In the process of changing a flat tire , a motorist uses a hydraulic jack. She begins applying a force of F1=8.6N to the input piston. As a result, the output plunger applies a force of F2=305N to the car. The height difference between the input piston and the output plunger can be neglected. What is the ratio A2/A1 of the plunger and piston areas?
To find the ratio of the plunger area (A2) to the piston area (A1), we can use the equation related to hydraulic systems:
F1/A1 = F2/A2
Where F1 is the force applied to the input piston, A1 is the area of the piston, F2 is the force applied to the output plunger, and A2 is the area of the plunger.
Given:
F1 = 8.6 N
F2 = 305 N
Let's rearrange the equation to solve for the ratio A2/A1:
(A2/A1) = (F2/F1)
Now, substitute the given values:
(A2/A1) = (305 N) / (8.6 N)
Simplifying the equation:
(A2/A1) ≈ 35.465
Therefore, the ratio A2/A1 of the plunger and piston areas is approximately 35.465.