Chpter Exercise Q. 1. (i) 00 N,00 N F =,00 00 =,000 F = m,000 = 1,000 = m/s (ii) =, u = 0, t = 0, s =? s = ut + 1 t = 0(0) + 1 ()(00) = 00 m Q.. 0 N 100 N F = 100 0 = 60 F = m 60 = 10 = 1 m/s F = m 60 = 180 Q.. F = m = 1 m/s (t 0) = 10 ( 1 ) = 11 N F = m (t 0) = 0 ( 1 ) = 160 N Q.. 0 N F = m (0 ) = 10 ( 1 8 ) = N Q.. F = m 900 = (0.060) = 1,000 m/s u = 10, v = 0, = 1,000, s =? v = u + s 0 =,00 + ( 1,000)s s = 0.7 m = 7 cm Q. 6. u = 0, s = 8, t = 8, =? s = ut + t 8 = (0)8 + 1 ()(6) = 1 m/s F = m ( 0) = 80 ( 1 ) = 0 N Q. 7. (i) u = 0, v = 10, s = 0, =? v = u + s 100 = 0 + ()(0) (ii) F = m = 1 m/s 0 = (800)(1) = 1,10 N Q. 8. u = 00, v = 0, s = 1, =? v = u + s 0 = 0,000 + ()(1) = 0,000 F = m = (0.00) ( 0,000) = 1,000 N u = 00, v = 0, = 0,000, s =? v = u + s 0 = 160,000 + ( 0,000)s s = m 1
Q. 9. () F = 98 18 = 80 N F = m 80 = 10() = 8 m/s (b) (i) u = 0, = 8, t = 10, s =? s = ut + 1 t s = 0(10) + 1 (8)(100) = 00 m 18 N 10g = 98 N (ii) u = 0, = 8, t = 0, s =? v = u + t u = u u s t t = s u _ u = u, s = s, = u s, v =? v = u + s v = 9u _ + ( u s ) (s) v = 9u u = u v = u m/s v = u + t u = u u s t t = s u s = ut + 1 t s = (0)(10) + 1 (8)(00) = 1,600 m Distnce = 1,600 00 = 1,00 m Q. 1. F = 1..1 = 0.7 N F = m + 0.7 = ( 1 7 ) =.9 m/s.1 1 W = g = 1. v Q. 10. u = 00, v = 00, s = 0.1, =? v = u + s 0,000 = 90,000 + ()(0.1) = 0,000 F = m,000 = m( 0,000) m = 0.1 kg = 100 grmmes u = 00, v = 0, = 0,000, s =? v = u + s 0 = 90,000 + ( 0,000)s s = 0.18 m = 18 cm Q. 11. u = u, v = 0, s = s, =? v = u + s 0 = u + s _ = u s F = m _ = m ( u s ) = mu s u = 1., =.9, v = 0, s =? v = u + s 0 = 1.96 + (.9)s s = 0. m = 0 cm Q. 1. In ir u = 0, = 9.8, s =., v =? v = u + s v = 0 + (9.8)(.) = 9 v = 7 m/s In Mteril u = 7, v = 0, s = 0., =? v = u + s 0 = 9 + ()(0.) = 70 m/s W = (0.01)g = 0.098
F = m (0.098 ) = (0.01) ( 70) = 0.798 N Q. 1. (i) In ir u = 0, s = h, = g, v =? v = u + s v = 0 + (g)(h) v = _ h In Mrsh F = mg 8mg = 7mg F = m 7mg = m = 7g u = _ h, v = 0, = 7g, s =? v = u + s 0 = h + ( 7g)s s = 7 h In ir u = 0, s = h, = g, v =? v = u + s v = 0 + gh v = _ gh In Mrsh F = mg 8mg = mg F = m mg = (m) = g u = _ gh, = g, v = 0, s =? v = u + s 0 = gh + ( g)s s = h nswer: No 8mg mg 8mg mg Exercise B Q. 1. Q.. Q.. (i) m,000 N 00g =,900 N =,900 m = (0.)(,900) = 1,960 F = m (,000 1,960) = 00 =.08 m/s m = 90 m = 0.6(90) = 9 N 00 N 0g = 90 N F = m (00 9) = (0) = 0.1 m/s m = 9.8 Friction = m (ii) F = m 1g = 9.8 N = ( 1 7 ) (9.8) = 1. N ( 1.) = (1) = 1. m/s he decelertion is 1. m/s (iii) u =., v = 0, = 1., s =? v = u + s 0 = 1. + ( 1.)s s =.7 m
