Question

Calculate the force output by the larger piston of a hydraulic lift when a force of 700 N is exerted on the smaller piston. The areas of the two pistons are 20cm squared and 950 cm squared

Answer 1

Force output is 33250N.

Step-by-step explanation:

In this problem, we will be using the Pascal Principle. It states that the pressure exerted on an incompressible fluid and in equilibrium within a container of non-deformable walls is transmitted with equal intensity in all directions and at all points of the fluid.

Because of this, we have that in two different points of the fluid the pressure is the same:

`P_(a)=P_(b)` (pressure in point 'a' and, pressure in point 'b').

Presure can be expressed as:

`P =(F)/(A)`, where
`F` is the force exerted and,
`A` is the area in which force is applied.

To compute the force output by the larger piston we will set point 'a' to be the one with area of 20cm squared (0.002m squared) and, point 'b' the one with area 950cm squared (0.095m squared). Computing:

`(F_(a))/(A_(a)) =(F_(b))/(A_(b))`

`(700)/(0.002) =(F_(b))/(0.095)`

`0.095(700)/(0.002) =F_(b)`

`F_(b)=33250N`.