Mechanical Engineering Exam > Mechanical Engineering Questions > In slider -crank mechanism, the crank is rota...
Start Learning for Free
In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.
- a)12 cm
- b)25 cm
- c)20.5 cm
- d)18.4 cm
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In slider -crank mechanism, the crank is rotating with an angular velo...
Most Upvoted Answer
In slider -crank mechanism, the crank is rotating with an angular velo...
Degrees with the horizontal, the slider has a velocity of 5 m/s in the upward direction. The length of the crank is 0.5 m and the length of the connecting rod is 1.5 m. Find:
a) The angular velocity of the connecting rod
b) The velocity and acceleration of the slider when the crank makes an angle of 60 degrees with the horizontal.
c) The position of the slider when the crank makes an angle of 60 degrees with the horizontal.
Solution:
a) The angular velocity of the connecting rod can be found using the velocity diagram of the slider-crank mechanism. The velocity diagram is shown below:
From the velocity diagram, we can write:
v_a = v_b + v_c
where v_a is the velocity of the slider, v_b is the velocity of the crank pin and v_c is the velocity of the connecting rod.
We know that v_a = 5 m/s and v_b = rω, where r is the length of the crank and ω is the angular velocity of the crank. Substituting the values, we get:
5 = 0.5 × 10 + v_c
v_c = 0 m/s
Now, we can find the angular velocity of the connecting rod using the following equation:
ω_c = ω - arccos((r^2 + L^2 - d^2) / 2rL)
where L is the length of the connecting rod and d is the distance between the crank pin and slider. Substituting the values, we get:
ω_c = 10 - arccos((0.5^2 + 1.5^2 - 2(0.5)(1.5)cos60) / (2 × 0.5 × 1.5))
ω_c = 3.24 rad/s
Therefore, the angular velocity of the connecting rod is 3.24 rad/s.
b) To find the velocity and acceleration of the slider, we can use the velocity and acceleration diagrams. The velocity diagram is already shown above. The acceleration diagram is shown below:
From the acceleration diagram, we can write:
a_a = a_b + a_c + a_t
where a_a is the acceleration of the slider, a_b is the acceleration of the crank pin, a_c is the acceleration of the connecting rod and a_t is the tangential acceleration of the slider.
We know that a_b = rα, where α is the angular acceleration of the crank. Substituting the values, we get:
a_b = 0.5 × α
Now, we can find the angular acceleration of the crank using the following equation:
α = -ω^2 / r
Substituting the values, we get:
α = -400 rad/s^2
Therefore, a_b = -200 m/s^2
We also know that a_c = L(α_c - α_b), where α_c is the angular acceleration of the connecting rod. From the velocity diagram, we know that v_c = Lω_c. Differentiating with respect to time, we get:
a_c = Lα_c
Substituting the values, we get:
a_c = 1.5(α_c - α_b)
Now, we can write:
a_a = a_b + a_c + a_t
Substituting the values, we get:
a) The angular velocity of the connecting rod
b) The velocity and acceleration of the slider when the crank makes an angle of 60 degrees with the horizontal.
c) The position of the slider when the crank makes an angle of 60 degrees with the horizontal.
Solution:
a) The angular velocity of the connecting rod can be found using the velocity diagram of the slider-crank mechanism. The velocity diagram is shown below:
From the velocity diagram, we can write:
v_a = v_b + v_c
where v_a is the velocity of the slider, v_b is the velocity of the crank pin and v_c is the velocity of the connecting rod.
We know that v_a = 5 m/s and v_b = rω, where r is the length of the crank and ω is the angular velocity of the crank. Substituting the values, we get:
5 = 0.5 × 10 + v_c
v_c = 0 m/s
Now, we can find the angular velocity of the connecting rod using the following equation:
ω_c = ω - arccos((r^2 + L^2 - d^2) / 2rL)
where L is the length of the connecting rod and d is the distance between the crank pin and slider. Substituting the values, we get:
ω_c = 10 - arccos((0.5^2 + 1.5^2 - 2(0.5)(1.5)cos60) / (2 × 0.5 × 1.5))
ω_c = 3.24 rad/s
Therefore, the angular velocity of the connecting rod is 3.24 rad/s.
b) To find the velocity and acceleration of the slider, we can use the velocity and acceleration diagrams. The velocity diagram is already shown above. The acceleration diagram is shown below:
From the acceleration diagram, we can write:
a_a = a_b + a_c + a_t
where a_a is the acceleration of the slider, a_b is the acceleration of the crank pin, a_c is the acceleration of the connecting rod and a_t is the tangential acceleration of the slider.
We know that a_b = rα, where α is the angular acceleration of the crank. Substituting the values, we get:
a_b = 0.5 × α
Now, we can find the angular acceleration of the crank using the following equation:
α = -ω^2 / r
Substituting the values, we get:
α = -400 rad/s^2
Therefore, a_b = -200 m/s^2
We also know that a_c = L(α_c - α_b), where α_c is the angular acceleration of the connecting rod. From the velocity diagram, we know that v_c = Lω_c. Differentiating with respect to time, we get:
a_c = Lα_c
Substituting the values, we get:
a_c = 1.5(α_c - α_b)
Now, we can write:
a_a = a_b + a_c + a_t
Substituting the values, we get:
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
In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer?
Question Description
In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect 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 In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect 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 In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer?.
In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect 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 In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect 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 In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer?.
Solutions for In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect 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 In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In slider -crank mechanism, the crank is rotating with an angular velocity of 10 rad /s in counter clock wise direction. At the instant when the crank makes an angle of 60° with the direction of the piston movement, the velocity of the piston is 2 m/s. What will be the radius of the crank if the length of the connecting rod is four times of the radius of the crank.a)12 cmb)25 cmc)20.5 cmd)18.4 cmCorrect 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