Example 10.5 Two syringes of different Cross sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are 1.0 cm and 3.0 cm respectively. (a) Find the force exerted on the larger piston when a force of 10 N is applied to the smaller piston. (b) If the smaller piston is pushed in through 6.0 cm, how much does the larger piston move out?
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Explanation:
Since pressure is transmitted undiminished throughout the water
∴
A
1
F
1
=
A
2
F
2
where F
1
and F
2
are the forces on the smaller and on the larger pistons respectively and A
1
and A
2
are the respective areas.
∴F
2
=
A
1
A
2
F
1
=
π(D
1
/2)
2
π(D
2
/2)
2
F
1
=(
D
1
D
2
)
2
F
1
=
(1×10
−2
m)
2
(3×10
−2
m)
2
×10N=90N
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