SOLUTION. will destroy the integrity of the work and is not permitted

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1 The smooth block B of negligible size has a mass m and ests on the hoizontal plane. If the boad C pushes on the block at an angle u with a constant acceleation a 0, detemine the velocity of the block along the boad and the distance s the block moves along the boad as a function of time t. The block stats fom est when s = 0, t = 0. a 0 θ B C s Q+ F x = ma x ; 0 = ma B sin f a B = a C + a B>C a B = a 0 + a B>C Q+ a B sin f = -a 0 sin u + a B>C Thus, 0 = m(-a 0 sin u + a B>C ) a B>C = a 0 sin u 0 v B>C t dv B>C = a 0 sin u dt v B>C = a 0 sin u t t s B>C = s = a 0 sin u tdt 0 0 s = 1 a 0 sin u t sale of any pat of this wok (including on thewold Wide Web) 013 Peason Education, Inc., Uppe Saddle Rive, NJ. ll ights eseved. This publication is potected by

2 The 5-kg colla is sliding aound a smooth vetical guide od. t the instant shown, the speed of the colla is v = 4 m>s,which is inceasing at 3 m>s. Detemine the nomal eaction of the guide od on the colla, and foce P at this instant. v 4 m/s P m : + F t = ma t ; P cos 30 = 5(3) P = 17.3 N = 17.3 N +T F n = ma n ; N B sin 30 = 5a b N = N = 10 NT 013 Peason Education, Inc., Uppe Saddle Rive, NJ. ll ights eseved. This publication is potected by

3 The 0.8-Mg ca tavels ove the hill having the shape of a paabola. When the ca is at point, it is taveling at 9 m> s and inceasing its speed at 3m>s. Detemine both the esultant nomal foce and the esultant fictional foce that all the wheels of the ca exet on the oad at this instant. Neglect the size of the ca. y x y 0 (1 ) 6400 dy d y Geomety: Hee, and. The slope angle u at point dx = x dx = is given by 80 m x tan u = dy = (80) u = dx x = 80 m and the adius of cuvatue at point is = C1 + (dy>dx) D 3> d y>dx = C1 + ( x) D 3> = 3.61 m x = 80 m Equation of Motion: pplying Eq with u = 6.57 and = 3.61 m, we hlaws have F t = ma t ; 800(9.81) sin F f = 800(3) F f = N = 1.11 kn 9 of F n = ma n ; 800(9.81) cos N = United 800a 3.61 by N = N = 6.73 kn This wok is potected and is povided solely fo the use thei couses and assessing student States copyight instuctos in teaching leaning. Dissemination o 013 Peason Education, Inc., Uppe Saddle Rive, NJ. ll ights eseved. This publication is potected by

4 Mg aiplane is flying at a constant speed of 350 km> h along a hoizontal cicula path. If the banking angle u = 15, detemine the uplift foce acting on the aiplane and the adius of the cicula path. Neglect the size of the aiplane. u Fee-Body Diagam: The fee-body diagam of the aiplane is shown in Fig. (a). Hee, a n must be diected towads the cente of cuvatue (positive n axis). Equations of Motion: The speed of the aiplane is v = a350 km h ba1000 m 1km ba 1h 3600 s b = 97. m>s. Realizing that a n = v and efeing to Fig. (a), = c F b = 0; cos (9.81) = 0 = N = 50.8 kn ; + F n = ma n ; sin 15 = = m = 3.60 km thei couses and assessing student leaning. Dissemination o 013 Peason Education, Inc., Uppe Saddle Rive, NJ. ll ights eseved. This publication is potected by

5 * The 5-lb colla slides on the smooth od, so that when it is at it has a speed of 10 ft> s. If the sping to which it is attached has an unstetched length of 3 ft and a stiffness of k = 10 lb>ft, detemine the nomal foce on the colla and the acceleation of the colla at this instant. y 10 ft/s y 8 1 x y = 8-1 x - dy dx = tan u = x = u = x = d y dx = -1 O ft x = B1 + a dy dx b d y dx 3 R y = 8-1 () = 6 O = () + (6) = F s = kx = 10( ) = lb tan f = 6 ; f = = (1 + (-) ) 3-1 = ft +b F n = ma n ; 5 cos N cos 45.0 = a this 5 3. ba(10) b of N = 4.4 lb pat any +R F t = ma t ; 5 sin sin 4of 45.0 destoy = a 5 3. ba t sale wok (including on the Wold Wide Web) will the integity of the wok and is not pemitted. a t = 180. ft>s a n = v = (10) = ft>s a = (180.) + (8.9443) a = 180 ft>s 013 Peason Education, Inc., Uppe Saddle Rive, NJ. ll ights eseved. This publication is potected by