Q.. (i) m = 9,800 N m = 1 (9,800) =,0 N 100g = 9,800 N Limiting riction =,0 N (ii),0 0 = 9.8 (iii) 10 slves needed.,0 N F = m 1 ONNE W,00 N (c) he chnge in momentum per unit time is proportionl to the pplied orce nd tkes plce long the stright line in which the orce cts. (d) (i) 1,0 + 8(70) =,000 (ii),000,000,000g = 19,600 F = m (,000 19,600) =,000 =. m/s 70 Q.. (i) (,00,0) = (1,000) = 0.0 m/s m 800g F = m W = 70g = 686 N ( 686) = (70)(.) = 80 N Q. 7. esolved = 800g = 7,80 m = 1 8 (7,80) = 980 N limiting riction (ii) _ 980 =.9 dogs required. 00 (iii) = (00) = 1,000 N F = m 1000 980 = 800 800 = 0 = 0.0 m/s Q. 6. () Momentum is the product o mss nd velocity. (b) newton is the orce required to ccelerte one kilogrm t one metre per second squred. F = m Mg Mg sin = M = 1 7 g = 1. m/s v = u + t 7 = 0 + (1.)t t = s s = ut + 1 t = 0() + 1 (1.)() = 17. m q Mg cos Mg sin
Q. 8. W Q. 10. (i) 10 N m W 10g esolved m W 1W 6 W 1 6g 10 N 0 N + W 1 = W = 1W 1 m = 1W 6 Q. 9. (i) Dividing by gives m = 1 100 N (ii) F = m 10 6g = 10 = 6.1 m/s m 6g 10 N 0 N esolved 98 N 10g = 98 N 80 N 60 N + 0 = = 8. m = 1 (8.) = 7.1 F = m 10 6g 7.1 = 10 =.1 m/s + 60 = 98 = 8 N F = m 80 = 10 = 8 m/s (ii) (esolved) 1 98 N 80 N + 60 = 98 = 8 1 = 19 N = he riction orce F = m (80 19) = 10 = 6.1 m/s 60 N Q. 11.. ince sin = 1, cos =. 1. = g cos _ = g ( ) g _ = 6 g QED. F = m g sin = = 1 g QED esolved g cos cos
Exercise C Q. 1. (i) kg 11 kg dd equtions: 1 = g = g 7 =.8 m/s (ii) u = 0, =.8, t = Q.. (i) Q.. (i) g g = dd equtions: 1 = = g 7 =.6 m/s (ii) g = 9. = 16.8 = 6 N 11g 11g = 11 1 kg 1 kg g g = dd equtions: 1 = 1g = 6g 7 = 8. m/s (ii) u = 0, = 8., t = v = u + t v = 0 + (8.)() v =. m/s kg 9 kg g g = 1g 1g = 1 9g 9g = 9 Q.. (i) Q.. (i) s = ut + 1 t s = (0)() + 1 (.8)() s = 1.6 m kg g = g dd equtions: 7 = g = g 7 =. m/s kg g g = (ii) u = 0, s =, =., v =? v = u + s v = 0 + (.)() v = 16.8 m/s (iii) u = 16.8, v = 0, = 9.8, s =? v = u + s 0 = 16.8 + ( 9.8)(s) s = 6 7 m 6 kg 6g 6g = 6 dd equtions: 7 = g = g 7 = 7 m/s 1 kg g g = 1 6
Q. 6. (i) Q. 7. (i) (ii) v = u + t v = 0 + 7(1) = 7 m/s (iii) u = 7, v = 0, = 9.8, s =? v = u + s 0 = 9 + ( 9.8)s s =. m kg g g = Eqution 1 m = g g m = 1_ = g g = Eqution 1 kg g g = Eqution dd equtions: 7 = g = g 7 =.8 m/s (ii) = 1.6 N nd = 8 N 1 kg g g = Eqution 1 kg = g g = Eqution Q. 8. 10 kg 10g 10g = 10 Eqution dd equtions: 1 = 9g = g m/s (ii) dditionl orce o m = 1 (g) = g opposing the motion o the kg mss, i.e. to the let. Eqution becomes: g = Eqution 1: Eqution : kg g = 7g 1 m/s g = Eqution 1 kg g g = Eqution dd equtions: (i) 9 = g = 1 9 g m/s (ii) = 0 9 g N v = u + t v = 0 + ( 1 9 g ) () = 9 g m/s v = u + s 0 = ( 9 g ) + ( g)s s = 81 g metres g = 10g = 10 1 = 7g 7
