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The resultant of two forces acting at an angle of 150o is 10 N and is perpendicular to one of the forces. The other force is
- a)20/√3 N
- b)10/√3 N
- c)20 N
- d)None
Correct answer is option 'C'. Can you explain this answer?
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The resultant of two forces acting at an angle of 150o is 10 N and is ...
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Given Information:
Two forces acting at an angle of 150o have a resultant of 10 N. The resultant force is perpendicular to one of the forces.
Explanation:
Step 1: Finding the Components of Forces:
Let one force be F1 and the other force be F2. The resultant force R can be written as:
R = √(F1^2 + F2^2 + 2F1F2cosθ), where θ is the angle between the forces.
Given that R = 10 N and θ = 150o, we can substitute these values into the equation.
Step 2: Solving for F1 and F2:
Since the resultant force is perpendicular to one of the forces, the angle between R and that force is 90o. Therefore, cosθ = cos90o = 0.
The equation simplifies to R = √(F1^2 + F2^2).
Substitute R = 10 N into the equation:
10 = √(F1^2 + F2^2) ... (1)
Given that θ = 150o, the angle between F1 and F2 is 180o - 150o = 30o.
Using the formula for the resultant force with the angle between the forces:
10 = √(F1^2 + F2^2 - 2F1F2cos30o)
10 = √(F1^2 + F2^2 - F1F2√3) ... (2)
Step 3: Solving the Equations:
From equations (1) and (2), we have:
F1^2 + F2^2 = 100 ... (3)
F1^2 + F2^2 - F1F2√3 = 100 ... (4)
Subtract equation (3) from equation (4):
F1F2√3 = 0
F1F2 = 0
Since F1 and F2 are forces, neither can be zero. Therefore, F1 or F2 must be zero.
If F1 = 0, F2 = 10 N.
If F2 = 0, F1 = 10 N.
Therefore, the other force is 10 N, which is option C.
Two forces acting at an angle of 150o have a resultant of 10 N. The resultant force is perpendicular to one of the forces.
Explanation:
Step 1: Finding the Components of Forces:
Let one force be F1 and the other force be F2. The resultant force R can be written as:
R = √(F1^2 + F2^2 + 2F1F2cosθ), where θ is the angle between the forces.
Given that R = 10 N and θ = 150o, we can substitute these values into the equation.
Step 2: Solving for F1 and F2:
Since the resultant force is perpendicular to one of the forces, the angle between R and that force is 90o. Therefore, cosθ = cos90o = 0.
The equation simplifies to R = √(F1^2 + F2^2).
Substitute R = 10 N into the equation:
10 = √(F1^2 + F2^2) ... (1)
Given that θ = 150o, the angle between F1 and F2 is 180o - 150o = 30o.
Using the formula for the resultant force with the angle between the forces:
10 = √(F1^2 + F2^2 - 2F1F2cos30o)
10 = √(F1^2 + F2^2 - F1F2√3) ... (2)
Step 3: Solving the Equations:
From equations (1) and (2), we have:
F1^2 + F2^2 = 100 ... (3)
F1^2 + F2^2 - F1F2√3 = 100 ... (4)
Subtract equation (3) from equation (4):
F1F2√3 = 0
F1F2 = 0
Since F1 and F2 are forces, neither can be zero. Therefore, F1 or F2 must be zero.
If F1 = 0, F2 = 10 N.
If F2 = 0, F1 = 10 N.
Therefore, the other force is 10 N, which is option C.
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