The small piston has a diameter of 2cm and the large piston has a diameter of 6cm. How much more force can the larger piston exert compared with the force applied to the smaller piston?

The force is inversely proprtional to the area, since the hydraulic pressure is cnstant.

To determine the force exerted by the larger piston compared to the force applied to the smaller piston, we can use the concept of pressure in a hydraulic system.

The pressure exerted by a fluid in a hydraulic system is equal at all points, as long as the fluid is confined within a closed system. This principle is known as Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.

To find the force exerted by the pistons, we need to calculate the pressure on each piston using the formula:

Pressure = Force/Area

We can compare the two forces by comparing their respective pressures.

Given:
Diameter of small piston = 2 cm
Diameter of large piston = 6 cm

First, let's calculate the areas of the pistons using the formula:

Area = π * (radius)^2

The radius of the small piston is half its diameter, so the radius is 1 cm.
Area of small piston = π * (1 cm)^2

The radius of the large piston is half its diameter, so the radius is 3 cm.
Area of large piston = π * (3 cm)^2

Now, let's calculate the pressures on each piston by dividing the force by the respective areas.

For the small piston:
Pressure on small piston = Force on small piston / Area of small piston

For the large piston:
Pressure on large piston = Force on large piston / Area of large piston

Since the problem does not provide the actual force or any information requiring it, we cannot calculate the actual force or compare the two forces directly. However, we can use the concept of pressure to compare the forces indirectly.

Comparing the pressures (Pressure on small piston vs. Pressure on large piston) will give us an idea of the force ratio between the two pistons.

Keep in mind that the ratio of the areas of the pistons also represents the ratio of the forces they can exert. So, if the larger piston has a three times greater diameter than the small piston, the force it can exert will also be three times greater.

the force is proportional and therefore the pressure is not constant and in fact monkey balls.

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