Question

Piston 1 in the figure has a diameter of 1.08 cm.

Piston 2 has a diameter of 8.12 cm. In the absence of friction, determine the force F, necessary to support an object with a mass of 924 kg placed on piston 2. (Neglect the height difference between the bottom of the two pistons, and assume that the pistons are massless).

Answer 1

The force needed to support the object can be determined using Pascal's principle and the cross-sectional areas of the pistons.

Step-by-step explanation:

According to Pascal's principle, the force needed to support the object can be determined using the formula:

F1/A1 = F2/A2

Where F1 is the force applied on piston 1, A1 is the cross-sectional area of piston 1, F2 is the force needed to support the object, and A2 is the cross-sectional area of piston 2.

Given that the diameter of piston 1 is 1.08 cm and the diameter of piston 2 is 8.12 cm, we can calculate the cross-sectional areas as follows:

A1 = (π/4) * (d1)²

A2 = (π/4) * (d2)²

Plugging in the values, we have:

F2 = (F1 * A2) / A1

Calculating the values gives:

F2 = (F1 * 65.07) / 0.924

Therefore, the force F needed to support the object is equal to (F1 * 65.07) / 0.924.