Basic Engineering Mathematics, Fifth Edition

268 Basic Engineering Mathematics 0 c F 1 F 2 a b Figure 29.5 Problem 1. A force of 5N is inclined at an angle of 45◦to a second ...

Vectors 269 (iii) The resultant force is shown asRand is measured as18Nand angleθis measured as 34 ◦. Thus,the resultant of the ...

270 Basic Engineering Mathematics i.e.the horizontal component ofF=Fcosθ,and sinθ= ab 0 b from which,ab= 0 bsinθ=Fsinθ i.e.the v ...

Vectors 271 total horizontal component of the two forces, H=F 1 cosθ 1 +F 2 cosθ 2 The vertical component of forceF 1 isF 1 sinθ ...

272 Basic Engineering Mathematics The vertical component of the 15N force is 15sin0◦and the vertical component of the 10N force ...

Vectors 273 the horizontal component of the 20m/s velocity is 20cos90◦=0m/s and the horizontal component of the 15m/s velocity i ...

274 Basic Engineering Mathematics If velocity v 1 =25m/s at 60◦ and v 2 =15m/sat− 30 ◦,calculatethemagnitude and direction ofv ...

Vectors 275 a 12 a 2 a 11 a 2 2.6m/s^2 1268 a 1 2 a 2 a 2 a 1 1.5m/s^2 1458 Figure 29.35 Vertical component ofa 1 +a 2 , V= 1 .5 ...

276 Basic Engineering Mathematics R 0 27.67 6.99   Figure 29.38 Thus,v 2 −v 1 −v 3 = 28 .54 units at 194. 18 ◦ This result is ...

Vectors 277 From the geometry of thisvector triangle, the mag- nitude ofqp= √ 452 + 552 = 71 .06m/s and the direction ofqp=tan−^ ...

Chapter 30 Methods of adding alternating waveforms 30.1 Combining two periodic functions There are a number of instances in engi ...

Methods of adding alternating waveforms 279 waveformleadsy 1 =3sinAby 34◦or 34× π 180 rad= 0 .593rad. The sinusoidal expression ...

280 Basic Engineering Mathematics 2  angle t 19  19  i 1  20 sint iR  20 sint10 sin (t ) 90  180  270  360   30 ...

Methods of adding alternating waveforms 281 60  60   y 1  4 y y^2 ^3 R y 2 Figure 30.8 The relative positions ofi 1 andi 2 ...

282 Basic Engineering Mathematics y 155 y (^25) 4 308 Figure 30.12 y 1  5 y (^2)  4 (^0)  yR a b 30  150  Figure 30.13 from ...

Methods of adding alternating waveforms 283 from which sinφ= 10sin120◦ 26. 46 = 0. 327296 and φ=sin−^10. 327296 = 19. 10 ◦ = 19. ...

284 Basic Engineering Mathematics Hence, vR= √ 36. 652 +(− 12. 50 )^2 by Pythagoras’ theorem =38.72 volts tanφ= V H = − 12. 50 3 ...

Methods of adding alternating waveforms 285 (b) the frequency of the supply. If the supply to a circuit isv=20sin628. 3 t volts ...

Revision Test 12 : Vectors andadding waveforms This assignment covers the material contained in Chapters 29 and 30.The marks ava ...

Revision Test 12 : Vectors and adding waveforms 287 Givena=− 3 i+3j+5k,b= 2 i− 5 j+7kand c= 3 i+6j− 4 k, determine the followin ...