Two pistons of a hydraulic lift have radii of 2.67 cm and 20.0 cm.The downward force on the 2.67-cm piston that is required to lift a mass of 2000 kg supported by the 20-cm piston is

Question

Quizplus · Accepted Answer

We can use the formula for hydraulic lift:

F1/F2 = A2/A1

where F1 is the downward force on the smaller piston (2.67 cm), F2 is the upward force on the larger piston (20.0 cm), A1 is the surface area of the smaller piston, and A2 is the surface area of the larger piston.

Substituting the values given:

F1/F2 = (π * 2.67^2) / (π * 20.0^2)
F1/F2 = 1/49.67

We also know that the upward force on the larger piston (F2) is equal to the weight of the mass being lifted, which is 2000 kg * 9.8 m/s^2 = 19,600 N.

So, we can solve for F1:

F1 = F2 * A1/A2
F1 = 19,600 N * (π * 2.67^2)/(π * 20.0^2)
F1 = 347.9 N

Rounding to the nearest whole number gives us 348 N, which is closest to answer choice A (350 N).

Two Pistons of a Hydraulic Lift Have Radii of 2 ×\times×

Two Pistons of a Hydraulic Lift Have Radii of 2 $\times$