Answer:
The steel bed will contract by 0.13 m, and expand by 0.052 m
Explanation:
For contraction,
α = ΔL/(LΔθ)..................... Equation 1
Where α = Linear expansivity of steel, ΔL = decrease in length/ Increase in length, L = Original length, Δθ = Change in temperature
make ΔL the subject of the equation
ΔL = α(LΔθ)................. Equation 2
Given: α = 13×10⁻⁶/C, L = 200 m, Δθ = -30-20 = -50 °C
Substitute into equation 2
ΔL = 13×10⁻⁶(200)(-50)
ΔL = -0.13 m
Similarly, For expansion,
Using equation 2
ΔL = α(LΔθ)
Given: α = 13×10⁻⁶/C, L = 200 m, Δθ = 40-20 = 20 °C
Substitute into equation 2
ΔL = 13×10⁻⁶(200)(20)
ΔL = 0.052 m.
Hence the steel bed will contract by 0.13 m, and expand by 0.052 m
