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The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x?
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The sum of the magnitudes of two forces acting at a point is 16 N the ...
Given information:
- Sum of the magnitudes of two forces = 16 N
- Resultant of these forces is perpendicular to the smaller force
- Magnitude of the resultant force = 8 N
- Magnitude of the smaller force = x
To find:
The value of x.
Solution:
Let's assume that the magnitudes of the two forces are F1 and F2, where F1 is the smaller force.
Step 1: Express the given information mathematically:
- F1 + F2 = 16 N (Sum of the magnitudes of the two forces)
- F1^2 + F2^2 = 8^2 (Magnitude of the resultant force)
Step 2: Express one variable in terms of the other:
From the first equation, we can express F2 in terms of F1:
F2 = 16 N - F1
Step 3: Substitute the value of F2 in the second equation:
(F1)^2 + (16 N - F1)^2 = 8^2
Step 4: Simplify the equation:
Expanding and simplifying the equation:
F1^2 + (256 N^2 - 32 N F1 + F1^2) = 64
2F1^2 - 32 N F1 + 256 N^2 - 64 = 0
Step 5: Solve the quadratic equation:
Using the quadratic formula:
F1 = [32 N ± √((32 N)^2 - 4(2)(256 N^2 - 64))] / (2(2))
F1 = [32 N ± √(1024 N^2 - 2048 N^2 + 512)] / 4
F1 = [32 N ± √(-1024 N^2 + 512)] / 4
Since we are dealing with magnitudes, the value inside the square root cannot be negative. Therefore, we can disregard the negative sign:
F1 = [32 N + √(-1024 N^2 + 512)] / 4
Step 6: Simplify the expression:
F1 = [8 N + √(-256 N^2 + 128)] / 1
F1 = 8 N + √(-256 N^2 + 128)
Step 7: Substitute the given information to find the value of x:
Since F1 is the magnitude of the smaller force, we can equate F1 to x:
x = 8 N + √(-256 N^2 + 128)
Conclusion:
The value of x is 8 N + √(-256 N^2 + 128).
- Sum of the magnitudes of two forces = 16 N
- Resultant of these forces is perpendicular to the smaller force
- Magnitude of the resultant force = 8 N
- Magnitude of the smaller force = x
To find:
The value of x.
Solution:
Let's assume that the magnitudes of the two forces are F1 and F2, where F1 is the smaller force.
Step 1: Express the given information mathematically:
- F1 + F2 = 16 N (Sum of the magnitudes of the two forces)
- F1^2 + F2^2 = 8^2 (Magnitude of the resultant force)
Step 2: Express one variable in terms of the other:
From the first equation, we can express F2 in terms of F1:
F2 = 16 N - F1
Step 3: Substitute the value of F2 in the second equation:
(F1)^2 + (16 N - F1)^2 = 8^2
Step 4: Simplify the equation:
Expanding and simplifying the equation:
F1^2 + (256 N^2 - 32 N F1 + F1^2) = 64
2F1^2 - 32 N F1 + 256 N^2 - 64 = 0
Step 5: Solve the quadratic equation:
Using the quadratic formula:
F1 = [32 N ± √((32 N)^2 - 4(2)(256 N^2 - 64))] / (2(2))
F1 = [32 N ± √(1024 N^2 - 2048 N^2 + 512)] / 4
F1 = [32 N ± √(-1024 N^2 + 512)] / 4
Since we are dealing with magnitudes, the value inside the square root cannot be negative. Therefore, we can disregard the negative sign:
F1 = [32 N + √(-1024 N^2 + 512)] / 4
Step 6: Simplify the expression:
F1 = [8 N + √(-256 N^2 + 128)] / 1
F1 = 8 N + √(-256 N^2 + 128)
Step 7: Substitute the given information to find the value of x:
Since F1 is the magnitude of the smaller force, we can equate F1 to x:
x = 8 N + √(-256 N^2 + 128)
Conclusion:
The value of x is 8 N + √(-256 N^2 + 128).
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The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x?.
The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the magnitudes of two forces acting at a point is 16 N the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N of the smaller force is magnitude x find the value of x?.
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