What is the displacement of the blue piston?

[blue_print101]

The purpose is to investigate the relationship between the cylinder diameter and the range of motion of a piston in a hydraulic system.

The teacher didn't give any initial of final position at all, so I think the teacher means in general.

Homework Statement

What is the displacement of the blue piston?

a) If the blue cylinder has 2x the diameter of the red cylinder, and the red piston is moved a displacement of 4cm.

and

b) If the blue cylinder has 1/2x the diameter of the red cylinder, and the red piston is moved a displacement of 3cm
The attempt at a solution

a) I'm assuming the 2x means double so I did the following;

I just assumed that for example the red cylinder has a diameter of 20cm and given that the red piston of the red cylinder has a displacement of 4cm the blue cylinder would have a diameter of 40cm since it's twice the size of the red cylinder, which would double the displacement to 8cm.

Therefore I think the displacement of the blue piston would be 8 cm.b) I just supposed again, that the red cylinder has a diameter of 10 cm, Since the question tells us that the blue cylinder has half of the red cylinder, the blue cylinder's diameter would be 5cm, and since the displacement for the red piston for the red cylinder is 3cm, the displacement for the blue piston would be half also, which would be 1.5 cm.

Therefore, I think the displacement of the blue piston would be 1.5 cm.

 

[Rudipoo]

I guess you have a two cylinder system with an incompressible fluid?

For a) you may call, generally, the diameter of the red cylinder D, and thus the diameter of blue cylinder 2D. What are the areas associated with diameters? We thus may work out the volume V=Area x distance through which the red cylinder moves. Equate this to the volume through with the blue cylinder must move (by incompressibility) by calling the distance x.

Do that same method for b).