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Diberikan tiga buah benda , , dan . Koefisien gese...

Diberikan tiga buah benda begin mathsize 14px style m subscript A equals 20 space kg end style, begin mathsize 14px style m subscript B end style, dan begin mathsize 14px style m subscript C equals 25 space kg end style. Koefisien gesekan statik antara benda A dan B adalah 0,3 dan antara benda A dan meja adalah 0,2. Tentukan massa minimum benda B agar sistem tidak bergerak!

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Jawaban:

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript A end cell equals cell 20 space kg end cell row cell m subscript C end cell equals cell 25 space kg end cell row cell mu subscript A B end subscript end cell equals cell 0 comma 3 end cell row cell mu subscript m A end subscript end cell equals cell 0 comma 2 end cell end table end style 

Ditanyakan:

begin mathsize 14px style m subscript B equals ? end style, agar sistem tidak bergerak

Jawab:

Misalkan begin mathsize 14px style g equals 10 space straight m divided by straight s squared end style. Sistem tidak bergerak artinya seluruh benda dalam keadaan setimbang pada sumbu X dan Y.

Balok C:

Diagram benda bebas (DBB):

Kesetimbangan arah sumbu Y:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum F subscript y end cell equals 0 row cell negative w subscript C plus T end cell equals 0 row T equals cell open parentheses 25 close parentheses open parentheses 10 close parentheses equals 250 space straight N end cell end table end style 

Balok B:

Diagram benda bebas (DBB):

Kesetimbangan arah sumbu Y:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum F subscript y end cell equals 0 row cell negative w subscript B plus N subscript A B end subscript end cell equals 0 row cell N subscript A B end subscript end cell equals cell m subscript B g equals 10 m subscript B end cell end table end style 

Balok A:

Diagram benda bebas (DBB):

Kesetimbangan arah sumbu Y (substitusi begin mathsize 14px style N subscript A B end subscript end style dari persamaan balok B):

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum F subscript y end cell equals 0 row cell negative w subscript A plus N subscript m A end subscript minus N subscript A B end subscript end cell equals 0 row cell N subscript m A end subscript end cell equals cell w subscript A plus N subscript A B end subscript end cell row cell N subscript m A end subscript end cell equals cell open parentheses 20 close parentheses open parentheses 10 close parentheses plus 10 m subscript B end cell row blank equals cell 200 plus 10 m subscript B end cell end table end style 

Kesetimbangan arah sumbu X (substitusi begin mathsize 14px style N subscript A B end subscript end stylebegin mathsize 14px style N subscript m A end subscript end style, dan T):

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum F subscript x end cell equals 0 row cell negative f subscript A B end subscript minus f subscript m A end subscript plus T end cell equals 0 row 250 equals cell mu subscript A B end subscript N subscript A B end subscript plus mu subscript m A end subscript N subscript m A end subscript end cell row 250 equals cell open parentheses 0 comma 3 close parentheses open parentheses 10 m subscript B close parentheses plus open parentheses 0 comma 2 close parentheses open parentheses 200 plus 10 m subscript B close parentheses end cell row 250 equals cell 3 m subscript B plus 40 plus 2 m subscript B end cell row cell 5 m subscript B end cell equals 210 row cell m subscript B end cell equals cell bold 42 bold space bold kg end cell end table end style 

Dengan demikian, massa balok B sebesar 42 kg.

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