Q. 9. 1 kg Q. 10. (i) kg g kg 10 kg g = Eqution 1 kg g g = Eqution 1 g 1 kg = 1g 1g g = 1 Eqution 10 kg 10g 10g = 10 Eqution dd equtions: 6 = g = 6 g m/s Now, ind lest vlue o m or which the prticles will not move: Eqution 1: g = Eqution : 1mg = 1 Eqution : 10g = 10 dd 6g 1mg = 6 g 6mg = 1 Q. 11. (i) m 1 1 = g m 1 kg g m 1 = 1 (g) = g g = Eqution = g kg g m = 1 (g) = 1 g 1 g = Eqution olving equtions: = 7 g m/s (ii) = 1 g N nd = 7 16 g N 7 kg = 7g 7g = 7 Eqution 1 8 Let = 0 g(1 m) = 0 1 m = 0 m = 1 = g(1 m) _ 1 lest vlue o m or which the prticles will not move. kg g g = Eqution
Q. 1. dd equtions: 10 = g = g 10 =.9 m/s u = 0, =.9, s =.07 v = u + s v = (.9)(.07) v =.1 m/s t = v u =.1 0.9 = 1. s (ii) 7 kg mss now.07 m rom the edge o the tble nd moves t constnt speed o.1 m/s. ime = distnce speed = _.07.1 = 0.7 s M kg dd equtions: m 1 + M + m = m 1 g mg (m 1 + M + m) = (m 1 m)g m = ( 1 m m 1 + m + M ) g Exercise D Q. 1. (i) Pulley : 10g 10g = 10 g = Eqution 1 Prticle B: m kg m 1 kg 10g m kg mg mg = m Eqution 1 M kg Mg = M Eqution 10g = 10() 10g = 0 Eqution dding equtions 1 nd gives g = = g m/s (ii) g = = ( g ) + g = 6g N Q.. (i) Pulley : m 1 kg m 1 g m 1 g = m 1 Eqution 1g 1g = 1 Eqution 1 9
Prticle B: Prticle B: 9g 0g 9g = 9() 0g = 0() 1 = 6 Eqution 0g = 0 Eqution dding equtions 1 nd gives dding equtions 1 nd gives g = 9 = g 9 = 9 9 = 1 m/s (ii) ccelertion o B = = (1) Q.. 11g = 9 = 11g _ 9 9g = 9 = 9(.) + 9g = 108 N =. m/s = m/s (iii) 1g = 1 = 1(1) + 1g Q.. = 10. = 70. N B (i) Pulley : B = 8 g = Eqution 1 Pulley : Prticle B: 1 1 = 18 9g = 9 Eqution 1.g.g =.().g = Eqution 10
Q.. dding equtions 1 nd gives 18.g = 9 = 18.g 9 =.7 m/s (ii) ccelertion o B = = (.7) = 7. m/s (iii) g = = (.7) + g = N dding equtions 1 nd gives mg = m = 1 g (ii) mg = m mg = m ( g ) 10 mg = mg 10 = 6mg = mg Q. 6. (i) Prticle E: B I moves up 1 metre, B will move down metres, since there will be metres more string vilble. Hence, i moves up x metres while B moves down y metres, it ollows tht y = x. Hence, the velocity nd ccelertion o B will be twice those o. hereore, i the ccelertion o is, then the ccelertion o B will be. (i) Pulley : mg mg = m Eqution 1 Prticle B: mg mg = m() mg = m Eqution Pulley C: kmg (ii) mg = m() mg mg = m Eqution 1 kmg = km Eqution dding equtions 1 nd gives mg kmg = m + km g kg = + k ( k)g = ( + k) = (iii) Let k = 0. ( k)g _ + k _ = 1.g. = g = mg m rom Eqution 1 = mg m ( g ) = mg mg = 1 mg 11
Q. 7. kg Mss ccelertion o 0 kg m = g = g g pulley = 1 ( + b) = 1 ( g = 1 (g + 0) + g ) = g g = Eqution 1 0 kg Pulley 0g + b 0g = 0 ( + b ) 10g = ( + b) Eqution kg Mss g b g = b Eqution g = Eqution 1 = g g = b Eqution b = g 10g = ( + b) Eqution 10g = + b 10g = ( g ) ( + g 10g = g + g ) multiply by 0g = g + 0g 1 = 6g = g = g Q. 8. 10 kg Mss m = g = 10g 10g g = 10 Eqution 1 0 kg Pulley 0g + b 0g = 0 ( + b ) 10g = + b Eqution 6 kg Mss b N = 6g 6g mn = g g = 6b Eqution g = 10 Eqution 1 = g 10 1
g = 6b Eqution b = g 6 10g = + b Eqution 10g = ( g 10 ) ( + g 6 ) multiply by 6 60g 6 = 1g + 1g 1 = 90g = g _ 7 = 6 N = g 10 6 9 = 10 = 1. m/s ccelertion o 10 kg prticle. b = g 6 6 9. = 6 =.6 m/s ccelertion o 6 kg prticle + b = 1. +.6 =. m/s ccelertion o 0 kg pulley Q. 9. Note irstly tht, s M increses, the irst prticle to move will be the 6 kg mss. Initilly, thereore, the only moving prticles will be the 6 kg mss nd the pulley. he system orces, just s the 6 kg mss strts to move, will look like this: 6 kg Mss Pulley Mg Mg = M ( ) Eqution dding equtions 1 nd gives Mg 6g = M + 1 g(m 6) = ( M + 1 ) = = 0 g(m 6) g(m 6) M = + 1 M + M 6 = 0 M = 6 this is the vlue o M t which the riction between the 6 kg mss nd the tble is just overcome. I the vlue o M is below this, there will be no movement. Now, let M = 1 m = g = 6g 6g g = 6 Eqution 1 = 6g m = g 6g 1g + b g = 6 6g = 1 Eqution 1 1g = 1 ( + b ) 6g = + b Eqution 1
N = mn = g + b = g 10 + g _ 10 = g + g 0 Q. 10. (i) Mss m = g 0 = g m/s ccelertion o pulley b g = 8b Eqution g = 6 Eqution 1 = g 6 g = 8b Eqution b = g 8 6g = + b Eqution 6g = ( g 6 ) ( + g 8 ) 6g = ( g ) ( + g 8 ) 8 = 1g + 1g 1 = 7g = g _ N = g 6 g _ = g 6 _ g 1g = 0 = 9g 0 = g 10 m/s ccelertion o 6 kg mss b = g 8 _ = g g 8 _ g 0g = 0 = g 0 = g 10 m/s ccelertion o 8 kg mss Pulley B mg Mss m mg mg b + b (ii) Mss m: mg = m Eqution 1 Mss m: mg = mb Eqution Pulley B: Mg = M ( + b ) Eqution _ = mg m b = mg m rom Eqution 1 rom Eqution Mg = M ( + b ) Eqution Mg = M + Mb m ) + M ( mg Mg = M ( mg m ) multiply by m 1
6Mmg 1m = M Mmg + M Mmg 1Mmg = 1m + M divide by Mmg = m + M Mmg = (m + M) g = ( m + M Mm ) g = ( 1 M + 1 m ) s required Exercise E Q. 1. () tn = sin =, cos = 98 100g = 980 N (iii) Let M = m g = ( 1 m + 1 m ) g = ( m ) = mg = mg m mg = mg m = mg mg m = mg m = g m/s m mss will move. b = mg m mg _ = mg m = mg 6mg 6m = mg 6m = g m/s m mss will move. g + b = _ g = 0 m/s pulley B will not move. Q.. kg esolved F = m (98 78) = 100 = m/s (b) (esolved) 98 N 88 N 78 N 98 1 88 N 78 N = 88 Friction = 1 = 196 N F = m (98 78 196) = 100 = 0.0 m/s g 1
