Question

A 500-N weight sits on the small piston of a hydraulic machine. The small piston has area 2.0 cm2. If the large piston has area 40 cm2, how much weight can the large piston support?

Answer 1

W₂= 10000 N

Step-by-step explanation:

Pascal´s Principle can be applied in the hydraulic press:

If we apply a small force (F1) on a small area piston A1, then, a pressure (P) is generated that is transmitted equally to all the particles of the liquid until it reaches a larger area piston and therefore a force (F2) can be exerted that is proportional to the area (A2) of the piston:

Pressure is defined as the force (F) applied per unit area (A)

P=F/A (N/m²)

P1=P2

`(F_(1) )/(A_(1) ) = (F_(2) )/(A_(2) )`

`F_(2) = (F_(1)*A_(2)  )/(A_(1))` Equation (1)

Data

W₁ = weight sits on the small piston

F₁ = W₁= 500 N

A₁ = 2.0 cm²

A₂ = 40 cm²

Calculation of the weight (W₂) can the large piston support

We replace data in the equation (1)

`F_(2) = ((500)*(40) )/(2)`

F₂ = 10000 N

W₂= F₂= 10000 N