Question

A copper (Young's modulus 1.1 x 1011 N/m2) cylinder and a brass (Young's modulus 9.0 x 1010 N/m2) cylinder are stacked end to end, as in the drawing. Each cylinder has a radius of 0.20 cm. A compressive force of F = 9700 N is applied to the right end of the brass cylinder. Find the amount by which the length of the stack decreases.

Answer 1

Each cylinder will be compressed by an increment x, call these xc for the copper cylinder, xb for the brass cylinder. The total compression will be xc + xb

you can find x using the following relationship:

Y = stress/strain, giving:

strain = stress/Y

The stress (i.e.force/area) is the same for both cylinders, namely

9700/(pi*(0.20^*10^-2)^2) = 772 MN/m^2

For the copper cylinder:

strain = 772*10^6/(1.1 x 10^11 ) = 7.02*10^-3

xc = strain*length = 3*7.02*10^-3= 21.1*10^-3 cm

For the brass cylinder

strain = 772*10^6/(9 x 10^10) = 8.58*10^-3

xb = 325.7*10-3cm

total change in length = xb + xc = 46.8*10^-3cm