advertisement

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 PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.