A series of railroad track sections,each 17 m in length,are set together on a track.They each must be able to withstand a temperature range from -5 $\circ$ F to 95 $\circ$ F.How large a gap should be made between each track segment? The coefficient of expansion of steel is 13 * 10^-6 $\circ$ C^-1. A)0.6cm B)1.1cm C)1.2cm D)2.2cm E)More information is needed.

Question

Quizplus · Accepted Answer

First, we need to convert the temperature range from Fahrenheit to Celsius:
-5°F = -20.56°C
95°F = 35°C

Next, we can use the formula for thermal expansion:
ΔL = αLΔT
where:
ΔL = change in length
α = coefficient of linear expansion
L = original length
ΔT = change in temperature

We want to find the gap between each track segment, which is equivalent to the change in length between each segment. We can set up an equation:
ΔL = gap between tracks
α = 13 x 10^-6 /°C (we convert Fahrenheit to Celsius)
L = 17 m
ΔT = 55°C (the temperature difference between -20.56°C and 35°C)

ΔL = (13 x 10^-6 /°C) x 17 m x 55°C = 0.012 cm = 1.2 mm

Therefore, the answer is C) 1.2 cm.

A Series of Railroad Track Sections,each 17 M in Length,are ∘\circ∘

A Series of Railroad Track Sections,each 17 M in Length,are $\circ$