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The worlds largest hanging basket had a mass of 227 kg and can be found in London. To put on display, a hook is placed on the top of the handle and two ropes, one making an angle of 47 degrees with respect to the vertical in the positive direction and the other making an angle of 55 degrees in the negative direction with respect to the vertical, are connected to two supports, each array bed to the side of the building. What is the tension in each of the two ropes?

Sagot :

Answer:

T1 = 1862 N

T2 = 1663 N

Explanation:

We can represent the situation with the following figure

The system is in equilibrium, so the sum of vertical and horizontal forces is 0. It means that we can write the following equations

[tex]\begin{gathered} \\ T_1\sin47-T_2\sin55=0 \\ T_1\cos47+T_2\cos55-mg=0 \end{gathered}[/tex]

Replacing the values, we get:

[tex]\begin{gathered} T_1(0.731)-T_2(0.819)=0 \\ T_1(0.682)+T_2(0.574)-227(9.8)=0 \\ \\ 0.731T_1-0.819T_2=0 \\ 0.682T_1+0.574T_2-2224.6=0 \end{gathered}[/tex]

Now, we can solve the first equation for T1

[tex]\begin{gathered} 0.731T_1=0.819T_2 \\ \\ T_1=\frac{0.819T_2}{0.731} \\ \\ T_1=1.12T_2 \end{gathered}[/tex]

Then, replace this equation with the second equation and solve for T2

[tex]\begin{gathered} 0.682T_1+0.574T_2=2224.6 \\ 0.682(1.12T_2)+0.574T_2=2224.6 \\ 0.764T_2+0.574T_2=2224.6 \\ 1.338T_2=2224.6 \\ \\ T_2=\frac{2224.6}{1.338} \\ \\ T_2=1663 \end{gathered}[/tex]

Finally, the value of T1 is

[tex]\begin{gathered} T_1=1.12T_2 \\ T_1=1.12(1662.505) \\ T_1=1862 \end{gathered}[/tex]

Therefore, the tension of each rope is 1862 N and 1663 N.

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