esolved 1 kg s g cos g sin 1 1g ccelertion ccelertion F = m g sin = 10 kg 10 10g g = Eqution 1 ccelertions 10g = 10 Eqution olving these gives = 9 1 g, = 0g _ 1 Q.. (i) tn = sin =, cos =. 0 kg s esolved (ii) Q.. (i) kg s 1g = 1 Eqution olving these gives = 1 g ccelertion = 9.8 = 0.8 m/s he 1 kg rises (since the downwrd ws negtive i.e. it should be upwrd). esolved g g g g = Eqution 1 ccelertion 0g 0g cos = 1g 8 kg s ccelertion 0g sin = 16g ccelertion = 8 Eqution 16g = 0 Eqution 1 16
0 kg s 0g 0g = 0 Eqution dding these gives 17g = = 17 g (ii) kg s esolved m = g g m = 1 (g) = g ccelertion ccelertion g g = g = Eqution 1 8 kg s m = ccelertion m = 1 () = g g = 8 Eqution 0 kg s 0g ccelertion 0g = 0 Eqution dding gives 1g = _ = 1g Q.. ince tn =, sin =, cos = 18 kg s m _ = 1 m = 1 6 ( 1 ) = g F = m g _ g = 6 kg s 1 6g cos = g 6g sin = _ 7g = 6 Eqution 1 m 6g _ = 6g m = 1 6 ( 6g ) = 6g _ = M 6g = 1 dding these gives: g = 18 = 1 6 g = g _ ccelertion ccelertion _ g = 1 Eqution 17
Q. 6. ince tn =, sin = ( ), cos = (ii) 1 kg s (i) 0 kg s ccelertion ccelertion 1g m 1g 16g g 18 16g = 0 Eqution 1 ince tn B = 1, sin B =, cos B = 1 1 1 1 kg s 1g g g = 1 Eqution dding these gives 11g = ccelertion = 1 g (i.e. they go the other wy) he ccelertion o the msses is 1 g m/s nd = 8 g N (ii) 0 kg s = 1g 16g m 1g m = 1 (1g) = g 16g g = 0 ccelertion 1g = 0 Eqution 1 imilrly, = 1g m = 1 (1g) = g g g = 1 = 1 Eqution dding these gives: g = Exercise F Q. 1. = g m/s = _ 9 0 g N 6g g D C B E g : 6g = 6 C: = 0 = s D: g = ( + ) E: g = ( ) becomes 6g = 6 = + g D becomes g g = + 7 + = g
E becomes + g g = : Mg = M Q.. = 0 olving these gives = 1 1 g m/s, = 1 g m/s C: Mg + = M D: Mg = M(b ) E: Mg = m(b + ) D + E Mg = Mb + M b + = g + C D + E Mg = Mb + 6M m Mg b Mg B Mg C D Mg ince = Mg, m = 1 (Mg) = Mg : Mg = M B: Mg + = M C: Mg = M(b ) D: Mg = M(b + ) dding C nd D b + = g + B C + D b + 10 = g olving these gives = 11 9 g m/s, b = 6 9 g m/s b Q.. (i) b + 6 = g olving these gives = 17 g, b = 17 g ccelertion o D = b = g 17 i.e. 8 17 downwrd. ccelertion o E = b + = 9 17 g downwrd. b g B C : = 8 C: s = 0() g b Q.. = s D: ( kg): g = (b ) B E: ( kg): g = (b + ) C: = b Mg Mg D C Mg E Mg b becomes = 8 = + g D becomes + g g = (b ) 6 b = 0 E becomes g g = (b + ) + b = g olving these gives = g 11, b = g 11 19
