Find the force P that must be applied to a piston of area 10.60 cm^2 to produce

Question

Find the force P that must be applied to a piston of area 10.60 cm^2 to produce sufficient fluid pressure to support a car weighing 11,151 N by means of a column of fluid of cross sectional area 325 cm^2 as seen in the figure below. Find the increase in the car's gravitational potential energy when it is raised 1.00 m. How far must the smaller piston move in order for the larger one to move 1.00 m? Calculate the work done by P in moving the smaller piston. Compare your answer with the answer to part b. This answer has not been graded yet.

Explanation / Answer

Let F1 be force applied at the narrow part.

Area of narrow column A1 = 10.60cm2; Area of braod column A2 = 325cm2; Weight of car F2 = 11151 N

a) According to Pascal's law the pressure transimtted through a fluid is same so,

F1/A1 = F2/A2

F1 = F2/A2 * A1 = 11151*10.60/325 = 363.69N

b) Increase In gravitational potential energy U = Weight * height raised = 11151 * 1 = 11151J

c) The volume of water pushed at narrow end should be equal to volume of water raised at braod end

So, A1h1 = A2h2 h is the height raised

h1 = A2/A1 * h2 = 325/10.60 * 1 = 30.66 m

d) Work Done W = F * d where F is the force applied and d is displacement

W = 363.69 * 30.66 = 11151 J

The work done is equal to the increase in potential energy of the car

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