Question

A 40 lb box is suspended from two ropes which each make an angle of 45 degrees with the vertical. What is the tension (in pounds) on each rope?

Answer 1

Answer:

The tension on each rope is 28.28 lb

Explanation:

Given that,

Weight = 40 lb

Angle = 45°

We need to calculate the tension on each rope

Considering the symmetry of the system, the tension of each rope must be same

So,

$T\sin\theta+T\sin\theta=mg$

Put the value into the formula

$2T\sin\theta=mg$

$T\times\sin45=\dfrac{40}{2}$

$T=\dfrac{40\sqrt{2}}{2}$

$T=28.28\ lb$

Hence, The tension on each rope is 28.28 lb.