Computing the Tension in a Cable
Turn to the figure below. Assume that a weight Whangs from a cable as shown. The
cable is anchored firmly on the left and right. The respective angles the cable makes with
the horizontal are α1and α2respectively. The tensions in the cable—the tension in a cable
αα
W
TT
12
1 2
is the magnitude with which the cable pulls—are T1and T2respectively.
Problem 1. Consider the weight Wand the angles α1and α2as given and assume that the
configuration depicted in the figure is stable. Draw a force diagram for the point at which
the weight is suspended and use results of the section “Dealing with Forces” of Chapter 2 to
express both T1and T2in terms of Wand the angles α1and α2. Conclude that if α1=α2,
then T1=T2.
Problem 2. Look up the addition formula for the sine and use it to simplify the expressions
for T1and T2derived in Problem 1 to
T1=Wcos α2
sin(α1+α2)and T2=Wcos α1
sin(α1+α2).
Problem 3. Assume that W= 500 pounds, α1= 10◦, and α2= 5◦and use your the
formulas of Problem 2 to compute the tensions T1and T2. Repeat your computation of T1
and T2with W= 1000 pounds, α1= 5◦, and α2= 4◦. Finally, repeat the computations once
more with W= 2000 pounds and the angles α1= 4◦and α2= 2◦.
Problem 4. The figure below is an abstraction of Image 6. It shows a cable pulling on a
utility pole with a force of magnitude Tat an angle βwith the horizontal. Provide an
β
T
