small piston that has a diameter of 5.0 cm. The lift is operated by applying force on the small piston using a lever mechanism, that is similar to the one shown in the diagram below. The lever has a length of "𝐿". What is the pressure applied on the toolbox if 400 N is applied to the lever?