Example 1: Example 1: Example 2: a.) the elevator is at rest. Example 2: Example 2: c.) the elevator accelerates downward at 1.

Transcription

1 Exaple 1: 60 kg, v N (wet), v N (eat), a? Exaple 1: wo force parallel to the ground act upon a box with a a of 60 kg. One force i directed wet and ha a trength of 100 N. he other force i directed eat and ha a trength of 220 N. ind the acceleration of the box auing the urface i frictionle. orce Net force equation uing Newton 2 nd Law: a N g x a 2 1 a a 2 1 N g 220 N 100 N a kg 2 v a (eat) 2 Exaple 2: A cale i fixed to the botto of an elevator. A 50 kg box i on the cale. What i the cale reading when a.) the elevator i at ret? b.) the elevator accelerate upward at 2.0 / 2? c.) the elevator accelerate downward at 1.5 / 2? d.) the elevator ove at contant velocit? Exaple 2: a.) the elevator i at ret N g 50 kg a N g a N g N g ( 50 kg) N 490 N orce 3 4 Exaple 2: b.) the elevator accelerate upward at 2.0 / 2 Exaple 2: c.) the elevator accelerate downward at 1.5 / 2 50 kg a (upward) 50 kg a (downward) N N a a a g N g a (direction i conitent with a) N a + g N a + g N ( 50 kg) ( 50 kg) a g g N a N g a (direction i conitent with a) N g a N ( 50 kg) ( ( 50 kg) N 590 N N 415 N 5 6

2 Exaple 2: d.) the elevator ove at contant velocit N g 50 kg N g a (ae a if the elevator wa at ret) a N g N g ( 50 kg) N 490 N Exaple 3: wo ae are upended uing cord with negligible a. a.) Draw force diagra for each a. b.) ind the tenion in the cord if 1 and 2 55 kg orce 8 Exaple 3: , 2 55 kg, 1?, 2? g g2 1 g1 2 2 g2 1 g g + 2 g 1 ( ) ( 55 kg) N 1 2 a 2 g2 2 2 g 2 ( 55 kg) N 9 Exaple 4: A box i at ret on a rough horizontal urface. he coefficient of tatic and kinetic friction are 0.30 and 0.15 repectivel. a.) How uch force i needed to jut et the box in otion? b.) What i the acceleration of the box if a horizontal force of 100 N i applied to it? c.) How uch force i needed to ove the box at a contant velocit of 15 /? d.) How uch force i needed to ove the box with an acceleration of 1.5 / 2? orce 10 Exaple 4:,.30, k.15 Exaple 4:,.30, k.15 a.) Jut to get the box oving,? b.) 100 N, a? N N f fk a N g N g g g x a f f N g.30( ) N a N g N g g g x a fk a a f k k N 100 N 0.15( ) 9.8 a 2 ( k g 11 a

3 Exaple 4: Exaple 4:,.30, k.15 c.) v 15, a,? N fk a N fk g a x a fk a a + fk a + k N N g N g g.15( ) N fk fk k N k g x a N g N g g,? 2 g,.30, k.15 a 1.5 d.) a + k g ( ) ( ) N 13 Exaple 5: a 2.0 /2 Exaple 5: k 50 N, 15 kg, a 2.0 a.) orce diagra 50 N 15 kg N fk b.) g fk? x a b.) ind the frictional force. fk a c.) ind the coefficient of kinetic (liding) friction. c.) k? a N g N g g fk 50 N (15 kg) ( fk 20 N 15 fk a A 50 N force i applied to a 15 kg box cauing it to accelerate at a rate of 2.0 /2. a.) Draw a force diagra for the box. orce 2 fk k N o 20 N k 15 kg ( ) 9.8 k 2 fk f k N g Exaple 6: kg, kg, 60 N, k1 k2.25, a? and? Exaple 6: wo boxe are connected b a cord with negligible a, a hown in the figure below. A force of 60 N i applied horizontall to the 5.0 kg box cauing the boxe to accelerate to the right. he coefficient of kinetic friction between the boxe and the urface i ind the agnitude of the acceleration of the boxe and the tenion in the cord that connect the kg 5.0 kg 60 N N1 f1 orce N1 g1 1g (2) N2 g2 N2 g2 2 g ( 3) f1 1a a g2 (1) N1 g1 x a 2 f2 1 g1 a N2 ( 4 ) f 2 2 a ( 3) + ( 4) f1 f2 1a + 2 a ( ) a f f k1 N 1 k2 N k1 1g k2 2 g

