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Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is?
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Two equal forces are acting at a point with an angle 60 degree between...
Problem: Two equal forces are acting at a point with an angle 60 degree between them. If the resultant force is equal to 40 root 3N the magnitude of each force is?
Solution:
To solve this problem, we will use the law of cosines, which relates the cosine of an angle to the sides of a triangle. In this case, we have a triangle with two sides of equal length (the two forces) and an angle of 60 degrees between them. Let's call the magnitude of each force "F".
Step 1: Apply the Law of Cosines to find the magnitude of the third side of the triangle, which is the resultant force:
c^2 = a^2 + b^2 - 2ab cos(C)
c^2 = F^2 + F^2 - 2F*F*cos(60°)
c^2 = 2F^2 - 2F^2*cos(60°)
c^2 = 2F^2 - F^2
c^2 = F^2
c = F
So, the magnitude of the resultant force is equal to the magnitude of each force, which is F.
Step 2: Substitute the given value of the resultant force to find F:
F = 40 root 3N / sqrt(2)
F = 20 root 6N
Therefore, the magnitude of each force is 20 root 6N.
Conclusion: The magnitude of each force is 20 root 6N.
Solution:
To solve this problem, we will use the law of cosines, which relates the cosine of an angle to the sides of a triangle. In this case, we have a triangle with two sides of equal length (the two forces) and an angle of 60 degrees between them. Let's call the magnitude of each force "F".
Step 1: Apply the Law of Cosines to find the magnitude of the third side of the triangle, which is the resultant force:
c^2 = a^2 + b^2 - 2ab cos(C)
c^2 = F^2 + F^2 - 2F*F*cos(60°)
c^2 = 2F^2 - 2F^2*cos(60°)
c^2 = 2F^2 - F^2
c^2 = F^2
c = F
So, the magnitude of the resultant force is equal to the magnitude of each force, which is F.
Step 2: Substitute the given value of the resultant force to find F:
F = 40 root 3N / sqrt(2)
F = 20 root 6N
Therefore, the magnitude of each force is 20 root 6N.
Conclusion: The magnitude of each force is 20 root 6N.
Community Answer
Two equal forces are acting at a point with an angle 60 degree between...
Answer is A√3
where A - force
where A - force
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Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is?
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Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is? 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 Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is?.
Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is? 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 Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two equal forces are acting at a point with an angle 60 degree between them . If the resultant force is equal to 40 root 3N the magnitude of each force is?.
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