(a) Find the force P that must be applied to a piston of area 12.10 cm2 to produ
ID: 1480885 • Letter: #
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 11,651 N by means of a column of fluid of cross sectional area 310 cm2 as seen in the figure below.
(b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m.
(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.
Compare your answer with the answer to part b.
Image seen here: http://imgur.com/Qpzy5Im
Explanation / Answer
W = weight of the car = 11,651 N
Ap = cross-sectional area of the piston = 12.10 cm²
Ac = cross-sectional area of the column of fluid = 310 cm²
12.10/310 = P/11,651
310P = (12.10)(11,651)
310P = 140977.1
P = 140977.1 /310
P = 454.76 N ANSWER
(b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m.
PEg1 = gravitational potential energy = Wh
W = weight of the car = 11,651 N
h = height to which the car is raised = 1.00 m
PEg1 = Wh
PEg1 = (11,651 N)(1.00 m)
PEg1 = 11,651 Nm = 11,651 J = 11.651 kJ
PEg0 = gravitational potential energy at zero height = 0
So, the increase in the car's gravitational potential energy is:
PEg = PEg1 - PEg0 = 11,651 Nm = 11,651 J = 11.651 kJ ANSWER
(c) How far must the smaller piston move in order for the larger one to move 1.00 m?
Ratio = 310/12.10 = 25.61
So,
d = distance traveled of smaller cylinder = to be determined
d = 25.61(1.00 m) = 25.61 m ANSWER
(d) Calculate the work done by P in moving the smaller piston.
W = work done = to be determined
P = applied force on the smaller piston = 454.76 N
d = distance traveled by smaller cylinder = 25.61 m
W = Pd
W = (454.76 N)(25.61 m)
W = 11,650.87 Nm = 11,650.87 J = 11.650 kJ ANSWER
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