Piston circled 1 in the figure below has a diameter of 0.28 in.; Piston circled 2 has a diameter of 1.6 in. In the absence of friction, determine the force vector F necessary to support the 500-lb weight. in lb

i got 1.53 lb but it is incorrect

To solve this problem, we can use the principle of mechanical advantage, which states that the force exerted by a piston is equal to the force exerted on the other piston multiplied by the ratio of their areas.

First, let's determine the areas of the pistons. The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius.

For piston circled 1 with a diameter of 0.28 in., we can calculate the radius by dividing the diameter by 2:
r₁ = 0.28 in. / 2 = 0.14 in.

Now we can calculate the area of piston circled 1:
A₁ = π(0.14 in.)² = 0.0616 in²

For piston circled 2 with a diameter of 1.6 in., we can calculate the radius in the same way:
r₂ = 1.6 in. / 2 = 0.8 in.

Now we can calculate the area of piston circled 2:
A₂ = π(0.8 in.)² = 2.01 in²

Next, let's determine the force exerted by the weight. We are given that the weight is 500 lb.

Now we can use the principle of mechanical advantage to calculate the force vector F. The formula is given by F = (A₂ / A₁) * W, where F is the force vector, A₂ is the area of piston circled 2, A₁ is the area of piston circled 1, and W is the weight.

F = (2.01 in² / 0.0616 in²) * 500 lb
F = 65.116 * 500 lb
F ≈ 32558 lb

So, the correct force vector F necessary to support the 500-lb weight is approximately 32558 lb.