(ii) Pulley : ccelertion: = g 11 m/s Pulley C: ccelertion: = g 11 m/s kg prticle: ccelertion: b = g 11 m/s kg prticle: ccelertion: b + = 11 m/s Q.. 7m mss m pulley 7mg m(1 g) D becomes: mg = m( + b) multiply by m 6g 1 + g = 6 + 6b 18 + 6b = 11g Eqution F Eqution E ( ): 8 1b = 7g Eqution F ( ): 6 + 1b = g dd 8 = 9g = 9g _ 8 = 7 1 gm/s ccelertion o 7m mss Q. 6. 8 kg mss kg pulley = g m mss mg m mss m = g g g g b + b kg mss kg mss mg mg Equtions o Motion b + b : = 7m g g B: + mg = m + mg 7m = m = C: mg = m( b) D: mg = m( + b) m(1 g) m(1 g) C becomes: mg = m( b) multiply by m g 1 + g = b 16 b = 9g Eqution E 8 kg mss : = 8 = + 8 kg pulley B: g + = g + 8 = = + g kg mss C: g = ( b) kg mss D: g = ( + b) Eqution C becomes: g g = b 8 b = 0 Eqution E 0
Eqution D becomes: g g = + b 10 + b = g Eqution F Eqution E ( ): 0 1b = 0 Eqution F ( ): 0 + 1b = 6g dd 70 = 6g = 6g 70 = g m/s ccelertion o 8 kg mss Exercise G Q. 1. 0 Mg (i) he Prticle: Mg Q.. (ii) he Wedge: ccelertion F = m Mg 1 Mg 1 = M = M. Putting this result into eqution gives: Mg 8M = M = 9 g m/s Putting this result into eqution gives: g = ( 9 ) g = g m/s 0 Mg 9 1 Mg 1 kg 7 kg on 1 kg mss ccelertions 0 1 g g g long the slope : F = m on wedge 1 Mg = M( ) g =. Perpendiculr to the slope: F = m Mg = M ( 1 ) Mg = M. N 7g 1
ccelertion o 1 kg mss Now, ind speed o wedge when t = 1 u = 0, = 1 1 g, t = 1 v = u + t = 0 + ( g 8 ) g 1 ) ( 1 ccelertion o wedge 1 kg mss long slope: F = m g = 1( ) g = 1 kg mss perpendiculr to slope: F = m g = g = Q.. = 1 8 = 0.1 m/s he Prticle: 1g g Wedge horizontl: F = m = 7 = 7 Putting this result into eqution gives: g g 1 = 1 = g = 1 1 g m/s ccelertion o wedge Putting this result into eqution gives g = 1 1 g 1g = 1 g 1 = 16g ccelertion g 16 = 1 g _ = 8 1 g m/s ccelertion o prticle reltive to the wedge u = 0, v =, = 8 1 g t = v u = 1 ( ) = 1 seconds Prllel to the slope: F = m g = 1 ( ) g =. Perpendiculr to the slope: F = m g = 1 ( ) g =
he Wedge: g ccelertion Q.. ince tn =, sin =, cos = Mg Mg he Prticle: F = m = =. Putting this result into eqution gives: g ( ) = = 1 7 g m/s Putting this result into eqution gives: g = 1 7g = g m/s 7 Here re nd resolved: 7 gj 7 gi 1 i 7 g + = ( 7 g i 7 g j ) + 1 7 g i + = 7 g i 7 g j = 9 9 g + 16 9 g = = 7 g 9 g his is the mgnitude o the ctul ccelertion o the prticle. Prllel to the slope: F = m ccelertions Mg = M ( ) g = Perpendiculr to the slope: F = m Mg = M ( ) Mg = M he Wedge: F = m Mg = M Mg Mg ccelertion = 0 M Putting this result into eqution gives: Mg _ 100 M = M = 1g _ 109 m/s
