In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 41 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 9.1. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

This problem can be solved by using Pascal's law which states that in a hydraulic system the pressure exerted in any input piston produces an equal amount of pressure in output piston. P1 = P2 .........................................(1)F1A1 = F2A2 .....................................(2)where,P1 and P2 are the pressure exerted on input and output pistons respectivelyF1 and F2 are the force app;ies on input and output pistons respectivelyA1 and A2 are the cross sectional area of input and output pistons respectively Here, it is given that force applied to the input piston, F1 = 41 N ratio of radius of output piston and input piston is, r2r1 = 9.1Now, ratio of cross sectional area of output and input piston is given as A2A1 = Π(r2)2Π(r1)2A2A1 = r2r12A2A1 = 9.12A2A1 = 82.81 Now by using equation (2), we get F1A1 = F2A2F2 = F1 * A2A1F2 = 41 * 82.81F2 = 3395.21 N Thus, the force that the output plunger applies to the car is 3395.21 N

Answered: In the process of changing a flat tire,…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 41 N to the input piston, which has a radius r₁. As a result, the output plunger, which has a radius r₂, applies a force to the car. The ratio r₂/r₁ has a value of 9.1. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

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