Two bars, one copper and one aluminum, have the same length L1 = L2 = 1.50 m and
ID: 1474945 • Letter: T
Question
Two bars, one copper and one aluminum, have the same length L1 = L2 = 1.50 m and cross-sectional area A = 10.0 cm2 , and are fixed on immovable walls with a gap of 1.00 mm between them at 73.0 F, and the temperature is going up steadily. The linear thermal expansion coefficient and Young’s modulus of copper are 1.70× 10^5 K^1 and 1.10×10^11 Pa and of aluminum are 2.30×10^5 K^1 and 6.90 × 10^10 Pa, respectively.
What is the temperature when the gap just disappears?
What is the expansion of the aluminum bar when the gap just disappears?
What is the force (magnitude) exerted on each wall at 113.0 F?
Explanation / Answer
1.
T1 =73 F = 22.8 oC
T2=?
change in length of Aluminium + change in length of copper = total change in length
L(Al)*a(Al)*delta T + L(Cu)*a(Cu)*delta T =1*10^-3
L(Al)*a(Al)*(T-22.8) + L(Cu)*a(Cu)*(T-22.8) =1*10^-3
1.5*2.3*10^-5*(T-22.8) + 1.5*1.7*10^-5*(T-22.8) =1*10^-3
6*10^-5 *(T-22.8) =1*10^-3
T= 39.5 oC
=103 F
Answer: 103 F
2.
expansion of Aluminium = L(Al)*a(Al)*delta T
= 1.5*2.3*10^-5*(39.5-22.8)
= 5.75*10^-4 m
Answer: 5.75*10^-4 m