Key Points to Remember while Solving Problems

Key Points to Remember while Solving Problems

1. Use rectangular components for problems involving more than two forces and their resultant.

2. For two forces and their resultant:

a) Use either rectangular components or triangle law when magnitudes of two forces are unknown. Alternatively, Lami's theorem can be used.

b) Use either triangle law or parallelogram law when two angles are unknown.

3. Force is always resultant of its components.

4. If F1 and F2 are magnitudes of two given forces, the maximum magnitude of their resultant is F1 + F2 for angle α = 0° between F1 and F2. The minimum magnitude of their resultant is | F1 - F2 | for angle α = 180°. As angle α is increased from 0° to 180°, the magnitude of the resultant goes on decreasing.

5. In problems involving maximum or minimum, the following methods can be used. 

a) For maximum or minimum of any quantity, the mathematical condition is that its first order derivative is zero.

b) If the quantity required to be maximum or minimum can be obtained in the form of f = N / D and if N is constant, then D has to be maximum for minimum f and D has to be minimum for maximum f. If D is a constant, then N has to be maximum for maximum ƒ and minimum for minimum f

(N = Numerator and D = Denominator).

6. Components of a force are always adjacent to the force so that the angle between them is less than 180°.

7. Resultant of two forces lies between the two forces on that side where the angle between the forces is less than 180°. Equilibrant will be on opposite side.