Answer
3.15 N. The forces must be added as vectors. The magnitude of the resultant force is less than the sum of the magnitudes of the individual forces, and depends on the angle between them.
Work Step by Step
The x-components of the forces will cancel.
$F_{1,x}=T cos 52.5^{\circ}$
$F_{2,x}=T cos 127.5^{\circ}$
Add them to find the x-component of the sum.
$F_{sum,x}=0N$
Find the y-components of the forces.
$F_{1,y}=T sin 52.5^{\circ}$
$F_{2,y}=T sin 127.5^{\circ}$
Add them to find the y-component of the sum.
$F_{sum,y}=2T sin 52.5^{\circ}$
Find the resultant force magnitude by using the Pythagorean Theorem.
$F=2T sin 52.5^{\circ}$
Set this equal to the desired 5.00N to find a tension of 3.15 N.
