A hydraulic lift in the shape of the letter U, two pistons are formed, one with a larger diameter and other with a smaller. If the diameter of the smaller piston is 4.0 cm and the diameter of the larger piston is 40.0 cm, what weight can the larger piston support when a force of 250 N is applied to the smaller piston?

Fluid pressure = Force/Area and is the same in both tubes. The tube with larger area can support 100 times more weight weight.

P on piston 1 should equal to P on piston 2

Remember P = F/A

Plug your values into this:

F1/A1 = F2/A2

The weight is same as the force because it's the only vertical force opposing it

To calculate the weight that the larger piston can support, we need to understand the principle of Pascal's law for hydraulic systems. Pascal's law states that when an external pressure is applied to a confined fluid, the pressure is transmitted equally in all directions.

In this hydraulic lift, as force is applied to the smaller piston, it creates a pressure in the fluid. This pressure is then transmitted equally throughout the fluid and applies a force on the larger piston.

To find the weight that the larger piston can support, we can use the principle of pressure and area.

Step 1: Calculate the area of the smaller piston.
Given that the diameter of the smaller piston is 4.0 cm, we can calculate the radius as 2.0 cm (radius = diameter/2). Then, we can calculate the area using the formula for the area of a circle: Area = π * radius^2.

Area of smaller piston = π * (2.0 cm)^2.

Step 2: Calculate the area of the larger piston.
Given that the diameter of the larger piston is 40.0 cm, we can calculate the radius as 20.0 cm (radius = diameter/2). Then, we can calculate the area using the formula for the area of a circle: Area = π * radius^2.

Area of larger piston = π * (20.0 cm)^2.

Step 3: Calculate the force on the larger piston.
According to Pascal's law, the pressure in the liquid is transmitted equally, so the ratio of the area of the larger piston to the area of the smaller piston will be the same as the ratio of the force on the larger piston to the force on the smaller piston.

We can set up the following equation:

Force on larger piston / Force on smaller piston = Area of larger piston / Area of smaller piston.

Let x be the force on the larger piston.

x / 250 N = (π * (20.0 cm)^2) / (π * (2.0 cm)^2).

Step 4: Solve for x.
We can cancel out the common terms and solve for x:

x = 250 N * ((π * (20.0 cm)^2) / (π * (2.0 cm)^2)).

Evaluate the equation:

x = 250 N * (400 / 4).
x = 250 N * 100.

x = 25,000 N.

Therefore, the larger piston can support a weight of 25,000 N when a force of 250 N is applied to the smaller piston.