!"# $%" &'()*+,%--(./0 +,1 !2 3333333334333333333 5,6789:-;/< #=6 !" >+?@#!$%&' ()*+,-. /0-1(2345 6 /78/ #=69 (:; </=>?@1A; <B&' (1)' (CDE #=6A=>? <, -F "' (CB.(D E>, <!$ ( (' (C/ B B '+9C:-;/< B #<GH.I? ) 0 l 2J4/K;.&<!$ ( 3 2644(8<GHL +/M(2345 6 / E7 C (<GH/ ?E# <GH.IN4&O ?P (8%;.&<!$ ( 6 ?P (? B #?> H;<Q.?> & R4@1I!$3644G ( (S( 6D/M π = 3,14 / E78&TU) (./ ?E7 ?> H;@% (!S (H;,1!$&1 (J4/ B A#'V' (,1WRN&5 !S (X ( P ( (8A>1UH;G !$344 Y8* (X /M(2345 6 / E7 (S( 1 (H;*<DA>1" &* (X / ?E7 Z>(YH;!S (/ E"<&[ (?P (J\] (<!$ (8H; 1 ( !" D !"# $%" &'()*+,%--(./0 +,1 !2B 3333333334333333333 5,6789:-;/< #=6 !" >+?@#!$%&' ()*+,-. /0-1(2345 6 /78/ #=69 (:; </=>?@1A; <B&' (1)' (CDE #=6A=>? <, -F "' (CB.(D E>, <!$ ( (' (C/ B B '+9C:-;/< B #<GH.I? ) 0 l 2N4/K;.&<!$ ( 3 2644(8<GHL +/M(2345 6 / E7 C (<GH/ ?E# <GH.I^4&O ?P (8%;.&<!$ ( 6 ?P (? B #?> H;<Q.?> & R4@1I!$N44G ( (S( 3D/M π = 3,14 / E78&TU) (./ ?E7 ?> H;@% (!S (H;,1!$&1 (J4/ B A#'V' (,1WRN&5 !S (X ( P ( (8A>1UH;G !$344 Y8* (X /M(2345 6 / E7 (S( 1 (H;*<DA>1" &* (X / ?E7 Z>(YH;!S (/ E"<&[ (?P (J\] (<!$ (8H; 1 ( !" D A !"# !>"> $%" &'(),E-,%--+,1 !2 3333333334333333333 5,6789:-;/< #=6 !" >+?@#!$%&' ()*+,-. /0-1(2345 6 /78/F: _9`01 (X ( ) IU.! (X (C (UI* H ( !W/ _ a7,b ( -c() -U]Wb ((/ a7,> &> 7>9-U(&> / >+?@ 3 = = = 2 2 1 h gt 5.4 80m 2 _ = = =v g.t 10.4 40m / s F: F: F: F:3 #=6G,,6E?HI-8 • 01 (X ( ) IUF: • .! (X (C (UI* H (!W/:1JK5F: • = = = 2 2 1 h gt 5.4 80m 2 :1JKJ&,LJM.I8N6K5F: • = = =v g.t 10.4 40m / s :1JKJ&,LJM.I8N6K5F: • d `*F: #=69 (:; </=>?@1A; <B&' (1)' (CDE: _9 (:`#; <W@1<,<!$ (! (> (< @1<!$?P (<W> 1G ./ _# .@1 c, (>O ?P (U8e (>; <.H !W (<@1;I&f (f%?P (e (>; <.H!W (< @1 (!$I&f (f/ F: F: #=6G,,6E?HI-8 _#; <W@1<,<!$ (! (> (<@1<F: _!$?P (<W> 1G ./F: _# .@1 c, (>O ?P (U8e (>; <.H!W ( <@1;I&f (f%?P (e (>; <.H!W (<@1 (!$ I&f (fJOA5:1/P-5J,QF: :1JKJ,QF: #=6A=>? <, -F "' (CB.(D E>, <!$ ( (' (C/ _=>?`0-F (Y-g<Z W&<!$ (D (g<Z (W?8 ! (&% (>(YD (/ F:3 _hZC<-F <` 1 2 hd 2 m m F G r = _9 `i 3 U 6 <&<!$ (-B&(E i<&% (>(YD (BE iP (-F 2NUN^/34 j33 B/ 6 5&( 6 Eik <<-F BE F: F: #=6AG,,6E?HI-8 9 `i 3 U 6 <&<!$ (-B&(E i<&% (>(YD (BE iP (-F 2NUN^/34 j33 B/ 6 5&( 6 Eik <<-F BE -5I,&R:-;/S-/P-5RF: BB '+9C:-;/< B #<GH.I? ) 0 l 2J4/K;.&<!$ ( 3 2644(8<GHL +/M(2345 6 / E7 C (<GH/ ?E# <GH.IN4&O ?P (8%;.&<!$ ( 6 ?P (? /_ ∆ = 1 k. m .gl _ = = = 1 m .g 0,2.10 k 50N / m k 0,04 ?/_ − = 0 2 k.( ) m .gl l _ − − = = = 0 2 k( ) 50.(0,6 0,5) m 0,5kg g 10 l l F: FT: F: FT: B #?> H;<Q.?> & R4@1I3644G ( (S( 6D/M π = 3,14 / E78&TU) (./ ?E7 ?> H;@% (!S (H;,1!