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A line was measured with a steel tape which was exactly 30m at 200C at a pull of 100N. The measured length was 1500m. If the temperature during measurement was 400C and the pull applied was 150N, determine the correct length of line. Coefficient of thermal expansion of tape is 3.5 x 10-6 per0C, cross-sectional area of tape is 2.5mm2, Modulus of elasticity = 2.1 x105 N/mm2.
- a)1499.75m
- b)1499.60m
- c)1500.25m
- d)1500.40m
Correct answer is option 'C'. Can you explain this answer?
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A line was measured with a steeltape which was exactly 30m at 200C at ...
Given data:
Length measured at 20℃ and 100N pull = 30m
Measured length at 40℃ and 150N pull = 1500m
Coefficient of thermal expansion of tape = 3.5 x 10^-6 per ℃
Cross-sectional area of tape = 2.5 mm^2
Modulus of elasticity = 2.1 x 10^5 N/mm^2
To find: Correct length of the tape
Solution:
1. Convert the length measured at 20℃ and 100N pull to the length at 40℃ and 150N pull using the formula:
ΔL = LαΔT
Where,
ΔL = Change in length
L = Original length
α = Coefficient of thermal expansion
ΔT = Change in temperature
Here, the change in temperature is (40 - 20) = 20℃ and the change in pull is (150 - 100) = 50N
ΔL = 30 x 3.5 x 10^-6 x 20 x (150/100)
ΔL = 0.01575m
So, the length of the tape at 40℃ and 150N pull = 30 + 0.01575 = 30.01575m
2. Calculate the stress in the tape using the formula:
σ = P/A
Where,
σ = Stress
P = Pull
A = Cross-sectional area
σ = 150/2.5
σ = 60 N/mm^2
3. Calculate the strain in the tape using the formula:
ε = σ/E
Where,
ε = Strain
σ = Stress
E = Modulus of elasticity
ε = 60/2.1 x 10^5
ε = 2.857 x 10^-4
4. Calculate the change in length due to strain using the formula:
ΔL = Lε
Where,
ΔL = Change in length
L = Original length
ε = Strain
ΔL = 1500 x 2.857 x 10^-4
ΔL = 0.42855m
5. Calculate the correct length of the tape by subtracting the change in length due to strain from the length measured at 40℃ and 150N pull:
Correct length = 30.01575 - 0.42855
Correct length = 29.5872m
Therefore, the correct length of the tape is 1499.60m, which is option (b).
Length measured at 20℃ and 100N pull = 30m
Measured length at 40℃ and 150N pull = 1500m
Coefficient of thermal expansion of tape = 3.5 x 10^-6 per ℃
Cross-sectional area of tape = 2.5 mm^2
Modulus of elasticity = 2.1 x 10^5 N/mm^2
To find: Correct length of the tape
Solution:
1. Convert the length measured at 20℃ and 100N pull to the length at 40℃ and 150N pull using the formula:
ΔL = LαΔT
Where,
ΔL = Change in length
L = Original length
α = Coefficient of thermal expansion
ΔT = Change in temperature
Here, the change in temperature is (40 - 20) = 20℃ and the change in pull is (150 - 100) = 50N
ΔL = 30 x 3.5 x 10^-6 x 20 x (150/100)
ΔL = 0.01575m
So, the length of the tape at 40℃ and 150N pull = 30 + 0.01575 = 30.01575m
2. Calculate the stress in the tape using the formula:
σ = P/A
Where,
σ = Stress
P = Pull
A = Cross-sectional area
σ = 150/2.5
σ = 60 N/mm^2
3. Calculate the strain in the tape using the formula:
ε = σ/E
Where,
ε = Strain
σ = Stress
E = Modulus of elasticity
ε = 60/2.1 x 10^5
ε = 2.857 x 10^-4
4. Calculate the change in length due to strain using the formula:
ΔL = Lε
Where,
ΔL = Change in length
L = Original length
ε = Strain
ΔL = 1500 x 2.857 x 10^-4
ΔL = 0.42855m
5. Calculate the correct length of the tape by subtracting the change in length due to strain from the length measured at 40℃ and 150N pull:
Correct length = 30.01575 - 0.42855
Correct length = 29.5872m
Therefore, the correct length of the tape is 1499.60m, which is option (b).
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A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer?
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A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer?.
A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice A line was measured with a steeltape which was exactly 30m at 200C at a pull of 100N. The measuredlength was 1500m. If thetemperature during measurement was 400C and the pull applied was150N, determine the correct lengthof line. Coefficient of thermalexpansion of tape is 3.5 x 10-6per0C, cross-sectional area of tapeis 2.5mm2, Modulus of elasticity =2.1 x105 N/mm2.a)1499.75mb)1499.60mc)1500.25md)1500.40mCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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