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Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm,
angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead
centre is 120°. Find the angular velocity of the crank and connecting rod.?
angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead
centre is 120°. Find the angular velocity of the crank and connecting rod.?
Most Upvoted Answer
Ln a slider crank mechanism, crank length is 200mm and connecting rod ...
Given Data
- Crank Length (r) = 200 mm = 0.2 m
- Connecting Rod Length (L) = 600 mm = 0.6 m
- Angular Velocity of Crank (ω) = 50 rad/sec (clockwise)
- Crank Angle (θ) = 120°
Angular Position of Connecting Rod
1. **Position of Crank**: At θ = 120°, the crank is positioned in the mechanism.
2. **Angle of the Connecting Rod (φ)**: To find φ, we use the law of cosines in triangle formed by the crank, connecting rod, and the line connecting the two joints:
Cosine Rule:
φ = arccos((r^2 + L^2 - x^2) / (2*r*L))
where x is the horizontal distance from the crank's pivot to the connecting rod's pivot.
Angular Velocities
1. **Relative Angular Velocity (α)**: The angular velocity of the connecting rod can be derived from the angular velocity of the crank:
α = (r/L) * ω * sin(θ)
- Here, α is the angular velocity of the connecting rod, which we need to calculate.
2. **Substituting Values**:
- Convert θ into radians: θ = 120° = 2.094 rad.
- Using sin(θ): sin(2.094) = 0.866.
- Plug in the values:
α = (0.2 / 0.6) * 50 * 0.866
α = (1/3) * 50 * 0.866
α ≈ 14.43 rad/sec
Conclusion
- The angular velocity of the connecting rod is approximately **14.43 rad/sec**. This shows how the crank's motion is transferred to the connecting rod in the slider-crank mechanism.
- Crank Length (r) = 200 mm = 0.2 m
- Connecting Rod Length (L) = 600 mm = 0.6 m
- Angular Velocity of Crank (ω) = 50 rad/sec (clockwise)
- Crank Angle (θ) = 120°
Angular Position of Connecting Rod
1. **Position of Crank**: At θ = 120°, the crank is positioned in the mechanism.
2. **Angle of the Connecting Rod (φ)**: To find φ, we use the law of cosines in triangle formed by the crank, connecting rod, and the line connecting the two joints:
Cosine Rule:
φ = arccos((r^2 + L^2 - x^2) / (2*r*L))
where x is the horizontal distance from the crank's pivot to the connecting rod's pivot.
Angular Velocities
1. **Relative Angular Velocity (α)**: The angular velocity of the connecting rod can be derived from the angular velocity of the crank:
α = (r/L) * ω * sin(θ)
- Here, α is the angular velocity of the connecting rod, which we need to calculate.
2. **Substituting Values**:
- Convert θ into radians: θ = 120° = 2.094 rad.
- Using sin(θ): sin(2.094) = 0.866.
- Plug in the values:
α = (0.2 / 0.6) * 50 * 0.866
α = (1/3) * 50 * 0.866
α ≈ 14.43 rad/sec
Conclusion
- The angular velocity of the connecting rod is approximately **14.43 rad/sec**. This shows how the crank's motion is transferred to the connecting rod in the slider-crank mechanism.
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Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.?
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Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.?.
Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ln a slider crank mechanism, crank length is 200mm and connecting rod length is 600mm, angular velocity of crank is 50 rad/sec clockwise. crank angle when turned from inner dead centre is 120°. Find the angular velocity of the crank and connecting rod.?.
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