Statics Class 12 Mathematics Solutions has been updated according to the latest syllabus of 2080. It means the notes of statics chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.
Chapter – 18
Statics
Statics deals with the study of bodies at rest or in equilibrium under the action of forces. It focuses on the analysis of forces and their effects on objects that are not in motion. The chapter introduces various concepts such as force, moments, and equilibrium, which are fundamental to understanding the behavior of static objects.
Statics is a crucial chapter for students pursuing engineering and physics, as it lays the foundation for understanding the behavior of structures and mechanisms in real-world applications. Through the study of statics, students gain a deeper understanding of how forces interact and how objects maintain stability under different conditions.
Statics Class 12 Mathematics Solutions PDF
This PDF will provide the solutions of every question from the 1st exercise of class 12 statics chapter. If you want the notes of other chapters then you can search them in our site.
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Triangle of forces
The Triangle of Forces is a concept in statics used to analyze the equilibrium of a point under the influence of three forces. It states that if three forces acting on a point are in equilibrium, they can be represented in magnitude and direction by the sides of a triangle taken in order.
Converse of the triangle of forces
If three forces acting at a point be in equilibrium, they can be represented in magnitude and direction by the three sides of a triangle, taken in order. Let the three forces P, Q, R acting at a point O be in equilibrium.
Take OA in the direction of P such that OA represents the force P. Similarly (on the same scale) take OB in the direction of Q such that OB represents the force Q in magnitude and direction. Complete the parallelogram OACB. Join OC.
By the law of parallelogram of forces, the diagonal OC represents the resultant of the forces P and Q. But the forces P, Q, R are in equilibrium so that the force R balances the resultant of the forces P and Q, i.e. R balances the force represented by OC or R is represented by CO in magnitude and direction. Hence the sides OA, AC and CO, taken in order, represent the given forces P, Q and R acting at O.
If any other triangle LMN is drawn so that the sides LM, MN and NL are parallel to OA, AC and CO, the triangles OAC and LMN will be similar. Therefore, $latex \frac{OA}{LM} = \frac{AC}{MN} = \frac{CO}{NL} \quad \text{or,} \quad \frac{P}{LM} = \frac{Q}{MN} = \frac{R}{NL}$
Lami’s theorem
If three forces acting at a point, be in equilibrium, each force is proportional to the sine of the angle between the other two.
The Triangle of Forces is closely related to Lami’s Theorem, which states that if three coplanar, concurrent forces acting on a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces. Mathematically: $latex \frac{F_1}{\sin \alpha} = \frac{F_2}{\sin \beta} = \frac{F_3}{\sin \gamma}$ where $latex \alpha, \beta, \gamma$ are the angles opposite to the forces $latex F_1, F_2, F_3$, respectively.
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