hw2_sol

# hw2_sol - Determine the magnitude of the resultant ﬂ and...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Determine the magnitude of the resultant ﬂ and the angle 8 between the x axis and the line of action of the resultant for the two forces shown in Fig. PZ—Z SOLUTION From Eq. 2—1: 2 .2 I . £1 + E2 + JF1F2 cos ¢ 602 + 542 + 2i60}(541 cos 60° 98.?? 3 98.8 N Eq. 2-2: sin ¢ R _ . 0 sinui 3i+§i3:§9— = = 98.8 N z 23.3° 98.x! . -1 2 311} ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES Determine the magnitude of the resultant ﬂ and the angle 6 between the x axis and the line of action of the resultant for the two forces shown in Fig. P2-3. SOLUTION 0 ¢ = 90° + 29° - 21 = 98° From Eqs. 2—1 and 2-2: 2 2 - F1 + F2 + 2F1F2 cos ¢ a’4802 + 4002 + 2(480)(400) cos 989 = 580.48 a 580 lb 51“ ¢ _ . -1 400 sin 98° T—Sln W 0 580.48 ' 43°03 B + 21° = 43.03° + 21° = 64.030 g 64.0° § = 580 lb A 64.00 Ans. ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2—7 Determine the magnitude of the resultant R and the angle 9 between the x axis and the line of action of the resultant for the two forces shown in Fig. P2-7. SOLUTION O = 45° + 60 2 2 - F1 + F2 + 2F1F2 cos ¢ 5 6002 + 8002 + 2(600)(800) cos 105° 866.91 lb 2 867 lb 31“ ¢ _ S. -1 300 sin 105° R “ 1“ 866.91 B + 30 = 63.046 + 30 = 93.046° e 93.0° ﬁ = 867 lb 5 87.00 Ans. = 63.0460 ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2-13 Determine the magnitude of the resultant E and the angle 9 between the x axis and the line of action of the resultant for the two forces shown in Fig. P2-13. SOLUTION From Eqs. 2 2 , — F1 + F2 + ZFlF2 cos ¢ 6002 + 5002 + 2(600)(500) cos 54.1s° 980.47 lb 3 980 lb 51“ ¢ _ 811.1 500 sin 54.160 R ’ ‘ 980.47 ' E + 21.80 = 24.42 + 21.80 = 46.22 g 46.‘ 980 lb & 46.20 Ans. ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2—15* Determine the magnitude of the resultant R and the angle 6 between the x axis and the line of action of the resultant for the two forces shown in Fig. P2-15. SOLUTION -1 = tan tan—1 = 32.01° 180° - 20.850 - 32.01° = 127.14° Eq. 2—1: 2 2 F1 + F2 + 2F1F2 cos ¢ 8002 + 10002 + 2(800)(1000) cos 127.140 820.96 lb a 821 lb Eq. 2-2: -1 F2 31" ¢ _ . -1 1000 sin 127.14° _, o R - 5m - 16.17 8 + 20.35° = 76.17 + 20.85 = 97.02° e 97.o° ﬁ = 821 lb s 83.00 ENGINEERING MECHANICS - STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2-29* Determine the magnitude of the resultant § and the angle 9 between the x axis and the line of action of the resultant for the four forces shown in Fig. P2-29. SOLUTION From Eq. 2-1: 2 2 R12 — F1 + F2 + 2F1F2 cos ¢1 2502 + 3502 + 2(250)(350) cos 50° R12 545.42 lb 2 545 lb From Eq. 2-2: ' _1 F2 sin \$1 1 R -1 350 sin 50° 545.42 B sin = 29.44° Similarly: = 130° — 20° - 30° = 130° 3 2 + F4 + ZFaF‘1 cos \$2 3002 + 6002 + 2(300)(600) cos 130° 467.54 lb a 468 lb F4 Sln ¢2 R34 -1 000 sin 130° 0 467.54 — 100.56 ENGINEERING MECHANICS — STATICS, 2nd. Ed. W. F. RILEY AND L. D. STURGES 2-29* (Continued) 360° - 80° - 31 — B 2 360° - 80° — 29.44° - 100.560 = 150.oo° 2 2 R12 + R3“ + 2R12R34 cos ¢3 545.422 + 467.542 + 2(545.42)(467.54] cos 150° 272.75 lb 2 273 lb Sln \$3 R -1 467.54 sin 150° 272.75 34 = 58.99° 0 81 + 83 — 30 0 29.44° + 58.990 - 30 ﬁ = 273 lb & 58.4° Ans. Two cables are used to support a stoplight as shown in Fig. P2~38. The resultant R of the cable forces F" and Fv has a magnitude of 1350 N and its line of action is vertical. Determine the magnitudes of forces F and F . u V SOLUTION F U sin 36.870 sin 45° sin 98.130 1350 sin 93.13° 1350 sin 98.13° sin 36.37° = 818 N sin 45° 964 N ...
View Full Document

## hw2_sol - Determine the magnitude of the resultant ﬂ and...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online