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30 meter steel tape, standardized at 20 ºC using a tensile
force of 70 N. Measured against a standard tape, the tested
tape had a length of 29.998m.The 30 m tape has a weight of
0.196 N/m and a cross sectional area of 1.69 mm2.A field
measurement (Lf) of 29.663 was found at a temperature of
30 ºC using a tensile force of 50 N. Find the actual or true
le?
force of 70 N. Measured against a standard tape, the tested
tape had a length of 29.998m.The 30 m tape has a weight of
0.196 N/m and a cross sectional area of 1.69 mm2.A field
measurement (Lf) of 29.663 was found at a temperature of
30 ºC using a tensile force of 50 N. Find the actual or true
le?
Most Upvoted Answer
30 meter steel tape, standardized at 20 ºC using a tensile force of 70...
Introduction
To find the actual or true length of the 30-meter steel tape, we must consider the effects of temperature and tensile force on the tape’s length during the field measurement.
Step 1: Correction for Temperature
- The tape was standardized at 20 ºC but was used at 30 ºC.
- The coefficient of linear expansion for steel is approximately 12 × 10⁻⁶ °C⁻¹.
- The temperature change (ΔT) = 30 ºC - 20 ºC = 10 ºC.
Length Correction for Temperature
- The correction for temperature (ΔL) can be calculated as:
ΔL = Lf × α × ΔT
Where:
- Lf = 29.663 m (field length)
- α = 12 × 10⁻⁶ °C⁻¹
- ΔT = 10 ºC
ΔL = 29.663 × 12 × 10⁻⁶ × 10
ΔL ≈ 0.00356 m
- Thus, the corrected length (Lct) at 20 ºC:
Lct = Lf + ΔL = 29.663 + 0.00356
Lct ≈ 29.66656 m
Step 2: Correction for Tensile Force
- The tensile force used in the field (50 N) differs from the standardized force (70 N).
- The weight of the tape per meter is 0.196 N/m; thus, the total weight for 30 m is 5.88 N.
- The effective force (F) acting on the tape is:
F = 70 N - 5.88 N = 64.12 N (standardized condition)
- The ratio of tensile forces (K = Ff/Fs) can be calculated:
K = 50 N / 64.12 N ≈ 0.780
- The correction due to tensile force can be approximated as:
ΔL_tensile = (Lct) × (1 - K)
ΔL_tensile = 29.66656 × (1 - 0.780) ≈ 6.477 m
True Length Calculation
- Finally, we find the true length:
True Length (Le) = Lct + ΔL_tensile
Le ≈ 29.66656 + 6.477 ≈ 29.67356 m
Hence, the actual or true length of the tape is approximately 29.674 m.
To find the actual or true length of the 30-meter steel tape, we must consider the effects of temperature and tensile force on the tape’s length during the field measurement.
Step 1: Correction for Temperature
- The tape was standardized at 20 ºC but was used at 30 ºC.
- The coefficient of linear expansion for steel is approximately 12 × 10⁻⁶ °C⁻¹.
- The temperature change (ΔT) = 30 ºC - 20 ºC = 10 ºC.
Length Correction for Temperature
- The correction for temperature (ΔL) can be calculated as:
ΔL = Lf × α × ΔT
Where:
- Lf = 29.663 m (field length)
- α = 12 × 10⁻⁶ °C⁻¹
- ΔT = 10 ºC
ΔL = 29.663 × 12 × 10⁻⁶ × 10
ΔL ≈ 0.00356 m
- Thus, the corrected length (Lct) at 20 ºC:
Lct = Lf + ΔL = 29.663 + 0.00356
Lct ≈ 29.66656 m
Step 2: Correction for Tensile Force
- The tensile force used in the field (50 N) differs from the standardized force (70 N).
- The weight of the tape per meter is 0.196 N/m; thus, the total weight for 30 m is 5.88 N.
- The effective force (F) acting on the tape is:
F = 70 N - 5.88 N = 64.12 N (standardized condition)
- The ratio of tensile forces (K = Ff/Fs) can be calculated:
K = 50 N / 64.12 N ≈ 0.780
- The correction due to tensile force can be approximated as:
ΔL_tensile = (Lct) × (1 - K)
ΔL_tensile = 29.66656 × (1 - 0.780) ≈ 6.477 m
True Length Calculation
- Finally, we find the true length:
True Length (Le) = Lct + ΔL_tensile
Le ≈ 29.66656 + 6.477 ≈ 29.67356 m
Hence, the actual or true length of the tape is approximately 29.674 m.
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30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le?
Question Description
30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le?.
30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le?.
Solutions for 30 meter steel tape, standardized at 20 ºC using a tensile force of 70 N. Measured against a standard tape, the tested tape had a length of 29.998m.The 30 m tape has a weight of 0.196 N/m and a cross sectional area of 1.69 mm2.A field measurement (Lf) of 29.663 was found at a temperature of 30 ºC using a tensile force of 50 N. Find the actual or true le? in English & in Hindi are available as part of our courses for UPSC.
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