In a hydraulic piston, the small piston has a diameter of 2cm and the large piston has a diameter of 6m. How much more force can the larger piston exert compared with the force applied to the smaller piston?
To calculate the force exerted by each piston, we can use the formula:
Force = Pressure * Area
The pressure is equal throughout the hydraulic system, so we can ignore it in this comparison.
To find the area of each piston, we use the formula:
Area = π * (Radius)^2
Let's calculate the areas of the two pistons:
For the small piston:
Radius = diameter / 2 = 2cm / 2 = 1cm = 0.01m
Area = π * (0.01m)^2 = 0.000314m^2
For the large piston:
Radius = diameter / 2 = 6m / 2 = 3m
Area = π * (3m)^2 = 28.27m^2
Now, to compare the forces, we can divide the area of the large piston by the area of the small piston:
Force (large piston) / Force (small piston) = Area (large piston) / Area (small piston)
Force (large piston) / Force (small piston) = 28.27m^2 / 0.000314m^2
Force (large piston) / Force (small piston) ≈ 90,143
Therefore, the larger piston can exert approximately 90,143 times more force compared to the force applied to the smaller piston.