Q.. b Mg Mg s Mg ince tn =, sin =, cos = ince tn B =, sin B =, cos B = First Prticle: long plne: Mg Mg ccelertions b F = m Mg = M ( b ) g = b Perpendiculr to the plne: F = m Mg = M ( ) Mg = M = Mg M s B long the plne: Mg = M ( + c ) g = + c.. Perpendiculr to the plne: Mg = M ( ) Mg = M = he Wedge: M + Mg. ccelertion = M Mg M ( ) ( b b Mg M + Mg ) = M (rom nd ) 1 (1Mg 16M 9M 1Mg) = M = 0 it remins t rest. QED Q. 6. (i) m mss mg mg 8mg Other Prticle: ccelertions Wedge Mg q Mg s q c N 1 N mg
ccelertions m mss Q. 7. Mg Mg Mg he M mss: Wedge (ii) m prticle long the plne: F = m _ 8mg = m ( g = ) multiply by m m prticle perpendiculr to the plne: F = m _ mg = m ( ) multiply by m g = m Wedge horizontl: F = m 1 N = m N = mg + 1 mg + ( ) = m multiply by 6 mg = m = m ( + g) = m ( + g) Putting this result into eqution gives: g m( m ( + g) ) = multiply by g ( + g) = 8 g = 11 = g 11 ccelertion o the wedge Mg Mg ccelertion long the plne: Mg = M ( b ) g = b Perpendiculr to the plne: Mg = M ( ) = Mg M he M mss: Mg Mg b ccelertions long the plne: Mg = M ( c + ) g = c +. Perpendiculr to the plne: Mg = M ( ) = M + Mg c
he Wedge: ccelertion o 1 kg mss Mg ccelertion long the horizontl: = M Mg M M = M Mg Mg M M Mg = 6M = M (rom nd ) = 1 9 g m/s Q. 8. (i) tn q =, cos q =, sin q = q m on m mss on wedge N mg m mg mg N mg ccelertion o wedge kg mss long slope: F = m mg = m ( ) g = ( ) kg mss perpendiculr to slope: F = m mg = m ( ) mg = m Wedge horizontl: F = m N = m N = mg + 1 mg + ( ) = m 6 mg = 10m = m( + g) = m ( + g) Putting this result into eqution gives: mg m ( + g) = m multiply by m 10 g = 6 16 = g = g ccelertion o wedge 16 Putting this result into eqution gives g = ( ( g 16 )) g = g 1g = 0 g 0 = 1g = g ccelertion o the prticle reltive to the wedge 6
Q. 9. (ii) Motion o wedge: u = 0, s = 1, = g 16, s = ut + 1 t 1 = 1 ( g 16 ) t _ gt = 1 t = g s Motion o prticle reltive to wedge: u = 0, t = g, = g s = ut + 1 t = 1 ( g = m )( g g ) g ince tn =, sin =, cos = he kg Mss: g he 1kg Mss: 1g ccelertion: (iii) long the verticl : g = (iv) long the horizontl: = he Wedge: P P ccelertion (v) = 8 g Q. 10. g ccelertion (i) long the plne: g = ( ) (ii) Perpendiculr to the plne g = ( ) g he 1kg Mss: q g g g 7
ccelertions he Wedge: 1. g = 1 ( ). g = 1 ( ) p esolved he kg Mss: q sin q cos q g cos q sin q g ccelertions ccelertion cos q q. sin q = 8 sin q. g cos q = (cos q). sin q = ( sin q) 8