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The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.?
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The resultant of two forces 3p and 2p is R.If the first force is doubl...
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The resultant of two forces 3p and 2p is R.If the first force is doubl...
Given:
- Two forces are 3p and 2p.
- The resultant of these forces is R.
- When the first force is doubled, the resultant is also doubled.
To Find:
- The angle between the two forces.
Explanation:
Let's assume the angle between the two forces is θ.
Step 1: Finding the Magnitude of the Resultant
According to the given information, the resultant of the two forces is R. We can calculate the magnitude of the resultant using the Pythagorean theorem.
The magnitude of the resultant (R) can be found using the equation:
R² = (3p)² + (2p)²
R² = 9p² + 4p²
R² = 13p²
R = √(13p²)
R = √13p
Step 2: Doubling the First Force
According to the given information, when the first force is doubled, the resultant is also doubled. Let's denote the doubled force as 2F.
The magnitude of the new resultant (2R) can be found using the equation:
(2R)² = (2(2p))² + (2p)²
(2R)² = 4(4p²) + 4p²
(2R)² = 16p² + 4p²
(2R)² = 20p²
2R = √(20p²)
2R = 2√5p
Step 3: Equating the Resultants
Since the magnitude of the resultant is doubled when the first force is doubled, we can equate the two resultants.
√13p = 2√5p
Squaring both sides:
13p = 4(5p)
13p = 20p
Subtracting 13p from both sides:
0 = 20p - 13p
0 = 7p
Therefore, p = 0.
Conclusion:
Since p = 0, it means that the forces are collinear and not at an angle. The angle between the two forces is 0 degrees.
- Two forces are 3p and 2p.
- The resultant of these forces is R.
- When the first force is doubled, the resultant is also doubled.
To Find:
- The angle between the two forces.
Explanation:
Let's assume the angle between the two forces is θ.
Step 1: Finding the Magnitude of the Resultant
According to the given information, the resultant of the two forces is R. We can calculate the magnitude of the resultant using the Pythagorean theorem.
The magnitude of the resultant (R) can be found using the equation:
R² = (3p)² + (2p)²
R² = 9p² + 4p²
R² = 13p²
R = √(13p²)
R = √13p
Step 2: Doubling the First Force
According to the given information, when the first force is doubled, the resultant is also doubled. Let's denote the doubled force as 2F.
The magnitude of the new resultant (2R) can be found using the equation:
(2R)² = (2(2p))² + (2p)²
(2R)² = 4(4p²) + 4p²
(2R)² = 16p² + 4p²
(2R)² = 20p²
2R = √(20p²)
2R = 2√5p
Step 3: Equating the Resultants
Since the magnitude of the resultant is doubled when the first force is doubled, we can equate the two resultants.
√13p = 2√5p
Squaring both sides:
13p = 4(5p)
13p = 20p
Subtracting 13p from both sides:
0 = 20p - 13p
0 = 7p
Therefore, p = 0.
Conclusion:
Since p = 0, it means that the forces are collinear and not at an angle. The angle between the two forces is 0 degrees.
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The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.?
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The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.? 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 resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.?.
The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.? 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 resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.?.
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