Chapter 11 Exercise 11A. Exercise 11B. Q. 1. (i) = 2 rads (ii) = 5 rads (iii) 15 = 0.75 rads. Q. 1. T = mv2 r = 8(25) (iv) 11 = 0.

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1 Chpte Execise A Q.. (i) 0 0 = ds (ii) 00 0 = ds (iii) = 0.7 ds 0 (iv) = 0. ds 0 Q.. (i) = cm (ii) 0.8 = cm (iii). = 6 cm (iv).7 = 8. cm Q.. =. = cm Q.. =.07 =. cm.8 Q.. Angu speed = 8 =.8 ds/sec 0 Q. 6. = 7 =.7 cm Q. 7. In 60 seconds it tuns times. In second it tuns times = (p) ds/sec =.7 ds/sec Q. 8. In second it tuns though 0 dins. In 60 seconds it tuns though 600 dins. 600 dins = 600 p 600 fu tuns = (.) = 9 v = 0(0.) = m/s Q w min = 00(p) d 60 s = 00(p) d s 60 = 0.9 d/s Q w min = 70(p)d 60 s = 70(p) d s 60 w = 9p d/s now, v= w v = 0.06(9p) =.8 m/s Execise B Q.. = mv _ = 8() = 00 N Q.. w = 8, m = 7, w = d/s NZL: ΣF = m = mw = 7() 8 = N Q.. Foces esoved A g = 9 p o 9 (i) p = op + o = 6 + o o = m (ii) + = 9 F c = mv = _ () = N (iii) + () = 9 = 9 N

2 Q.. Foces 0g = (i) sin A = A esoved (ii) + = Fc = mw = A = = (0)()() = 0 N (iii) + 0 = Q.. Foces p Mg = 8 N o Q. 6. (i) _ But = Mg ( Mg ) = Mv v = g 0 = sin 0 0 Foces = = 6.8 m/s cos 0 = = (ii) NZL: ΣF = m sin 0 = mw = mw sin 0 sin 0 w = m w _ = m w =.6 d/s Mg esoved Q. 7. (i). 0. =. Foces sin () : Mg = = Mg _ Fc = mv = Mv (ii) = cos = =.8 N

3 (iii) NZL: ΣF = m cos = mw = 0w () w _ =.8() 0(.) w =.7 d/s Q. 8. Eo in uestion: ed 0. m fo 0. m 0. = 0. = 0. = 0. cos sin 0 (i) Fom tinge we get = 0. (ii) = sin + 0 = = 78 (iii) NZL: ΣF = m (iv) = 97. N cos = mw 97. ( ) = 0(w )(0.) ' w =.6 d/s ' cos = = =. d/s (to one decim pce) =. ' Sin θ cos = mw. ( ) = 0w (0.) w = _. d/s Q. 9. P g 0. Q.g Since Q is in euiibium, =.g =. N. Fo P, F c = mw = w (0.). = w w =. P g =. ds/sec Q.g Q:.g = (.) P: = Adding gives:.g = 6. = g = 9 m/s u = 0, = 9, s = 0., v =? v = u + s v = 0 + ( 9 ) (0.) 7 v = Q. 0. (i) Foces esoved h h Mg sin Mg cos Since cos = h, sin = h (ii) cos = Mg h Mg Mg = h sin = Mw ( h ) ( h ) = Mw h = Mw

4 Q.. (iii) Euting the two vues of gives: Mg h = Mw g h = w h = g w (iv) h 0. g 0. w w g 0. w 6. ds/sec 8 = N + = 8g... θ cos (i) NZL: 8 = mv (ii) Fom (iii) 8 = 8v 8 = v N sin 8g Fo contct with tbe N > 0 N = 8g sin 8g > v v < 8g I v = 9.g = sin cos 8g h = cos = sin = 8g = 8g _ sin... NZL: ΣF = m cos = mv Fom Execise C Q.. Mg m : = 8g _ sin cos = 8(9.g) cos cos = 9. sin ( sin ) = 9. sin sin + 9. sin = 0 0 sin + 9 sin 0 = 0 ( sin + 0)(0 sin ) = 0 sin = 0 Fom digm, h = sin = ( 0 ) h = 0 m : m = mv m = m() 0 m = 0.9 Q.. (i) : = : m = mv () = mv (ii) : = : m = mv v = 6g v = g =. m/s _ m() = m(7) m =

