Mechanical Engineering Exam > Mechanical Engineering Questions > A body of weight W is required to move up on ...
Start Learning for Free
A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)
- a)P = W tanα
- b)P = W tan(α + φ)
- c)P = W (sinα + μcosα)
- d)P = W (cosα + μsinα)
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A body of weight W is required to move up on rough inclined plane whos...
Answer: c
Explanation: The minimum force required to slide a body of weight W on a rough horizontal plane is W sinϴ. A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by P = W (sinα + μ cosα).
Most Upvoted Answer
A body of weight W is required to move up on rough inclined plane whos...
Given information:
Weight of the body, W
Angle of inclination with the horizontal, α
Coefficient of friction between the plane and the body, μ=tanφ
Effort applied parallel to the plane is given by P.
To determine the relation between P, W, α, and μ, we need to analyze the forces acting on the body.
Analysis:
When the body is placed on the inclined plane, the weight of the body, W, acts vertically downwards. The weight can be resolved into two components, one perpendicular to the plane and the other parallel to the plane.
The component of weight perpendicular to the plane is Wcosα, which is balanced by the normal reaction of the plane.
The component of weight parallel to the plane is Wsinα, which tends to slide the body down the plane. To prevent the body from sliding down, a force of friction acts on the body in the opposite direction to the force of weight.
The force of friction can be expressed as F = μN, where N is the normal reaction of the plane. As the body is in equilibrium, the force parallel to the plane must balance the force of friction.
Therefore, P = F = μN = μ(Wcosα) = Wμcosα
Substituting μ = tanφ, we get P = Wsinαcosφ
As φ = tan⁻¹μ, we can write cosφ = 1/√(1+μ²) and sinφ = μ/√(1+μ²)
Substituting these values, we get P = Wsinαμ/√(1+μ²)
Simplifying further, we get P = Wsinαcosα = W(sinα)(cosα)/1 = W(sinα)(cosα)/(sin²α + cos²α) = W(sinα)(cosα)/sinα = Wcosαμ = W(cosα)(tanφ)
Therefore, the required relation between P, W, α, and μ is given by P = W(sinα)(cosα)/√(1+μ²) or P = W(cosα)(tanφ)
Hence, the correct answer is option 'C': P = W(sinα)(cosα)/√(1+μ²)
Weight of the body, W
Angle of inclination with the horizontal, α
Coefficient of friction between the plane and the body, μ=tanφ
Effort applied parallel to the plane is given by P.
To determine the relation between P, W, α, and μ, we need to analyze the forces acting on the body.
Analysis:
When the body is placed on the inclined plane, the weight of the body, W, acts vertically downwards. The weight can be resolved into two components, one perpendicular to the plane and the other parallel to the plane.
The component of weight perpendicular to the plane is Wcosα, which is balanced by the normal reaction of the plane.
The component of weight parallel to the plane is Wsinα, which tends to slide the body down the plane. To prevent the body from sliding down, a force of friction acts on the body in the opposite direction to the force of weight.
The force of friction can be expressed as F = μN, where N is the normal reaction of the plane. As the body is in equilibrium, the force parallel to the plane must balance the force of friction.
Therefore, P = F = μN = μ(Wcosα) = Wμcosα
Substituting μ = tanφ, we get P = Wsinαcosφ
As φ = tan⁻¹μ, we can write cosφ = 1/√(1+μ²) and sinφ = μ/√(1+μ²)
Substituting these values, we get P = Wsinαμ/√(1+μ²)
Simplifying further, we get P = Wsinαcosα = W(sinα)(cosα)/1 = W(sinα)(cosα)/(sin²α + cos²α) = W(sinα)(cosα)/sinα = Wcosαμ = W(cosα)(tanφ)
Therefore, the required relation between P, W, α, and μ is given by P = W(sinα)(cosα)/√(1+μ²) or P = W(cosα)(tanφ)
Hence, the correct answer is option 'C': P = W(sinα)(cosα)/√(1+μ²)
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer?
Question Description
A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer?.
A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer?.
Solutions for A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)a)P = W tanαb)P = W tan(α + φ)c)P = W (sinα + μcosα)d)P = W (cosα + μsinα)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup