Question

As shown in figure below a cable used to support an actor as he swung onto the stage. Suppose that the tension in the cable is 940 N as the actor reaches the lowest point. What diameter should a 10-m-long steel wire have if we do not want it to stretch more than 0.5 cm under these conditions! ram YAL (940 N) (10 m) (20 X 100 N/m)(0.005 m) = 9.4 x 10-6 m Because A = the radius of the wire can be found from 9.4 x 10-6m? 13

should youngs modulus be given here or is there a way to find it? question also goes for shear and bulk.

Answer 1

Youngs modulus of steel must be given

otherwise we take standard value.

given
L = 10 m
delta_L = 0.5cm = 0.005 m
T = F = 940 N
d = ?

youngs mdoulus of steel, Y = 200 Gpa = 2.0*10^11 pa
let A is the corss sectional area of the wire.

we know, Y = (F/A)/(delta_L/L)

Y = F*L/(A*delta_L)

A = F*L/(Y*delta_L)

= 940*10/(2*10^11*0.005)

= 9.4*10^-6 m^2

let d is the diamter of the wire.

A = pi*d^2/4

==> d = sqrt(4*A/pi)

= sqrt(4*9.4*10^-6/pi)

= 3.46*10^-3 m (or) 3.46 mm <<<<<<<-------------Answer