Question

A force of 200 N is applied on small piston of a pascal press. What would be the

force applied on the big piston, if the diameter of the small piston is 4.37 cm and the area of the big piston is 98 cm2?

Answer 1

The force applied on the big piston of a Pascal press can be calculated using Pascal's principle and the formula F1/A1 = F2/A2. Calculate the area of the small piston with the given diameter and use the given area of the big piston to find the force on the big piston.

Step-by-step explanation:

To calculate the force applied on the big piston of a Pascal press, given a force of 200 N on the small piston, we must use Pascal's principle. Pascal's principle states that when an external pressure is applied to a confined fluid, the pressure increases at every point in the fluid by the same amount. This means that the force exerted on the small piston is transmitted equally to the larger piston. The relationship is given by the formula F1/A1 = F2/A2, where F1 is the force applied on the small piston, A1 is the area of the small piston, F2 is the force on the big piston, and A2 is the area of the big piston.

First, calculate the area of the small piston (A1) using its diameter:
A1 = π(d/2)^2 = π(4.37 cm / 2)^2, then apply the above formula to find the force on the large piston (F2), where the area of the big piston (A2) is 98 cm².

The resulting force is the increase in area multiplied by the initial force, calculated as F2 = (A2/A1) × F1.

Answer 2

The force applied on the big piston is 1306.67 N

Step-by-step explanation:

Given;

force applied on small piston, F₁ = 200 N

diameter of the small piston, d₁ = 4.37 cm

radius of the small piston, r₁ = d₁/2 = 2.185 cm

Area of the small piston, A₁ = πr₁² = π(2.185 cm)² = 15 cm²

Area of the big piston, A₂ = 98 cm²

The pressure of the piston is given by;

`P = (F)/(A) \\\\(F_1)/(A_1) = (F_2)/(A_2)\\\\ F_2 = (F_1A_2)/(A_1)`

Where;

F₂ is the force on big piston

`F_2 = (200*98)/(15) \\\\F_2 = 1306.67 \ N`

Therefore, the force applied on the big piston is 1306.67 N