(a) Find the force P that must be applied to a piston of area 12.10 cm2 to produ

Question

(a) Find the force P that must be applied to a piston of area 12.10 cm2 to produce sufficient fluid pressure to support a car weighing 10,801 N by means of a column of fluid of cross sectional area 275 cm2 as seen in the figure below. (answer is 475.244 N) (b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m. (answer is 10801 J) (c) How far must the smaller piston move in order for the larger one to move 1.00 m? (d) Calculate the work done by P in moving the smaller piston.

Explanation / Answer

You didn't provide the figure, so I can't be sure about the answers to parts (c) and (d)

(a) Pascal's principle: Pressure is transmitted evenly throughout a fluid.

Pressure is imply the force per area, P = F/A. Since this pressure is constant throughout the fluid:

F1/A1 = F2/A2 or F1 = P = (A1/A2) F2

A1 = 12.1 cm2; A2 = 275 cm2; F2 = w = 10,801 N

Plug in the numbers and you'll find that the answer is indeed 475.244 N.

(b) The change in gravitational potential energy is simply the weight times the distance raised:

PE = w h = (10,801 N)(1 m) = 10.801 J

(c) The volume of fluid moved is the cross-sectional area times the distance moved: V = A h. Since this volume is constant:

A1h1 = A2h2 or h1 = (A2/A1) h2

A2 = 275 cm2; A2 = 275 cm2; h2 = 1 m

(d) Work is simply force times distance: W = F h, in this case, W = P h1

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