The resultant of two equal forces may have a magnitude equal toone of the forces. At what angle between the two equal forces,this is possible? Justify your answer.
Let the forces be F1 and F2 at an angle A and their resultant be F. According to question,
| F1 | = | F2 | = | F |
F^2 = F1^2 + F2^2 + 2 F1 F2 cos A
or, F^2 = F^2 + F^2 + 2 F F cos A
or, F^2 - 2F^2 = 2 F^2 cos A
or, - F^2 = 2 F^2 cos A
or, -1 = 2 cos A
or, cos A = -1/2
or, cos A = cos 120
So, A = 120 degrees.
Hence, when two forces of equal magnitude act at an angle of 120 degrees, the resultant is equal to one of the forces.