Question

2. An object of mass 100 kg is hanging from a ceilingby means of two strings. The first string (T₁) makes anangle of 35 degree with the horizontal-right. The second string (T₂)makes an angle of 30 degree with the horizontal-left. Theequations relating the x-components and the y-componentsof the forces acting on the object respectively are (2 point)A. O0.574 *T₁+0.5 * T₂ = 0-0.819 * T₁+0.866 *T₂-980 N=0B. O-0.819 *T₁ +0.5 * T₂ = 0-0.819 * T₁+0.5 *T₂-980 N=0C. O0.574 *T₁+0.5 *T₂-980 N=0-0.819 * T₁+0.866 * T₂ = 0D. O-0.819 *T₁ +0.866 * T₂ = 00.574* T₁+0.5 * T₂-980 N = 0-T*T0966 *T0807

Answer 1

`\begin{gathered} D.\text{ }-0.819*T_1+0.866*T_2=0 \\ \\ 0.574*T_1+0.5*T_2-980N=0 \end{gathered}`

Step-by-step explanation

First, let us make a sketch of the problem:

We want to find the x and y-components of the forces acting on the object.

HORIZONTAL COMPONENT

The horizontal forces acting on the object are the horizontal components of the tension on the two strings.

Therefore, the x-component of the forces are:

`\begin{gathered} T_2\cos30=T_1\cos35 \\ \\ -T_1\cos35+T_2\cos30=0 \\ \\ -0.819*T_1+0.866*T_2=0 \end{gathered}`

VERTICAL COMPONENT

The vertical forces acting on the object are the vertical components of the tension and the weight of the object.

Therefore, the y-components of the forces are:

`\begin{gathered} T_1\sin35+T_2\sin30=mg \\ \\ T_1*\sin35+T_2\sin30-mg=0 \\ \\ 0.574*T_1+0.5*T_2-(100*9.8)=0 \\ \\ 0.574*T_1+0.5*T_2-980N=0 \end{gathered}`

Therefore, the correct option is option D.