To compare the force exerted by the two pistons, we can use the concept of pressure in a hydraulic system. The pressure in a hydraulic system is the same throughout, so we can set the pressure on the smaller piston equal to the pressure on the larger piston:
Pressure on smaller piston = Pressure on larger piston
The formula for pressure is:
Pressure = Force / Area
The area of the smaller piston is:
Area of smaller piston = π * (radius)^2
= π * (1 cm)^2
= π cm^2
The area of the larger piston is:
Area of larger piston = π * (radius)^2
= π * (3 cm)^2
= 9π cm^2
Let F1 be the force exerted by the smaller piston and F2 be the force exerted by the larger piston. The equation for pressure is:
F1 / (π cm^2) = F2 / (9π cm^2)
F1 = F2 / 9
Therefore, the larger piston can exert 9 times more force compared to the force applied to the smaller piston.
In the hydraulic pistons shown in the sketch, the small piston has a diameter of 2 cm; the large has a diameter of 6 cm. How much more force can the larger piston exert compared with the force applied to the smaller piston
1 answer