5 Q.. : = : m = mw Q.. : = 8 () = mw (0.) w =. w =. ds/sec : m = mv () = m(6) = 7 g Q.. Foce mn m = 0. = 0 = N = NZL: ΣF = m = 70 = 60 9 = 7 m (to neest mete) N mn = mv Mg m = mv v = v = 0.(9.8)(0) Q. 6. tn A = v g v = 7 m/s 8 =,900 (9.8) =,000 m = km Q. 7. tn A = v g = _ v 0(,800) v = 0,000 = m/s Q. 8. (i) Q. 9. x 8 x Let p = x = 8 x A By Pythgos, x = () + (8 x) x = x + x x = sin A =, cos A = = (ii) Foces. : = = : + = mw 8 ( ) = mw = mw g = w g = w esoved w = g d/s. + (.) = (. ) (i) Soving gives = 0.7 m (Pythgos)

6 (ii) Foces = 9m = sin = _ = NZL: ΣF = m + cos = mw 7 _ [ + 7 ] = mw (0.7) w g = (0.7)() [ ] w = 0g Q. 0. (i) Since tn =, sin =, cos = 0 Foces esoved : + = = : F c = mw ( 0 ) = m(7) (ii) But = = 9m = g = 0 But tn = = h h = = ( 0 ) = m Foces esoved 0 : = + = : F c = mw ( + 0 ) = m(9)() But = 0 = 9m () = 9m 0 = g = 0 h = = ( 0 ) = m 6

7 Q.. (i) y y y y (ii) he eft hnd ptice: : = : F c = mw + y = mw (y) + y = mw y Eution A he ight hnd ptice: : = : F c = mw y = mw y y = mw y Eution B Adding eutions A nd B gives y = mw y w = g w = g Q.. Foces g sin A g sin A sin A esoved cos A cos A he kg ptice: Ups = Downs A sin A g cos A = cos A + g F c = mw cos A sin A + sin A = ()() ( sin A) + = 96 C he kg ptice: Ups = Downs cos A = g Lefts = ights sin A = g = cos A Putting this into eution gives: cos A = cos A + cos A = Eution eds: + = 96 = 8 N = N Eution eds: cos A = g 8 cos A = (9.8) cos A = 9. 8 Execise D = 7 0 = 0. A = 70 Q.. Foces esoved sin Cos cos Stndd position Let = the nge with the upwd vetic. 7

8 + cos = mv Mg(0) + m(g) = ( + cos ) + mv mv = cos Putting this esut into eution gives: + cos = cos = cos When the sting goes sck, = 0 0 = cos cos = Q.. Foces esoved cos Stndd position cos sin cos = mv + m ( g ) = cos + mv mv = cos Putting this esut into eution gives: cos = cos When the ptice eves the sphee, = 0 cos = cos cos = 6 = ʹ Putting this esut bck into eution gives: mv = ( 6 ) v = g 6 Q.. Foces esoved cos cos o Assume tht it just eches the top Mg0 + mu = () + m(0) u = g u = g cos sin 8

9 cos = mv (0) + m(g) = ( cos ) + mv mv = + m cos When = 60, cos = mv = Putting these esuts into eution gives ( ) = _ = 7 Q.. Foces esoved cos Stndd position cos cos sin cos = mv (0) + m ( 7g ) = ( cos ) + mv mv = + cos Putting this esut into eution gives cos = + cos When the mbe eves the sphee, = 0 cos = + cos cos = = 0 It hs isen cos = ( ) = Q.. Foces esoved Putting this esut into eution gives: 60º Let v = the speed when = 60 = mv 60º Mg(0) + mu = ( ) + mu mv = mu = mu = + mu = mu = m ( u g ) 9

10 Q. 6. (ii) Foces At NZL: ΣF = m = mv... Dtum P.E. = h K.E. = mv (i) Enegy P.E. + K.E. = P.E. + K.E. mv = + mv v v = g... At _ + = mv... : = m [ v v ] Fom En : = m [g] = + 6 QED 0

Mark Scheme (Results) January 2008

Mark Scheme (Results) January 2008 Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question