# Dynamics_1e_Answers - Engineering Mechanics Dynamics 1e...

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Unformatted text preview: Engineering Mechanics: Dynamics 1e Gray, Costanzo, Plesha Answers to Selected Even-Numbered Problems Please note that answers are not provided for the following type of even-numbered problems: Concept Problems. Computer Problems. Design Problems. For Concept and Computer problems, please consult the solutions manual. Chapter 1 1.2 .r B=A / ` D 3:88 ft 1.4 E r B=A D .4:00 O { 1:00 O |/ ft E r B=A D .3:31 O u p 2:46 O u q / ft ˇ ˇ E r B=A ˇ ˇ xy system D ˇ ˇ E r B=A ˇ ˇ pq system D 4:12 ft 1.6 The angle is dimensionless (or nondimensional) Observe that since angles can be expressed in a variety of units, such as radian or degree, this problem illustrates the idea that some nondimensional quantities still require proper use of units. 1.8 OEI xx Ł D OEI yy Ł D OEI ´´ Ł D OEMŁOELŁ 2 Units of I xx , I yy , and I ´´ in the SI system: kg m 2 ; Units of I xx , I yy , and I ´´ in the U.S. Customary system: slug ft 2 D lb s 2 ft. 1.10 Concept problem. Chapter 2 2.2 E v.15 s / D .72:1 O { C 6:24 O |/ ft = s E a.15 s / D . 15:8 O { 1:39 O |/ ft = s 2 .15 s / D 4:95 ı .15 s / D 180 ı 2.4 Concept problem. 2.6 y.x/ D 2:00 C 3:00x C 2:00x 2 m 2.8 Concept problem. 2.10 E r.t 1 ;t 2 / D .0:899 O { C 41:3 O |/ ft E v avg .t 1 ;t 2 / D .0:450 O { C 20:7 O |/ ft = s 2.12 v.t/ D P r.t/ D OE.4:08e 13:6t / O { C . 0:720 1:28e 13:6t / O |Ł m = s a.t/ D P v.t/ D OE. 55:5e 13:6t / O { C .17:4e 13:6t / O |Ł m = s 2 The impact angle is the slope of the stone’s trajectory at the time that the stone enters the water. Then, recalling that the velocity is always tangent to the trajectory, we have D 26:1 ı 2.14 y.x/ D 5:25 C 3:25x C 1:00x 2 m x max D 3:00 m and x min D 1:00 m 2.16 E v D .29:3 ft = s /OE1 C cos OE.25:5 rad = s /tŁ O { .29:3 ft = s / sin OE.25:5 rad = s /tŁ O | v D .29:3 ft = s / p 2 C 2 cos OE.25:5 rad = s /tŁ E a D 748 ft = s 2 sin OE.25:5 rad = s /tŁ O { 748 ft = s 2 cos OE.25:5 rad = s /tŁ O | 2.18 Computer problem. 1 Last modified: January 20, 2011 Engineering Mechanics: Dynamics 1e Gray, Costanzo, Plesha 2.20 Computer problem. 2.22 . E v P=O / 1 D OE.1 C cos t/ O { 1 C .4 2t/ O | 1 Ł m = s . E v P=O / 2 D ˚ OE.1 C cos t/ cos 2.t 2/ sin Ł O { 2 OE2.t 2/ cos C .1 C cos t/ sin Ł O | 2 m = s . E a P=O / 1 D . sin t O { 1 2 O | 1 / m = s 2 . E a P=O / 2 D OE. cos sin t 2 sin / O { 2 C . sin sin t 2 cos / O | 2 Ł m = s 2 jE v P=O .t D 2 s / j 1 D 0:584 m = s jE v P=O .t D 2 s / j 2 D 0:584 m = s 2.24 E v P=B D . 6:14 O { B C 23:7 O | B / ft = s v P=A D 24:5 ft = s v P=B D 24:5 ft = s E a P=A D .1:78 O { A C 5:96 O | A / ft = s 2 a P=A D 6:22 ft = s 2 a P=B D 6:22 ft = s 2 2.26 E v A D . 20:0 O { 12:8 O |/ ft = s E a A D p 2 O { C 3 p 2 O | ft = s 2 D . 1:41 O { C 4:24 O |/ ft = s 2 2.28 Computer problem....
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Dynamics_1e_Answers - Engineering Mechanics Dynamics 1e...

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