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The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ?
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The sum of the magnitudes of two forces acting at point is 18 and the ...
Given Information
- The sum of the magnitudes of two forces (F1 + F2) = 18
- The magnitude of the resultant force (R) = 12
- The angle between the resultant and the smaller force (F1) = 90°
Understanding the Forces
When two forces act at a point, their resultant can be calculated using the Pythagorean theorem if they are at right angles. In this case:
- F1^2 + F2^2 = R^2
Since R = 12, we can substitute to find:
- F1^2 + F2^2 = 12^2
- F1^2 + F2^2 = 144
Setting Up the Equations
Given that F1 + F2 = 18, we can express F2 in terms of F1:
- F2 = 18 - F1
Substituting this into the equation for the resultant gives:
- F1^2 + (18 - F1)^2 = 144
Expanding the Equation
Now, we expand (18 - F1)^2:
- F1^2 + (324 - 36F1 + F1^2) = 144
- 2F1^2 - 36F1 + 324 = 144
Simplifying yields:
- 2F1^2 - 36F1 + 180 = 0
Solving the Quadratic Equation
Dividing through by 2:
- F1^2 - 18F1 + 90 = 0
Using the quadratic formula (F1 = [18 ± sqrt(18^2 - 4*90)]/2):
- F1 = 15 or 6
Thus,
- If F1 = 15, then F2 = 3.
- If F1 = 6, then F2 = 12.
Final Magnitudes
- The magnitudes of the forces are:
- F1 = 6, F2 = 12 (Smaller force)
- F1 = 15, F2 = 3 (Larger force)
Therefore, the solution provides the magnitudes of the two forces acting at the point, with one force being smaller than the other.
- The sum of the magnitudes of two forces (F1 + F2) = 18
- The magnitude of the resultant force (R) = 12
- The angle between the resultant and the smaller force (F1) = 90°
Understanding the Forces
When two forces act at a point, their resultant can be calculated using the Pythagorean theorem if they are at right angles. In this case:
- F1^2 + F2^2 = R^2
Since R = 12, we can substitute to find:
- F1^2 + F2^2 = 12^2
- F1^2 + F2^2 = 144
Setting Up the Equations
Given that F1 + F2 = 18, we can express F2 in terms of F1:
- F2 = 18 - F1
Substituting this into the equation for the resultant gives:
- F1^2 + (18 - F1)^2 = 144
Expanding the Equation
Now, we expand (18 - F1)^2:
- F1^2 + (324 - 36F1 + F1^2) = 144
- 2F1^2 - 36F1 + 324 = 144
Simplifying yields:
- 2F1^2 - 36F1 + 180 = 0
Solving the Quadratic Equation
Dividing through by 2:
- F1^2 - 18F1 + 90 = 0
Using the quadratic formula (F1 = [18 ± sqrt(18^2 - 4*90)]/2):
- F1 = 15 or 6
Thus,
- If F1 = 15, then F2 = 3.
- If F1 = 6, then F2 = 12.
Final Magnitudes
- The magnitudes of the forces are:
- F1 = 6, F2 = 12 (Smaller force)
- F1 = 15, F2 = 3 (Larger force)
Therefore, the solution provides the magnitudes of the two forces acting at the point, with one force being smaller than the other.
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The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ?
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The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ?.
The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. if the resultant is at 90° with force of smaller magnitude , what are the magnitudes of forces ?.
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