Given:
The mass of the sign, m=4.89 kg
The force applied by the first cable, T₁=31.5 N
To find:
The force applied by the second cable.
Explanation:
For the sign to stay up, all the vertical forces acting on the object must be balanced. The vertical forces acting on the sign are the weight of the sign and the upward forces applied by the cables.
Thus,
[tex]mg=T_1+T_2[/tex]Where g is the acceleration due to gravity and T₂ is the force/tension applied by the second cable.
On substituting the known values,
[tex]\begin{gathered} 4.89\times9.8=31.5+T_2 \\ \implies T_2=4.89\times9.8-31.5 \\ T_2=16.42\text{ N} \end{gathered}[/tex]Final answer:
The force exerted by the second cable is 16.42 N
