Equilibrium of Forces | Physics for JAMB PDF Download

Equilibrium of Coplanar Forces:

When multiple forces act on a particle in a plane and the net force and net torque acting on the particle are zero, the particle is said to be in equilibrium. The conditions for equilibrium of coplanar forces can be applied to solve problems.

• Triangle and Polygon of Forces: The triangle and polygon laws of forces can be used to solve equilibrium problems. According to the triangle law, if three forces acting on a particle can be represented by the sides of a triangle taken in order, the forces are in equilibrium. Similarly, according to the polygon law, if the vectors representing the forces acting on a particle can be arranged to form a closed polygon, the forces are in equilibrium.
• Lami's Theorem: Lami's theorem states that for three coplanar concurrent forces in equilibrium, the ratio of the magnitude of each force to the sine of the angle between the other two forces is constant. This theorem can be applied to solve problems involving equilibrium of three forces.

Principles of Moments

The principles of moments deal with the concept of torque or moment of a force.

• Moment of a Force: The moment of a force about a point is the product of the magnitude of the force and the perpendicular distance from the point to the line of action of the force. It is also known as the torque. The moment of a force can be positive or negative, depending on the direction of rotation it tends to produce.
• Treatment and Moment of a Couple (Torque): A couple consists of two equal and opposite parallel forces acting on a body but not along the same line. The moment of a couple is the product of one of the forces and the perpendicular distance between the forces. Couples produce rotation without translation.
• Applications: The principles of moments have various applications, including problems involving equilibrium of beams, levers, and rotating objects.

Action of Parallel and Non-parallel Forces

The conditions for equilibrium of rigid bodies involve resolving and composing forces in two perpendicular directions, and determining the resultant and equilibrant.

• Resolution and Composition of Forces in Two Perpendicular Directions: When forces act on a rigid body, they can be resolved into two perpendicular components. By resolving forces, we can determine the effect of each force in the x and y directions. Composition of forces involves combining forces acting along different directions to find their resultant.
• Resultant and Equilibrant: The resultant of a system of forces is the vector sum of all the forces. If the resultant of a system of forces is zero, then the equilibrant is a force of equal magnitude but opposite in direction to the resultant. The equilibrant balances the other forces in the system to maintain equilibrium.

Centre of Gravity and Stability

The concept of the center of gravity is important in understanding the stability of objects.

• Stable, Unstable, and Neutral Equilibrium: An object is in stable equilibrium when, if displaced slightly, it returns to its original position. Unstable equilibrium occurs when a slight displacement causes the object to move further away from its original position. Neutral equilibrium exists when a displaced object remains in its new position without any tendency to return or move further away.

Candidates should be able to apply the conditions for the equilibrium of coplanar forces, use triangle and polygon laws of forces, and apply Lami's theorem to solve problems. They should also be able to analyze the principles of moments, determine the moment of a force and couple, and describe applications of moments. Additionally, candidates should be able to apply the conditions for the equilibrium of rigid bodies, resolve forces into two perpendicular directions, determine the resultant and equilibrant, and differentiate between stable, unstable, and neutral equilibrium.