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 0.28 cm. A compressive force of F = 8300 N is applied to the right end of the brass cylinder. Find the amount by which the length of the stack decreases.

Answer 1

See that drawing is not given, so please comment below the values of Lc and Lb from the figure

where Lc = length of copper cylinder

Lb = length of brass cylinder

Comment these value for final answer.

Answer:

strain = Increase in length /original length = Stress/ (modulus Y )

Increase in length = Stress*original length / (modulus Y )

Stress = force /area.

Increase in length = load *original length / ( Area *modulus Y )

dL = L*F/(A*Y)

Now see that compressive force will be expierneced by both parts, and will be equal to sum of both parts

Compression in copper part will be

dLc = Lc*8300/(3.14*(0.28*10^-2)^2*1.1*10^11)

dLc =

Compression in brass part will be

dLb = Lb*8300/(3.14*(0.28*10^-2)^2*9*10^10)

dLb =

Total amout by which the length of stack decreases will be

dL = dLc + dLb

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