Answer:
We can start by using the formula for pressure in a hydraulic lift:
P1/P2 = A2/A1
where P1 is the input pressure, P2 is the output pressure, A1 is the area of the input piston, and A2 is the area of the output piston. We can rearrange this formula to solve for A2:
A2 = (P2/P1) * A1
We are given that the maximum gauge pressure in the lift is 17.0 atm, which is the output pressure. We can assume that the input pressure is atmospheric pressure, which is approximately 1 atm. We are also given the diameter of the output line, which we can use to find the area of the output piston:
r = d/2 = 28.0 cm/2 = 14.0 cm
A2 = πr^2 = π(14.0 cm)^2 ≈ 615.75 cm^2
Now we can use the formula above to find the area of the input piston, which will depend on the size of the vehicle we want to lift. Let's call the mass of the vehicle M:
A1 = (P2/P1) * A2 = (17.0 atm/1 atm) * 615.75 cm^2 ≈ 10,465.75 cm^2
We can use the formula for the area of a circle to find the diameter of the input piston:
r = √(A1/π) = √(10,465.75 cm^2/π) ≈ 57.63 cm
d = 2r ≈ 115.26 cm
Therefore, the largest size vehicle the lift can handle is one with a mass M that corresponds to an input piston with a diameter of approximately 115.26 cm. Note that we would need to know more about the specifications of the lift (such as its maximum weight capacity) to determine the actual mass of the vehicle it can lift.
Step-by-step explanation: