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VIVALVISS5-10.574 * T₁+0.5 * T₂ = 03. An object of mass 900 kg is hanging from a ceilingby means of two strings. The first string (T₁) makes anangle of 40 degree with the horizontal-right. The second string(T₂) makes an angle of 20 degree with the horizontal-left.Calculate the tension in the first string ( 7₁ ) (2 point)A.12034.001 NB.14675.062 NC. O 5790.32 ND. 9570.261 NE. O13316.872 N1.

VIVALVISS510574 T05 T 03 An object of mass 900 kg is hanging from a ceilingby means of two strings The first string T makes anangle of 40 degree with the horizo class=

Respuesta :

We can find the Tension using newton's second law:

[tex]\begin{gathered} \Sigma Fy=0 \\ mg-T1sin(40)-T2sin(20)=0 \\ so: \\ T2=\frac{mg-T1sin(40)}{sin(20)} \end{gathered}[/tex][tex]\begin{gathered} \Sigma Fx=0 \\ T1cos(40)-T2cos(20)=0 \\ \end{gathered}[/tex]

Replace T2 into the previous equation:

[tex]\begin{gathered} T1cos(40)-cos(20)(\frac{mg-T1sin(40)}{sin(20)})=0 \\ T1cos(40)-cot(20)mg+T1cot(20)sin(40)=0 \\ T1=\frac{cot(20)mg}{cos(40)+cot(20)sin(40)} \\ T1\approx9570.261N \end{gathered}[/tex]

Answer:

D

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