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Chapter 9: Q. 60 (page 631)

Static EquilibriumA weight of 2000pounds is suspended from two cables, as shown in the figure. What are the tensions in each cable?

Short Answer

Expert verified

The tension in the cable is approximately equal to 1843.21lband 1630.41lb.

Step by step solution

01

Step 1. Given information 

We are given a figure,

02

Step 2. Finding the tension

Under the equilibrium conditions, the vertical components of the tension in the cables will balance the weight of chandelier, and horizontal component will balance each other, so

For vertical direction,

T1sin40鈭�+T2sin30鈭�=20000.643T1+12T2=2000

For horizontal direction,

T1cos40鈭�=T2cos30鈭�T1=1.13T2

03

Step 3. Finding the tension 

Substituting the value of T1in first equation, we get

localid="1647059749047" 0.6431.13T2+12T2=2000T2=1630.41lb

So,

localid="1647059921184" T1=1.13(1630.54)=1843.21lb

The tension in the cable is localid="1647059931398" 1843.21lband localid="1647059756761" 1630.41lb.

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