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Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.?
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Two forces, while acting on a particle in opposite directions, have th...
Solution:
Given:
Resultant force when two forces act in opposite directions = 10 N
Resultant force when two forces act at right angles = 50 N
Let the two forces be F1 and F2
Finding the Magnitude of Forces
Using Pythagoras theorem, we can find the magnitude of the resultant force when two forces act at right angles:
Resultant force = √(F1^2 + F2^2) = 50 N
Squaring both sides:
(F1^2 + F2^2) = 2500
Now, we are given that the resultant force when the two forces act in opposite directions is 10 N. This means:
F1 - F2 = 10 (since they are acting in opposite directions)
Squaring both sides:
(F1 - F2)^2 = 100
Expanding the square:
F1^2 - 2F1F2 + F2^2 = 100
Solving the Equations
We now have two equations:
F1^2 + F2^2 = 2500
F1^2 - 2F1F2 + F2^2 = 100
We can solve these equations simultaneously to find the values of F1 and F2.
Adding the two equations:
2F1^2 - 2F1F2 + 2F2^2 = 2600
Dividing by 2:
F1^2 - F1F2 + F2^2 = 1300
Subtracting the second equation from this:
3F1F2 = 1200
F1F2 = 400
Now, we can solve for F1 and F2 using substitution:
F1 = 400/F2
Substituting in the first equation:
(400/F2)^2 + F2^2 = 2500
Expanding and simplifying:
160000 + F2^4 - 5000F2^2 = 0
This is a quadratic equation in F2^2. Solving for F2^2 using the quadratic formula:
F2^2 = (5000 ± √(5000^2 - 4*160000))/2
F2^2 = 100 or F2^2 = 400
If F2^2 = 100, then F2 = 10 N and F1 = 40 N (from F1F2 = 400)
If F2^2 = 400, then F2 = 20 N and F1 = 20 N
Therefore, the two forces are either 10 N and 40 N or 20 N and 20 N.
Given:
Resultant force when two forces act in opposite directions = 10 N
Resultant force when two forces act at right angles = 50 N
Let the two forces be F1 and F2
Finding the Magnitude of Forces
Using Pythagoras theorem, we can find the magnitude of the resultant force when two forces act at right angles:
Resultant force = √(F1^2 + F2^2) = 50 N
Squaring both sides:
(F1^2 + F2^2) = 2500
Now, we are given that the resultant force when the two forces act in opposite directions is 10 N. This means:
F1 - F2 = 10 (since they are acting in opposite directions)
Squaring both sides:
(F1 - F2)^2 = 100
Expanding the square:
F1^2 - 2F1F2 + F2^2 = 100
Solving the Equations
We now have two equations:
F1^2 + F2^2 = 2500
F1^2 - 2F1F2 + F2^2 = 100
We can solve these equations simultaneously to find the values of F1 and F2.
Adding the two equations:
2F1^2 - 2F1F2 + 2F2^2 = 2600
Dividing by 2:
F1^2 - F1F2 + F2^2 = 1300
Subtracting the second equation from this:
3F1F2 = 1200
F1F2 = 400
Now, we can solve for F1 and F2 using substitution:
F1 = 400/F2
Substituting in the first equation:
(400/F2)^2 + F2^2 = 2500
Expanding and simplifying:
160000 + F2^4 - 5000F2^2 = 0
This is a quadratic equation in F2^2. Solving for F2^2 using the quadratic formula:
F2^2 = (5000 ± √(5000^2 - 4*160000))/2
F2^2 = 100 or F2^2 = 400
If F2^2 = 100, then F2 = 10 N and F1 = 40 N (from F1F2 = 400)
If F2^2 = 400, then F2 = 20 N and F1 = 20 N
Therefore, the two forces are either 10 N and 40 N or 20 N and 20 N.
Community Answer
Two forces, while acting on a particle in opposite directions, have th...
30and 40N
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Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.?
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Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.?.
Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two forces, while acting on a particle in opposite directions, have the resultant of 10 N. If they act at right angles to each other, the resultant is found to be 50 N. Find the two forces.?.
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