In the sketch, the small hydraulic piston has a diameter of 2.5cm cm . The large piston has a diameter of 6.4cm cm .
For each newton of force applied to the small piston, how many newtons of force are exerted by the large piston?
Express your answer using two significant figures.
To solve this problem, we can use Pascal's principle, which states that the pressure applied to an enclosed fluid is transmitted uniformly throughout the fluid.
First, we need to calculate the areas of the two pistons. The area of a piston can be calculated using the formula:
Area = π * (radius^2)
Given the diameter of the small piston is 2.5 cm, we can find the radius by dividing the diameter by 2:
Radius (small piston) = 2.5 cm / 2 = 1.25 cm
Similarly, given the diameter of the large piston is 6.4 cm, we can find the radius:
Radius (large piston) = 6.4 cm / 2 = 3.2 cm
Next, we calculate the areas of the pistons:
Area (small piston) = π * (1.25 cm)^2
Area (large piston) = π * (3.2 cm)^2
Now we can find the ratio of the areas:
Area ratio = Area (large piston) / Area (small piston)
Finally, we can determine the force ratio using the principle that pressure is force divided by area:
Force ratio = Area ratio
To find the force ratio, we substitute the calculated values:
Area ratio = (π * (3.2 cm)^2) / (π * (1.25 cm)^2)
Area ratio = (3.2 cm / 1.25 cm)^2
Now we can calculate:
Area ratio = (2.56)^2
Area ratio = 6.5536
Therefore, for each Newton of force applied to the small piston, approximately 6.6 Newtons of force are exerted by the large piston (rounded to two significant figures).