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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 ...
The given angle between the two forces is 150 degrees.
Let the magnitude of the two forces be F1 and F2, with F2 being perpendicular to the resultant force.
The given resultant force is 10 N.
Using the formula for the magnitude of the resultant force of two forces at an angle:
Resultant force = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(theta))
where theta is the angle between the two forces (150 degrees in this case)
Substituting the given values:
10 = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(150))
cos(150) = -0.866
Simplifying:
100 = F1^2 + F2^2 + 2*F1*F2*(-0.866)
Dividing both sides by 4:
25 = (F1 + F2*(-0.433))^2 + 0.75*F2^2
To minimize F2, we set the first term in the right-hand side to zero:
F1 + F2*(-0.433) = 0
F2 = (1/0.433) * F1
Substituting in the above equation:
25 = (1.733*F1)^2 + 0.75*(1.733^2)*(F1^2)
Solving for F1:
F1 = 20.56 N
Substituting in the expression for F2:
F2 = 47.48 N
Therefore, the other force is approximately 47.48 N.
Let the magnitude of the two forces be F1 and F2, with F2 being perpendicular to the resultant force.
The given resultant force is 10 N.
Using the formula for the magnitude of the resultant force of two forces at an angle:
Resultant force = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(theta))
where theta is the angle between the two forces (150 degrees in this case)
Substituting the given values:
10 = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(150))
cos(150) = -0.866
Simplifying:
100 = F1^2 + F2^2 + 2*F1*F2*(-0.866)
Dividing both sides by 4:
25 = (F1 + F2*(-0.433))^2 + 0.75*F2^2
To minimize F2, we set the first term in the right-hand side to zero:
F1 + F2*(-0.433) = 0
F2 = (1/0.433) * F1
Substituting in the above equation:
25 = (1.733*F1)^2 + 0.75*(1.733^2)*(F1^2)
Solving for F1:
F1 = 20.56 N
Substituting in the expression for F2:
F2 = 47.48 N
Therefore, the other force is approximately 47.48 N.
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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 isa)20/√3 Nb)10/√3 Nc)20 Nd)NoneCorrect answer is option 'C'. Can you explain this answer?
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