Question

GOAL Apply the concept of linear expansion and relate it to stress. PROBLEM (a) A steel railroad track has a length of 30.000 m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C? (b) Suppose the track is nailed down so that it cant expand. What stress results in the track due to the temperature change? STRATEGY (a) Apply the linear expansion equation. (b) A track that cannot expand by ?L due to external constraints is equivalent to compressing the track by ?L, creating a stress in the track. Using the equation relating tensile stress to tensile strain together with the linear expansion equation, the amount of (compressional) stress can be calculated using the proper equation. SOLUTION (A) Find the length of the track at 40.0°C. Substitute given quantities into the equation to right, finding the change in length. ?L = ?L??T = [1.1 × 10??(°C)?¹](30.000 m)(40.0°C) = 0.013 m Add the change to the original length to find the final length. L = L? + ?L = 30.013 m (B) Find the stress if the track cannot expand. Substitute into the equation to right to find the stress. F/A = Y(?L/L) = (2.00 × 10¹¹ Pa)(0.013 m / 30.0 m) = 8.7 × 10? Pa LEARN MORE REMARKS Repeated heating and cooling is an important part of the weathering process that gradually wears things out, weakening structures over time. QUESTION What happens to a piano wire when the temperature decreases? - Nothing, because the fixed distance between supports of the stretched wire and allows no expansion or contraction. - Nothing. Piano wires are designed to show no effect. - The tension decreases. - The tension increases. PRACTICE IT Use the worked example above to help you solve this problem. (a) A steel railroad track has a length of 30.800 m when the temperature is 0°C. What is its change in length on a hot day when the temperature is 42.5°C? (Enter your answer to the closest 0.001 m.) (b) Suppose the track is nailed down so that it can't expand. What stress results in the track due to the temperature change? EXERCISE Use the values from PRACTICE IT to help you work this exercise. What is the length of the same railroad track on a cold winter day when the temperature is 8°F?

          GOAL Apply the concept of linear expansion and relate it to stress.

PROBLEM (a) A steel railroad track has a length of 30.000 m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C? (b) Suppose the track is nailed down so that it cant expand. What stress results in the track due to the temperature change?

STRATEGY (a) Apply the linear expansion equation. (b) A track that cannot expand by ?L due to external constraints is equivalent to compressing the track by ?L, creating a stress in the track. Using the equation relating tensile stress to tensile strain together with the linear expansion equation, the amount of (compressional) stress can be calculated using the proper equation.

SOLUTION
(A) Find the length of the track at 40.0°C.
Substitute given quantities into the equation to right, finding the change in length. ?L = ?L??T = [1.1 × 10??(°C)?¹](30.000 m)(40.0°C) = 0.013 m
Add the change to the original length to find the final length. L = L? + ?L = 30.013 m

(B) Find the stress if the track cannot expand.
Substitute into the equation to right to find the stress. F/A = Y(?L/L) = (2.00 × 10¹¹ Pa)(0.013 m / 30.0 m) = 8.7 × 10? Pa

LEARN MORE
REMARKS Repeated heating and cooling is an important part of the weathering process that gradually wears things out, weakening structures over time.

QUESTION What happens to a piano wire when the temperature decreases?
- Nothing, because the fixed distance between supports of the stretched wire and allows no expansion or contraction.
- Nothing. Piano wires are designed to show no effect.
- The tension decreases.
- The tension increases.

PRACTICE IT
Use the worked example above to help you solve this problem.
(a) A steel railroad track has a length of 30.800 m when the temperature is 0°C. What is its change in length on a hot day when the temperature is 42.5°C? (Enter your answer to the closest 0.001 m.)
(b) Suppose the track is nailed down so that it can't expand. What stress results in the track due to the temperature change?

EXERCISE
Use the values from PRACTICE IT to help you work this exercise. What is the length of the same railroad track on a cold winter day when the temperature is 8°F?

GOAL Apply the concept of linear expansion and relate it to stress.

PROBLEM (a) A steel railroad track has a length of 30.000 m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C? (b) Suppose the track is nailed down so that it cant expand. What stress results in the track due to the temperature change?

STRATEGY (a) Apply the linear expansion equation. (b) A track that cannot expand by ?L due to external constraints is equivalent to compressing the track by ?L, creating a stress in the track. Using the equation relating tensile stress to tensile strain together with the linear expansion equation, the amount of (compressional) stress can be calculated using the proper equation.

SOLUTION
(A) Find the length of the track at 40.0°C.
Substitute given quantities into the equation to right, finding the change in length. ?L = ?L??T = [1.1 × 10??(°C)?¹](30.000 m)(40.0°C) = 0.013 m
Add the change to the original length to find the final length. L = L? + ?L = 30.013 m

(B) Find the stress if the track cannot expand.
Substitute into the equation to right to find the stress. F/A = Y(?L/L) = (2.00 × 10¹¹ Pa)(0.013 m / 30.0 m) = 8.7 × 10? Pa

LEARN MORE
REMARKS Repeated heating and cooling is an important part of the weathering process that gradually wears things out, weakening structures over time.

QUESTION What happens to a piano wire when the temperature decreases?
- Nothing, because the fixed distance between supports of the stretched wire and allows no expansion or contraction.
- Nothing. Piano wires are designed to show no effect.
- The tension decreases.
- The tension increases.

PRACTICE IT
Use the worked example above to help you solve this problem.
(a) A steel railroad track has a length of 30.800 m when the temperature is 0°C. What is its change in length on a hot day when the temperature is 42.5°C? (Enter your answer to the closest 0.001 m.)
(b) Suppose the track is nailed down so that it can't expand. What stress results in the track due to the temperature change?

EXERCISE
Use the values from PRACTICE IT to help you work this exercise. What is the length of the same railroad track on a cold winter day when the temperature is 8°F?

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