Mechanical Engineering Exam > Mechanical Engineering Questions > The maximum and minimum magnitude of resultan...
Start Learning for Free
The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?
- a)500 N, 500 N
- b)450 N, 550 N
- c)300 N, 700 N
- d)250 N, 750 N
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The maximum and minimum magnitude of resultant forces is 1000 N and 50...
Let us suppose, F1 and F2 are two forces acting at a given point and a is the angle between them.
Resultant of these two forces will be,
R =√( F1^2+ F2^2 + 2 F1 F2 cos a)
It will be maximum or minimum, when
dR/da = 0
Now, dR/da = - (F1 F2 sin a)/R
It will be zero, when a = 0�, 180�.
Again, d^2R/da^2 = -(F1 F2 cos a)/R - (F1 F2 sin a)^2 / R^3.
This second order derivative is less than zero, when a = 0�(i.e. when they are parallel), so the maximum resultant force will be
Rmax = F1 + F2
= 1000 N,
whereas the derivative is greater than zero when a = 180� (i.e. when they are in opposite direction), so the resultant force will be minimum
Rmin = F1 - F2
= 500 N.
Solving this two, we get
F1 = 750 N and F2= 250 N.
Most Upvoted Answer
The maximum and minimum magnitude of resultant forces is 1000 N and 50...
Given:
- Maximum magnitude of resultant forces = 1000 N
- Minimum magnitude of resultant forces = 500 N
To determine the values of the two forces acting on the point, we can use the concept of vector addition. The resultant force is the vector sum of the two forces.
Let's assume the two forces as F1 and F2, and the resultant force as R.
To find the maximum magnitude of the resultant force, we need to consider the forces in the same direction. In this case, both forces should act in the same direction to give the maximum magnitude.
When both forces act in the same direction, the maximum magnitude of the resultant force is the sum of the magnitudes of the two forces.
Therefore, F1 + F2 = 1000 N
To find the minimum magnitude of the resultant force, we need to consider the forces in opposite directions. In this case, both forces should act in opposite directions to give the minimum magnitude.
When both forces act in opposite directions, the minimum magnitude of the resultant force is the difference between the magnitudes of the two forces.
Therefore, F1 - F2 = 500 N
We have two equations:
1) F1 + F2 = 1000 N
2) F1 - F2 = 500 N
We can solve these equations simultaneously to determine the values of F1 and F2.
Adding both equations, we get:
2F1 = 1500 N
Dividing by 2, we find:
F1 = 750 N
Substituting the value of F1 in equation 1, we can solve for F2:
750 N + F2 = 1000 N
F2 = 1000 N - 750 N
F2 = 250 N
Therefore, the values of the two forces acting on the point are:
F1 = 750 N
F2 = 250 N
The correct answer is option 'D' (250 N, 750 N).
- Maximum magnitude of resultant forces = 1000 N
- Minimum magnitude of resultant forces = 500 N
Determination of the Forces
To determine the values of the two forces acting on the point, we can use the concept of vector addition. The resultant force is the vector sum of the two forces.
Let's assume the two forces as F1 and F2, and the resultant force as R.
Determining the Maximum Magnitude of Resultant Force
To find the maximum magnitude of the resultant force, we need to consider the forces in the same direction. In this case, both forces should act in the same direction to give the maximum magnitude.
When both forces act in the same direction, the maximum magnitude of the resultant force is the sum of the magnitudes of the two forces.
Therefore, F1 + F2 = 1000 N
Determining the Minimum Magnitude of Resultant Force
To find the minimum magnitude of the resultant force, we need to consider the forces in opposite directions. In this case, both forces should act in opposite directions to give the minimum magnitude.
When both forces act in opposite directions, the minimum magnitude of the resultant force is the difference between the magnitudes of the two forces.
Therefore, F1 - F2 = 500 N
Solving the Equations
We have two equations:
1) F1 + F2 = 1000 N
2) F1 - F2 = 500 N
We can solve these equations simultaneously to determine the values of F1 and F2.
Adding both equations, we get:
2F1 = 1500 N
Dividing by 2, we find:
F1 = 750 N
Substituting the value of F1 in equation 1, we can solve for F2:
750 N + F2 = 1000 N
F2 = 1000 N - 750 N
F2 = 250 N
Therefore, the values of the two forces acting on the point are:
F1 = 750 N
F2 = 250 N
The correct answer is option 'D' (250 N, 750 N).
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
The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer?
Question Description
The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. 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 The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. 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 The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer?.
The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. 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 The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. 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 The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. 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 The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The maximum and minimum magnitude of resultant forces is 1000 N and 500 N at point. What are the values of two forces acting on it?a)500 N, 500 Nb)450 N, 550 Nc)300 N, 700 Nd)250 N, 750 NCorrect answer is option 'D'. 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