Question

Ronny has a hydraulic jack. The input force is 250 N, while the output force is 7,500 N. If the area of the pipe below the input is 0.2 m2, what is the area of the pipe below the load?

Answer 1

6 m²

Step-by-step explanation:

application of fluid pressure according to Pascal's principle for the two pistons is given as:

`P_1=P_2`

Where P₁ is the pressure at the input and P₂ is the pressure at the output.

But P₁ = F₁ / A₁ and P₂ = F₂ / A₂

Where F₁ and F₂ are the forces applied at the input and output respectively and A₁ and A₂ are the area of the input pipe and output pipe respectively

Since,
`P_1=P_2`

`(F_1)/(A_1) =(F_2)/(A_2)\\`

But A₁ = 0.2 m², F₁ = 250 N, F₂ = 7500 N. Substituting values to get:

`(F_1)/(A_1) =(F_2)/(A_2)\\(250)/(0.2)=(7500)/(A_2)\\ A_2=(7500*0.2)/(250) = 6m^2`

Therefore, the area of the pipe below the load is 6 m²