$& 1 (J4 /_ = = = t 120 T 0,1s N 1200 _ π ω = = = 2 2.3,14 62,8rad / s T 0,1 ?/_ = ω = =v .R 62,8.0,3 18,84m / s _ = = =S v.t 18,84.50 942m F: F: F: F: B A#'V' (,1WRN&5 !S (X ( P ( (8A>1UH;G !$344 Y8* (X /M(2345 6 / /7 (S( 1 (H;*<DA>1" &* (X / ?/7 Z>(YH;!S (/ /"<&[ (?P (J\] (<!$ (8H; 1 ( !" /_ = − 2 2 0 2aS v v ⇒ − − = = = − 2 2 2 2 0 v v 10 a 0,5m / s 2S 2.100 _ − − = = = − 0 v v 10 t 20s a 0,5 ?/_ −µ =mg ma ⇒ − − µ = = = a 0,5 0,05 g 10 /_ − =5%mg 0,05mg 0 ⇒ =a 0 H;1 (X (I/ F: F: F: F: jjjjjjjjjjjjjjjjjhl7jjjjjjjjjjjjjj !"# !>"> $%" &'(),E-,%--+,1 !2 3333333334333333333 5,6789:-;/< #=6 !" >+?@#!$%&' ()*+,-. /0-1(2345 6 /78/F: _9`01 (X ( ) IU.! (X (C (UI* H ( !W/ _ a7,b ( -c() -U]Wb ((/ a7,> &> 7>9-U(&> / >+?@ 3 = = = 2 2 1 h gt 5.4 80m 2 _ = = =v g.t 10.4 40m / s F: F: F: F:3 #=6G,,6E?HI-8 • 01 (X ( ) IUF: • .! (X (C (UI* H (!W/:1JK5F: • = = = 2 2 1 h gt 5.4 80m 2 :1JKJ&,LJM.I8N6K5F: • = = =v g.t 10.4 40m / s :1JKJ&,LJM.I8N6K5F: • d `*F: #=69 (:; </=>?@1A; <B&' (1)' (CDE: _9 (:`#; <W@1<,<!$ (! (> (< @1<!$?P (<W> 1G ./ _# .@1 c, (>O ?P (U8e (>; <.H !W (<@1;I&f (f%?P (e (>; <.H!W (< @1 (!$I&f (f/ F: F: #=6G,,6E?HI-8 _#; <W@1<,<!$ (! (> (<@1<F: _!$?P (<W> 1G ./F: _# .@1 c, (>O ?P (U8e (>; <.H!W ( <@1;I&f (f%?P (e (>; <.H!W (<@1 (!$ I&f (fJOA5:1/P-5J,QF: :1JKJ,QF: #=6A=>? <, -F "' (CB.(D E>, <!$ ( (' (C/ _=>?`0-F (Y-g<Z W&<!$ (D (g<Z (W?8 ! (&% (>(YD (/ _hZC<-F <` 1 2 hd 2 m m F G r = _9 `i 3 U 6 <&<!$ (-B&(E i<&% (>(YD (BE iP (-F 2NUN^/34 j33 B/ 6 5&( 6 Eik <<-F BE F:3 F: F: C #=6AG,,6E?HI-8 9 `i 3 U 6 <&<!$ (-B&(E i<&% (>(YD (BE iP (-F 2NUN^/34 j33 B/ 6 5&( 6 Eik <<-F BE -5I,&R:-;/S-/P-5RF: BB '+9C:-;/< B #<GH.I? ) 0 l 2N4/K;.&<!$ ( 3 2644(8<GHL +/M(2345 6 / E7 C (<GH/ ?E# <GH.I^4&O ?P (8%;.&<!$ ( 6 ?P (? /_ ∆ = 1 k. m .gl _ = = = 1 m .g 0,2.10 k 50N / m k 0,04 ?/_ − = 0 2 k.( ) m .gl l _ − − = = = 0 2 k( ) 50.(0,7 0,6) m 0,5kg g 10 l l F: FT: F: FT: B #?> H;<Q.?> & R4@1IN44G ( (S( 3D/M π = 3,14 / E78&TU) (./ ?E7 ?> H;@% (!S (H;,1!$& 1 (J4 /_ = = = t 60 T 0,1s N 600 _ π ω = = = 2 2.3,14 62,8rad / s T 0,1 ?/_ = ω = =v .R 62,8.0,3 18,84m / s _ = = =S v.t 18,84.50 942m F: F: F: F: B A#'V' (,1WRN&5 !S (X ( P ( (8A>1UH;G !$344 Y8* (X /M(2345 6 / /7 (S( 1 (H;*<DA>1" &* (X / ?/7 Z>(YH;!S (/ /"<&[ (?P (J\] (<!$ (8H; 1 ( !" /_ = − 2 2 0 2aS v v ⇒ − − = = = − 2 2 2 2 0 v v 10 a 0,5m / s 2S 2.100 _ − − = = = − 0 v v 10 t 20s a 0,5 ?/_ −µ =mg ma ⇒ − − µ = = = a 0,5 0,05 g 10 /_ − =5%mg 0,05mg 0 ⇒ =a 0 H;1 (X (I/ F: F: F: F: jjjjjjjjjjjjjjjjjhl7jjjjjjjjjjjjjj