Your answer is partially correct. Try again. The figure shows a composite bar of

Question

Your answer is partially correct. Try again. The figure shows a composite bar of length L= L1+L2 and consisting of two materials. One material has length L1 and coefficient of linear expansion a1; the other has length L2 and coefficient of linear expansion a2. (a) What is the coefficient of linear expansion a for the composite bar? Put your answer in terms of L1, L2, a1 and a2. For a particular composite bar, L is 53.5 cm, material 1 is steel, and material 2 is brass. If a = 1.4 x 10-5/C", what are the lengths (b) L1 and (c) L2? Li LD - Unit-t (b) Number 44.58 Units cm (c) Number TT 8.916

Explanation / Answer

a) If the composite bar is uniformly heated then both parts will increase in length and as a result the whole bar will increase in length.
L = L1 + L2 …………. (# 1)
Now the definition of a =(L/L)/T. Rearranging gives L = L*a*T
Substituting in #1 gives
L*a*T = L1*a1*T1 + L2*a2*T2
But since the bar was heated uniformly all the T's are equal and cancel.
L*a = L1*a1 + L2*a2
a = (L1*a1 + L2*a2)/L

b) and c)    L1 + L2 = L = 0.535.…………(2)

a = 1.4*10^-5 K^-1

a1 (steel) = 1.3e-5 K^-1

a2(brass) = 1.9e-5 K^-1

Then   1.4*10^-5 = (L1*1.3*10^-5 + L2*1.9*10^-5)/0.535

1.3*L1 + 1.9*L2 = 0.749 …………. (3)

Solving (2) and (3),

L1 = 0.45 m = 45 cm

L2 = 8.5 cm

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