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If two equal vector forces are mutually perpendicular in the cable subjected to its own weight then the resultant force is acting at which angle as compared to one of the vector?
- a)45 degree
- b)90 degree
- c)180 degree
- d)0 degree
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If two equal vector forces are mutually perpendicular in the cable sub...
The vectors are mutually perpendicular, this means that the angle between the forces is 90 degree. Thus the resultant will form at 45 degrees to any of the vector.
Most Upvoted Answer
If two equal vector forces are mutually perpendicular in the cable sub...
Given:
- Two equal vector forces
- Forces are mutually perpendicular
- Cable is subjected to its own weight
To find:
- The angle at which the resultant force is acting compared to one of the vectors
Explanation:
1. Let's assume the two vector forces are represented by vectors A and B.
2. Since the forces are equal and mutually perpendicular, the magnitude of vector A will be equal to the magnitude of vector B.
3. The resultant force can be calculated by adding the two vector forces together.
4. The resultant force can be represented by the vector sum of A and B, which we'll call vector R.
5. The magnitude of the resultant force can be calculated using the Pythagorean theorem:
- |R| = sqrt(|A|^2 + |B|^2)
(where |A| and |B| represent the magnitudes of vectors A and B)
6. In this case, since the two forces are equal, |A| = |B|, and the equation simplifies to:
- |R| = sqrt(2 * |A|^2)
- |R| = sqrt(2) * |A|
7. The angle at which the resultant force is acting can be determined using trigonometry.
8. Since the forces are mutually perpendicular, the angle between A and R can be found using the inverse tangent function:
- θ = atan(|B| / |A|)
- θ = atan(1) = 45 degrees
9. Therefore, the resultant force is acting at a 45-degree angle compared to one of the vectors.
Conclusion:
The correct answer is option A) 45 degrees. The resultant force is acting at a 45-degree angle compared to one of the vector forces.
- Two equal vector forces
- Forces are mutually perpendicular
- Cable is subjected to its own weight
To find:
- The angle at which the resultant force is acting compared to one of the vectors
Explanation:
1. Let's assume the two vector forces are represented by vectors A and B.
2. Since the forces are equal and mutually perpendicular, the magnitude of vector A will be equal to the magnitude of vector B.
3. The resultant force can be calculated by adding the two vector forces together.
4. The resultant force can be represented by the vector sum of A and B, which we'll call vector R.
5. The magnitude of the resultant force can be calculated using the Pythagorean theorem:
- |R| = sqrt(|A|^2 + |B|^2)
(where |A| and |B| represent the magnitudes of vectors A and B)
6. In this case, since the two forces are equal, |A| = |B|, and the equation simplifies to:
- |R| = sqrt(2 * |A|^2)
- |R| = sqrt(2) * |A|
7. The angle at which the resultant force is acting can be determined using trigonometry.
8. Since the forces are mutually perpendicular, the angle between A and R can be found using the inverse tangent function:
- θ = atan(|B| / |A|)
- θ = atan(1) = 45 degrees
9. Therefore, the resultant force is acting at a 45-degree angle compared to one of the vectors.
Conclusion:
The correct answer is option A) 45 degrees. The resultant force is acting at a 45-degree angle compared to one of the vector forces.
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If two equal vector forces are mutually perpendicular in the cable subjected to its own weight then the resultant force is acting at which angle as compared to one of the vector?a)45 degreeb)90 degreec)180 degreed)0 degreeCorrect answer is option 'A'. Can you explain this answer?
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