Question

A student is testing a 1.0 m length of 2.0-mm-diameter steel wire.

Part A How much force is required to stretch this wire by 1.0 mm? Young's modulus for steel is 20×1010N/m2. Express your answer to two significant figures and include the appropriate units.

F=

Part B What length of 4.0-mm-diameter wire would be stretched by 1.0 mm by this force? Express your answer to two significant figures and include the appropriate units.

L2 =

Answer 1

Since, Young's modulus (E) = Stress/Strain = (F*L)/(A*dL)

here, F = force

L = length of wire

A = cross section of wire

dL = expansion in wire

a.) So, we can caluculate Force(F) = (E*A*dL)/L

given, E = 2*10^11 N/m2

A = (pi/4)*(2.0*10^-3)^2 = pi*10^-6 m2

dL = 1 mm = 1*10^-3 m

L = 1.0 m

So, F = (2*10^11*pi*10^-6*10^-3)/1

F = 628.32 N

b.) here, L2 = (E*A*dL)/F

given, F = 628.32 N = 628.3 N

E = 2*10^11 N/m2

A = (pi/4)*(4*10^-3)^2 = 1.26*10^-5 m2

dL = 1.0 mm = 10^-3 m

So, L2 = (2*10^11*1.26*10^-5*10^-3)/628.32

L2 = 4.011 m = 4.0 m

please upvote.