diketahui :
W = 12 N
Kesetimbangan ΣFy = 0
T - W = 0
T = W
T = 12 N
ditanya : T1, T2?
dijawab :
T1 sin 45° + T2 sin 30° = 0
T1 ½√2 + (T1 √2 / √3) ½ = 12...(1)
Kesetimbangan ΣFx = 0
T2 cos 30° - T1 cos 45° = 0
T2 ½√3 = T1 ½√2
T2 = T1 √2 / √3...(2)
- subtitusi pers 2 ke pers 1
T1 √2 / 2 + T1 √2 / 2√3 = 12
T1 (√2 / 2 + √2 / 2√3) = 12
T1 (√6 / 2√3 + √2 / 2√3) = 12
T1 (√6 + √2 / 2√3) = 12
T1 (√6 + √2) = 24√3
T1 = 24√3 / √6 + √2
- merasionalkan penyebut
T1 = 24√3 / (√6 + √2) . (√6 - √2) / (√6 - √2)
T1 = 24√3 . (√6 - √2) / 6 - 2
T1 = 24√3 . (√6 - √2) / 4
T1 = 6√3 . (√6 - √2)
T1 = 6√18 - 6√6 N
T2 = T1 √2 / √3
= (6√18 - 6√6) √2 / √3
= 6√36 - 6√12 / √3
= 6. 6 - 6. 2√3 / √3
= 36 - 12√3 / √3
= 36 / √3 - 12√3 / √3
- merasionalkan penyebut
= (36 / √3 . √3 / √3) - 12
= (36√3 / 3) - 12
= 12√3 - 12 N
- pembuktian
T1 ½√2 + T2 ½ = 12
(18√2 - 6√6) ½√2 + (12√3 - 12))½ = 12
9. 2 - 3. 2√3 + (12√3 - 12) ½ = 12
18 - 6√3 + 6√3 - 6 = 12
18 - 6 - 6√3✓
bawahnya, "dijawab" itu, T1 sin 45° + T2 sin 30° = T