PROBLEM 7.125*
Using the property indicated in Problem 7.124, determine the curve assumed by a cable of span L and sag
h carrying a distributed load w=w0 cos (
π
x/L), where x is measured from mid–span. Also determine the
maximum and minimum values of the tension in the cable.
PROBLEM 7.124 Show that the curve assumed by a cable that carries a distributed load w(x) is defined
by the differential equation d2y/dx2=w(x)/T0, where T0is the tension at the lowest point.
PROBLEM 7.126*
If the weight per unit length of the cable AB is w0/cos2
θ
, prove that the
curve formed by the cable is a circular arc. (Hint: Use the property
indicated in Problem 7.124.)
PROBLEM 7.124 Show that the curve assumed by a cable that carries a
distributed load w(x
) is defined by the differential equation
d2y/dx2=w(x)/T0, where T0is the tension at the lowest point.
PROBLEM 7.127
A 25–ft chain with a weight of 30 lb is suspended between two points at the same elevation. Knowing that
the sag is 10 ft, determine (a) the distance between the supports, (b) the maximum tension in the chain.
PROBLEM 7.128
A 500–ft–long aerial tramway cable having a weight per unit length of 2.8 lb/ft is suspended between two
points at the same elevation. Knowing that the sag is 125 ft, find (a) the horizontal distance between the
supports, (b) the maximum tension in the cable.
PROBLEM 7.129
A 40–m cable is strung as shown between two buildings. The
maximum tension is found to be 350 N, and the lowest point
of the cable is observed to be 6 m above the ground.
Determine (a) the horizontal distance between the buildings,
(b) the total mass of the cable.
PROBLEM 7.130
A 50–m steel surveying tape has a mass of 1.6 kg. If the tape is stretched between two points at the same
elevation and pulled until the tension at each end is 60 N, determine the horizontal distance between the
ends of the tape. Neglect the elongation of the tape due to the tension.
PROBLEM 7.131
A 20–m length of wire having a mass per unit length of 0.2 kg/m is
attached to a fixed support at A and to a collar at B. Neglecting the
effect of friction, determine (a) the force P for which h= 8 m, (b) the
corresponding span L.
PROBLEM 7.132
A 20–m length of wire having a mass per unit length of 0.2 kg/m is
attached to a fixed support at A and to a collar at B. Knowing that
the magnitude of the horizontal force applied to the collar is
P = 20 N, determine (a) the sag h, (b) the span L.
PROBLEM 7.133
A 20–m length of wire having a mass per unit length of 0.2 kg/m is
attached to a fixed support at A and to a collar at B. Neglecting the
effect of friction, determine (a) the sag h for which L= 15 m, (b) the
corresponding force P.
PROBLEM 7.134
Determine the sag of a 30–ft chain that is attached to two points at the same elevation that are 20 ft apart.