if a dentist chair weighs 1600N and is raised by a large piston with a cross sectional area 75.0cm2, what force must be exerted on a small piston of crosssectional area 3.75cm2 to lift the chair

F1/A1=F2/A2

F1=F2A1/A2
F1=1600N*3.75cm2/75CM2= 80N

To determine the force that must be exerted on the small piston to lift the chair, we can use Pascal's law, which states that the pressure exerted at any point of a confined fluid is transmitted uniformly in all directions.

The formula to calculate pressure is:

Pressure = Force / Area

In this case, the pressure exerted by the large piston is equal to the pressure exerted by the small piston, since they are interconnected.

Let's calculate the pressure exerted by the large piston first:

Pressure large piston = Force large piston / Area large piston

Given:
Force large piston = 1600 N
Area large piston = 75.0 cm² = 0.0075 m² (since 1 cm² = 0.0001 m²)

Plugging in the values:

Pressure large piston = 1600 N / 0.0075 m²

Pressure large piston = 213,333.33 Pa (rounded to the nearest hundredth)

Since the pressure is the same for both pistons, we can calculate the force exerted on the small piston using the pressure and area of the small piston:

Pressure large piston = Pressure small piston
Force small piston / Area small piston = Force large piston / Area large piston

We need to solve for the force small piston, so we rearrange the equation:

Force small piston = (Force large piston / Area large piston) * Area small piston

Now let's calculate the force exerted on the small piston:

Area small piston = 3.75 cm² = 0.000375 m² (since 1 cm² = 0.0001 m²)

Plugging in the values:

Force small piston = (1600 N / 0.0075 m²) * 0.000375 m²

Force small piston = 400 N

Therefore, the force that must be exerted on the small piston to lift the chair is 400 Newtons.