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The sum of magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag of forces?
Most Upvoted Answer
The sum of magnitude of two forces acting at point is 18 and the mag o...
Explanation:
Given,
- Sum of magnitudes of two forces = 18
- Magnitude of resultant force = 12
- Resultant force makes 90 degrees angle with the force of small magnitude.
Let the two forces be F1 and F2.
Resolve the Resultant force:
We can resolve the resultant force into its components using the following formulae:
R^2 = F1^2 + F2^2 + 2*F1*F2*cosθ
where R is the magnitude of the resultant force, θ is the angle between the two forces
Here, R = 12 and cosθ = 0 (since they are at 90 degrees)
So,
12^2 = F1^2 + F2^2 + 2*F1*F2*0
144 = F1^2 + F2^2
or,
F1^2 + F2^2 = 144 ------(i)
Find the Magnitude of Forces:
From the given data, we know that F1 + F2 = 18
Now, we can use equation (i) to solve for F1 and F2:
Let F1 = x
Then, F2 = 18 - x
Substituting in equation (i), we get:
x^2 + (18 - x)^2 = 144
Simplifying and solving for x, we get:
x = 6 or 12
So, F1 = 6 and F2 = 12 or F1 = 12 and F2 = 6
Therefore, the magnitudes of the forces are 6 N and 12 N or 12 N and 6 N.
Conclusion:
Thus, the magnitudes of the two forces are 6 N and 12 N or 12 N and 6 N.
Given,
- Sum of magnitudes of two forces = 18
- Magnitude of resultant force = 12
- Resultant force makes 90 degrees angle with the force of small magnitude.
Let the two forces be F1 and F2.
Resolve the Resultant force:
We can resolve the resultant force into its components using the following formulae:
R^2 = F1^2 + F2^2 + 2*F1*F2*cosθ
where R is the magnitude of the resultant force, θ is the angle between the two forces
Here, R = 12 and cosθ = 0 (since they are at 90 degrees)
So,
12^2 = F1^2 + F2^2 + 2*F1*F2*0
144 = F1^2 + F2^2
or,
F1^2 + F2^2 = 144 ------(i)
Find the Magnitude of Forces:
From the given data, we know that F1 + F2 = 18
Now, we can use equation (i) to solve for F1 and F2:
Let F1 = x
Then, F2 = 18 - x
Substituting in equation (i), we get:
x^2 + (18 - x)^2 = 144
Simplifying and solving for x, we get:
x = 6 or 12
So, F1 = 6 and F2 = 12 or F1 = 12 and F2 = 6
Therefore, the magnitudes of the forces are 6 N and 12 N or 12 N and 6 N.
Conclusion:
Thus, the magnitudes of the two forces are 6 N and 12 N or 12 N and 6 N.
Community Answer
The sum of magnitude of two forces acting at point is 18 and the mag o...
Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.
As the resultant force makes 90
∘
with the smaller force P then Q forms the hypotenuse of the triangle.
Thus, it can be written as,
Q ^2 −P^2=R^2
Q ^2 −P^2 =(12)^2
Q ^2 −P^2 =144 (1)
The sum of magnitudes of two forces is given as,
P+Q=18
Q=18−P (2)
Substituting the value from equation (2) in equation (1), we get
(18−P) ^2 −P^2 =144
P=5N
Substituting the value of P in equation (1), we get
Q=18−5
=13N
Thus, the magnitude of the forces are 5N and 13N.
As the resultant force makes 90
∘
with the smaller force P then Q forms the hypotenuse of the triangle.
Thus, it can be written as,
Q ^2 −P^2=R^2
Q ^2 −P^2 =(12)^2
Q ^2 −P^2 =144 (1)
The sum of magnitudes of two forces is given as,
P+Q=18
Q=18−P (2)
Substituting the value from equation (2) in equation (1), we get
(18−P) ^2 −P^2 =144
P=5N
Substituting the value of P in equation (1), we get
Q=18−5
=13N
Thus, the magnitude of the forces are 5N and 13N.
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The sum of magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag of forces?
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The sum of magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag 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 magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag of forces? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag of forces?.
The sum of magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag 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 magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag of forces? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of magnitude of two forces acting at point is 18 and the mag of their resultant is 12 if the resultant is 90• with the force of small mag what are the mag of forces?.
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