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For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.
Correct answer is between '0.26,0.27'. Can you explain this answer?
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For an inline slider-crank mechanism, the length of the crank and conn...
Given Data:
- Length of the crank (r) = 3 m
- Length of the connecting rod (l) = 4 m
- Velocity of the slider (v) = 1 m/s
Solution:
To find the magnitude of the angular velocity of the crank, we can use the velocity analysis of the slider-crank mechanism.
1. Velocity Analysis:
At the instant when the connecting rod is perpendicular to the crank, the configuration forms a right triangle with sides r, l, and the crank angle (θ). Using the law of cosines, we can relate the angles and side lengths in the mechanism.
2. Law of Cosines:
r^2 = l^2 + v^2 - 2lv*cos(θ)
3. Differentiate with respect to time:
0 = 2lv*sin(θ)*dθ/dt
0 = l*sin(θ)*ω
4. Solve for angular velocity (ω):
sin(θ) = 1 (when the connecting rod is perpendicular to the crank)
ω = v/l
ω = 1/4
ω ≈ 0.25 rad/s
Therefore, the magnitude of the angular velocity of the crank is approximately 0.25 rad/s.
- Length of the crank (r) = 3 m
- Length of the connecting rod (l) = 4 m
- Velocity of the slider (v) = 1 m/s
Solution:
To find the magnitude of the angular velocity of the crank, we can use the velocity analysis of the slider-crank mechanism.
1. Velocity Analysis:
At the instant when the connecting rod is perpendicular to the crank, the configuration forms a right triangle with sides r, l, and the crank angle (θ). Using the law of cosines, we can relate the angles and side lengths in the mechanism.
2. Law of Cosines:
r^2 = l^2 + v^2 - 2lv*cos(θ)
3. Differentiate with respect to time:
0 = 2lv*sin(θ)*dθ/dt
0 = l*sin(θ)*ω
4. Solve for angular velocity (ω):
sin(θ) = 1 (when the connecting rod is perpendicular to the crank)
ω = v/l
ω = 1/4
ω ≈ 0.25 rad/s
Therefore, the magnitude of the angular velocity of the crank is approximately 0.25 rad/s.
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For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. Can you explain this answer?
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For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. 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 For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. 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 For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. Can you explain this answer?.
For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. 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 For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. 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 For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. Can you explain this answer?.
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For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. Can you explain this answer?, a detailed solution for For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. Can you explain this answer? has been provided alongside types of For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.Correct answer is between '0.26,0.27'. Can you explain this answer? theory, EduRev gives you an
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