Menghitung Panjang Tali yang Melilit Beberapa Pipa

8 Maret 12

Sore kemaren di Blackberry grup ada yang menanyakan tentang cara menghitung panjang tali yang melilit beberapa pipa, dan saya memberi solusi dengan logika yaitu lingkaran yang tersentuh busurnya dianggap dililit separuh kelilingnya tetapi ternyata salah, itu hanya berlaku jika dua pipa saja yang dililit, dan syaratnya adalah semua pipa memiliki diameter yang sama.
Ilustrasi dari pipa yang dililit tersebut adalah seperti ini.

Nah, dari gambar di atas berapakah panjang tali yang digunakan untuk melilit pipa tersebut? Solusinya akan saya jelaskan dengan melengkapi gambar menjadi seperti berikut.

Dari gambar di atas panjang tali dapat dihitung dengan cara sebagai berikut.
Panjang tali = AB + Busur BC + CD + Busur DE + EF + Busur FA

AB = CD = EF = Garis Singgung Persekutuan Luar
AB = CD = EF = sqrt{(OP)^2)-(R-r)^2}
AB = CD = EF = sqrt{(2r)^2)-(r-r)^2}
AB = CD = EF = sqrt{(2r)^2)-0}
AB = CD = EF = sqrt{(4r)^2}
AB = CD = EF = 2r

Busur BC = Busur DE = Busur FA = {<BPC*2 pi r}/360^0
Busur BC = Busur DE = Busur FA = {(360^0-90^0-90^0-60^0)* 2 pi r}/360^0
Busur BC = Busur DE = Busur FA = {120 * 2 pi r}/360
Busur BC = Busur DE = Busur FA = {240 * pi r}/360
Busur BC = Busur DE = Busur FA = {240 * pi r}/360
Busur BC = Busur DE = Busur FA = 2/3 pi r

Jadi panjang tali =3(2r) + 3(2/3 pi r )
Jadi panjang tali =6r + 2 pi r
Jadi panjang tali =( 6 + 2 pi ) r

Nah sekarang panjang tali dapat dihitung dengan mudah asalkan diameter pipa diketahui.
Selamat belajar.

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