Question

In the hydraulic pistons shown in the sketch, the small piston has a diameter of 2 cm and the large piston has
a diameter of 6 cm. How much more force can the larger piston exert, compared with the force applied to the
smaller piston?

I know there is no sketch here but the picture has is shaped just like a U

Answer 1

Answer on Question #49186-Physics-Mechanics-Kinematics-Dynamics

In the hydraulic pistons shown in the sketch, the small piston has a diameter of 2 cm and the large piston has a diameter of 6 cm. How much more force can the larger piston exert, compared with the force applied to the smaller piston?

I know there is no sketch here but the picture has is shaped just like a U

Solution

The pressures in both pistons are equal:

$$p _ {1} = p _ {2}.$$

But,

$$p _ {1} = \frac {F _ {1}}{A _ {1}}; p _ {2} = \frac {F _ {2}}{A _ {2}}.$$

Thus

$$\frac {F _ {1}}{A _ {1}} = \frac {F _ {2}}{A _ {2}} \rightarrow \frac {F _ {2}}{F _ {1}} = \frac {A _ {2}}{A _ {1}} = \frac {\frac {\pi d _ {2} ^ {2}}{4}}{\frac {\pi d _ {1} ^ {2}}{4}} = \frac {d _ {2} ^ {2}}{d _ {1} ^ {2}} = \left(\frac {6 \mathrm {c m}}{2 \mathrm {c m}}\right) ^ {2} = 9.$$

Answer: 9.

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