4 Exaple 6: kg, kg, 60 N, k1 k2.25, a? and? a k 1 1 g k2 2 g N 0.25( 10 kg) ( 0.25( 5 kg) ( 10 kg + 5 kg a ( 3) f1 1 a ( 4) f2 2 a uing ( 3) 1 a + f1 1 a + k1 N1 1 a + k1 1 g ( 10 kg) ( 10 kg) N 19 k.20 Exaple 7: Auing that the te above i initiall at ret and that the pulle i frictionle and of negligible a a.) ind the acceleration of both boxe and the tenion in the cord that connect the. b.) How uch horizontal force ut be applied to the box to ove both boxe at a contant velocit of 15 / to the left? 15 kg orce 20 Exaple 7a: 1, 2 15 kg, k1.20, a? and? Exaple 7a: 1, 2 15 kg, k1.20, a? and? f1 N1 1 2 a 2g k1 1 g ( 15 kg) ( 0.20( ) kg + g1 g2 a a ( 1) N1 g1 N1 g1 1 g ( 2) g2 2 a ( 3) f1 1 a ( 2) g2 2 a x a ( 3) f1 1 a no x - force uing ( 3) 1 a + f1 1 a + k1 N1 1 a + k1 1 g ( 2) + ( 3) g2 f1 1 a + 2 a a g 2 f g k 1 N ( )a 2 g k 1 1 g ( ) ( ) N Exaple 7b: 1, 2 15 kg, k1.20, a, v 15 to the left,? N1 1 2 f1 a x a g1 ( 1) N1 g1 N1 g1 1 g g2 ( 3) f1 no x - force ( 2) + ( 3) g2 f1 ( 2) g2 g2 + f1 2 g + k1 N1 2 g + k1 1 g ( 15 kg) ( ) Exaple 8: 80 N A force of 80 N i applied to a 5.0 kg block that i in contact with a 10 kg block. Both block are initiall at ret on a horizontal urface and the coefficient of kinetic friction for both block i 0.20 on thi urface. ind the force that the 10 kg block exert on the 5.0 kg block. 196 N 23 orce kg 10.0 kg k.20

5 Exaple 8: kg, kg, k1 k2.20, 80 N, a? and 2,1? Exaple 8: kg, kg, k1 k2.20, 80 N, a? and 2,1? N2 N1 2,1 1,2 2 1 f1 g1 g2 f2 a k 1 N1 k2 N2 k 1 1 g k2 2 g N 0.20( 5.0 kg) 9.8 a 2 ( 0.20( 10.0 kg) ( 5.0 kg kg a x a ( 1) N1 g1 ( 2) N2 g2 N1 g1 1 g N2 g2 2 g ( 3) f1 2,1 1 a ( 4) 1,2 f2 2 a ( 3) + ( 4) f1 f2 1 a + 2 a ( 1,2 2,1 ) f1 f2 ( )a o a f 1 f k 1 N1 k2 N2 a ( 3) f1 2,1 1 a ( 4) 1,2 f2 2 a uing ( 4) 1,2 2 a + f2 2 a + k2 N2 2 a + k2 2 g 1,2 ( 10 kg) ( 10 kg) ,1 1, N Exaple 9: 25.0 kg (a) 160 N A box i being pulled b a force that ake a 53 angle above the horizontal a hown in figure (a). i.) ind the noral force acting on the box. ii.) ind the acceleration of the box. Repeat part (i) and (ii) if the force i applied below the horizontal a hown in figure (b) N 25.0 kg (b) orce 27 Exaple 9a: i.) N?, 160 N, 53, and k.20 f a ( 1) N + g N g N g in N ( ) ( ( 160 N)in 53 N 117 N N g x x co in 28 Exaple 9a:, 160 N, 53, and k.20 Exaple 9b:, 160 N, 53, and k.20 ii.) a? f N g x x co in i.) N? f N g x x co in x a ( 2) x f a a x f co k N ( a 160 N )co ( 117 N ) a a ( 1) N g N g + N g + in N ( ) ( 160 N)in 53 N 373 N 30

6 Exaple 9b: 245 N, 160 N, 53, and k.20 N x x a a ( 2) x f a a x f co k N (160 N) co ( 373 N) a.87 2 A box with a weight of 245 N held at ret on a 37 incline. he coefficient of kinetic friction between the box and the inclined urface i a.) ind the acceleration of the box if it i allowed to lide down the incline. b.) What force (parallel to the incline) hould be applied to the box if the block i to lide down the incline at a contant velocit? c.) What force (parallel to the incline) hould be applied to the box if the block i to ove up the incline with an acceleration of 3.0 /2? x co in g ii.) a? f Exaple 10: 31 orce 32 Exaple 10a Sliding down the? incline a g g N f g 245 N g // g Exaple 10b 37, g 245 N,, and k.15 37, g 245 N, and k.15 x x a f a gin k N a N gco gin k gco a a gin k gco a in( 37 ) ( co( 37 ) // g x g x a f a a + + f a + g in + k N a N N g co a + g in + k g co ( ) ( 245 N)in( 37 ) ( 245 N) co( 37 ) 252 N (up the incline) N g in k g co 37, g 245 N,, and k.15 orce needed to ove up incline with an acceleration of 3.0 /2.? f g in k N f x a N N g co f Exaple 10c g g x a // f a N N g co g N orce needed to lide with down incline contant velocit.? ( 245 N)in( 37 ) 0.15( 245 N) co( 37 ) N (up the incline) 34