Hydraulic Piston Supporting a 500lb weight

[AsuraSky]

Homework Statement

Piston 1 in the figure below has a diameter of 0.31 in.; Piston 2 has a diameter of 1.7 in. In the absence of friction, determine the force vector F necessary to support the 500 lb weight.

Homework Equations

F₁/A₁=F₂/A₂

The Attempt at a Solution

I used the equation above and found the areas of each piston and solved for F₁


F₁/.075477=500/2.2698

F₁=16.626

That answer was wrong so I thought about it some more and realized that the force I solved for was the force on the piston and not the lever that the question asked for. So I had this crazy idea that since there was sort of a rotational force on the hinge when you push the lever down you can use Torque = rF with torque being the force previously solved for

16.626 = 10(F) (r=10 for the 10 in distance between force F in the diagram and piston 1 in the diagram)

F= 1.6626

This answer was also marked wrong and I have run out of ideas on how to solve this problem. If anyone can point me in the right direction it would be greatly appreciated.

 

[NobodySpecial]

Right method, slight oops.

The ratio of force at the piston and the hand is the ratio of the distances from each of them to the pivot.

 

[AsuraSky]

Thanks, that cleared things up for me.