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A circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this?
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A circular surface area 200 cm is inclined to the x and y axes such th...
Solution:
Given data:
Surface area (A) = 200 cm²
Unit vector normal to the surface (n) = 0.41i+0.3j
Force acting on x-axis (F) = 2000 kg
Normal stress (σ) can be calculated by using the formula:
σ = F/Acosθ
Where, θ is the angle between the force vector and the normal vector.
To find θ, we can use the dot product as follows:
cosθ = n•i / |n| |i|
cosθ = 0.41 / 1
θ = cos⁻¹(0.41)
θ = 65.4°
Substituting the values in the formula, we get:
σ = 2000 / 200cos65.4°
σ = 10 kg/cm²
Therefore, the normal stress on the surface is 10 kg/cm².
Explanation:
The given problem is related to finding the normal stress on a circular surface area inclined to the x and y axes. To solve this problem, we need to use the formula for normal stress, which is given as force divided by area multiplied by the cosine of the angle between the force vector and the normal vector.
In this problem, we are given the surface area, the unit vector normal to the surface, and the force acting on the x-axis. We can find the angle between the force vector and the normal vector by using the dot product of the two vectors.
Once we have the angle, we can substitute the values in the formula for normal stress and calculate the answer.
Therefore, the normal stress on the surface is 10 kg/cm².
Given data:
Surface area (A) = 200 cm²
Unit vector normal to the surface (n) = 0.41i+0.3j
Force acting on x-axis (F) = 2000 kg
Normal stress (σ) can be calculated by using the formula:
σ = F/Acosθ
Where, θ is the angle between the force vector and the normal vector.
To find θ, we can use the dot product as follows:
cosθ = n•i / |n| |i|
cosθ = 0.41 / 1
θ = cos⁻¹(0.41)
θ = 65.4°
Substituting the values in the formula, we get:
σ = 2000 / 200cos65.4°
σ = 10 kg/cm²
Therefore, the normal stress on the surface is 10 kg/cm².
Explanation:
The given problem is related to finding the normal stress on a circular surface area inclined to the x and y axes. To solve this problem, we need to use the formula for normal stress, which is given as force divided by area multiplied by the cosine of the angle between the force vector and the normal vector.
In this problem, we are given the surface area, the unit vector normal to the surface, and the force acting on the x-axis. We can find the angle between the force vector and the normal vector by using the dot product of the two vectors.
Once we have the angle, we can substitute the values in the formula for normal stress and calculate the answer.
Therefore, the normal stress on the surface is 10 kg/cm².
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A circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this?
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A circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this? for Civil Engineering (CE) 2025 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 circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this?.
A circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this? for Civil Engineering (CE) 2025 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 circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular surface area 200 cm is inclined to the x and y axes such that the unit vector normal to the surface is given by n=0.41 0.3j. If a force of 2000 kg acts on the x-axis, then the normal stress on the surface will be a) 10 kg/cm² L b) 5 kg/cm c) 4 kg/cm² d) 3 kg/cm² What will be the answer and can you explain this?.
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