A Levels Physics

A lift is supported by two steel cables each of length 20 m.
Each of the cables consists of 100 parallel steel wires, each wire of cross-sectional area
3.2 x 10m?. The Young modulus of steel is 2.1 x 10"N m?.
Which distance does the lift move downward when a man of mass 70 kg steps into it?
A 0.010 mm
B 0.020 mm
C 0.10 mm
0.20 mm


Choice C is correct because:

Young Modulus (E) = Stress / Strain

Stress = Force (F) / Cross Sectional Area (A)

Strain = Extension (x) / Original Length (l)

E = (F/A) / (x/l)

E = Fl / Ax

x = Fl / AE

Cross-Sectional Area for 100 wires = 3.2 x 10-6 x 100 = 3.2 x 10 -4

There are 2 cables so the overall cross-sectional area for both cables (A) = 3.2 x 10-4 x 2 = 6.4 x 10-4 m2 

Force = Weight of man

Force = mg

Force = 70 x 9.81 N

Extension (x) = x  

Original Length (l) = 20 m 

x = Fl / AE

x = [ (70 x 9.81) x (20) ] / [ (6.4 x 10-4 ) x (2.1 x 1011) ]

x = 1 x 10-4 m Cross-Sectional= 0.10 mm

Deformation of Solids | 2013 - O/N - 9702/13 | Q22