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In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.
(Important - Enter only the numerical value in the answer)
Correct answer is '40.2'. Can you explain this answer?
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To solve this problem, we can use the concept of trigonometry in a slider crank mechanism.
Let's assume that the length of the crank is "c" and the length of the connecting rod is "r". Given that the length of the connecting rod is very large compared to the crank length, we can assume that "r >> c".
Now, let's consider the triangle formed by the crank, connecting rod, and the displacement of the piston. By using the Law of Cosines, we can relate the sides of the triangle:
r^2 = c^2 + x^2 - 2cx*cos(30°)
Since we are given that the crank has turned through an angle of 30°, we can substitute cos(30°) with its value (√3/2):
r^2 = c^2 + x^2 - 2cx*(√3/2)
Simplifying this equation, we get:
r^2 - c^2 = x^2 - cx√3
Since we assumed that "r >> c", we can neglect the term c^2 on the left side of the equation. This gives us:
r^2 = x^2 - cx√3
Now, we can solve this equation for x, the displacement of the piston:
x^2 - cx√3 = r^2
x^2 = r^2 + cx√3
x = √(r^2 + cx√3)
So, the displacement of the piston at the moment when the crank has turned through an angle of 30° is given by √(r^2 + cx√3).
Let's assume that the length of the crank is "c" and the length of the connecting rod is "r". Given that the length of the connecting rod is very large compared to the crank length, we can assume that "r >> c".
Now, let's consider the triangle formed by the crank, connecting rod, and the displacement of the piston. By using the Law of Cosines, we can relate the sides of the triangle:
r^2 = c^2 + x^2 - 2cx*cos(30°)
Since we are given that the crank has turned through an angle of 30°, we can substitute cos(30°) with its value (√3/2):
r^2 = c^2 + x^2 - 2cx*(√3/2)
Simplifying this equation, we get:
r^2 - c^2 = x^2 - cx√3
Since we assumed that "r >> c", we can neglect the term c^2 on the left side of the equation. This gives us:
r^2 = x^2 - cx√3
Now, we can solve this equation for x, the displacement of the piston:
x^2 - cx√3 = r^2
x^2 = r^2 + cx√3
x = √(r^2 + cx√3)
So, the displacement of the piston at the moment when the crank has turned through an angle of 30° is given by √(r^2 + cx√3).
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In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. Can you explain this answer?
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In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. 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 In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. 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 In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. Can you explain this answer?.
In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. 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 In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. 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 In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. Can you explain this answer?.
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In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. Can you explain this answer?, a detailed solution for In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. Can you explain this answer? has been provided alongside types of In a certain slider crank mechanism length of connecting rod is very large as compared to crank length. If x is the displacement of piston at the moment when the crank has turned through an angle of 30° from Inner dead centre, for crank length of 300 mm, value of x = –––– mm.(Important - Enter only the numerical value in the answer)Correct answer is '40.2'. Can you explain this answer? theory, EduRev gives you an
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