2-31
Review Problems
2-72 The deflection of the spring of the two-piston cylinder with a spring shown in the figure is to be
determined.
Analysis Summing the forces acting on the piston in the vertical direction gives
Fs F2 F3
F2
F1
kx P2 A2 P3 ( A1 A2 )
P1 A1
>P D P D P ( D D )@
S
>5000 u 0.08 10,000 u 0.03
4 u 800
S
x
4k
1
2
1
2
2
2
3
2
1
2
F3
Fs
which when solved for the deflection of the spring and
substituting A SD 2 / 4 gives
2
2
2
1000(0.08 2 0.03 2 )
@
F1
0.0172 m
1.72 cm
We expressed the spring constant k in kN/m, the pressures in kPa (i.e., kN/m2) and the diameters in m
units.
2-73 The pressure in chamber 1 of the two-piston cylinder with a spring shown in the figure is to be
determined.
Analysis Summing the forces acting on the piston in the vertical direction gives
Fs F1
kx P1 A1
F2 F3
which when solved for the P3 and substituting A SD 2 / 4
gives
P1
F2
P2 A2 P3 ( A1 A2 )
§ A · kx
A2
P3 ¨¨1 2 ¸¸ A1 ¹ A1
A1
©
2
ª § D · 2 º 4kx
§ D2 ·
¸¸ P3 «1 ¨¨ 2 ¸¸ » P2 ¨¨
D
« © D1 ¹ » SD12
1
©
¹
¬
¼
2
ª § 3 · 2 º 4(1200 kN/m)(0.05 m)
§3·
(8000 kPa)¨ ¸ (300 kPa) «1 ¨ ¸ » S (0.07 m) 2
©7¹
«¬ © 7 ¹ »¼
13,880 kPa 13.9 MPa
F3
Fs
P2
F1
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