Lesson Notes By Weeks and Term v3 - Senior Secondary 2
Equilbrium of forces.
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Equilbrium of forces.
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Subject: Physics
Class: Senior Secondary 2
Term: 1st Term
Week: 4
Theme: Interaction Of Matter, Space And Time
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Students should beable to: Distinguishbetweenresultant and equilibrantforces. Explain the concept of equilibrium and distinguishbetween staticand dynamicequilibrium. Explain the conditions thatmust be satisfiedif an object is to be kept in equilibrium by the action of non-parallelforces. Explain what is meant by the moment of aforce about apoint. Explain what, is meant by the centre- of gravityof a body and identify itsposition for someregular uniformbodies. Name and identify threetypes of equilibrium with respect to the stability of anobject Explain the effect of centreof gravity on the stability of abody.
Materials: Metre rule, masses/weights, spring balances, retort stands and clamps, irregular lamina (cardboard), pin, plumb line, water, beaker/container, small objects of varying densities (wood, stone, plastic, palm oil, groundnut oil). | Teacher Activities | Student Activities | Teacher will explain the definition of resultant force, emphasizing its nature as a single force equivalent to all individual forces. | Students will understand that the resultant is a net force.
Resultant Force: Definition: The resultant force is a single force that has the same effect as all the individual forces acting on an object. It is the vector sum of all forces acting on a body.
Determination: Graphically (Vector Addition): Using the parallelogram law of forces (for two forces) or the polygon law of forces (for multiple forces).
Analytically (Resolution of Forces): Resolving each force into its perpendicular components (usually horizontal and vertical components), summing the components in each direction, and then finding the resultant using Pythagoras' theorem and trigonometry for direction.
Example: For forces $F_1, F_2, ..., F_n$, the resultant $R = F_1 + F_2 + ... + F_n$ (vector sum).
Equilibrant Force: Definition: The equilibrant force is a single force that, when applied to a system of forces, brings the system into equilibrium. It is equal in magnitude to the resultant force but acts in the opposite direction.
Relationship to Resultant: If $R$ is the resultant force, then the equilibrant force $E = -R$. This means $E$ has the same magnitude as $R$ but points in the opposite direction (180° away from $R$).
Definition of Equilibrium: An object is said to be in equilibrium when the net external force acting on it is zero, and the net external torque (turning effect) acting on it is also zero. This implies that the object is either at rest (static equilibrium) or moving with a constant velocity (dynamic equilibrium).
Static Equilibrium: Definition: An object is in static equilibrium if it is at rest and remains at rest. Both its linear velocity and angular velocity are zero and remain zero.
Conditions: The vector sum of all forces acting on the object is zero ($\sum \vec{F} = 0$). This means there is no net linear acceleration. The vector sum of all moments (torques) about any point is zero ($\sum \vec{\tau} = 0$). This means there is no net angular acceleration.
Examples: A book lying on a table, a building standing, a parked car, a market stall.
Dynamic Equilibrium: Definition: An object is in dynamic equilibrium if it is moving with a constant velocity (constant speed in a straight line) and constant angular velocity (if rotating). There is no net linear acceleration and no net angular acceleration.
Conditions: The vector sum of all forces acting on the object is zero ($\sum \vec{F} = 0$). The vector sum of all moments (torques) about any point is zero ($\sum \vec{\tau} = 0$).
Examples: A car moving at a constant speed on a straight road, a satellite orbiting Earth at a constant speed, an aeroplane flying at a constant velocity, a bicycle moving at a steady pace. For an object to be in complete equilibrium (both translational and rotational) under the action of non-parallel forces, two conditions must be satisfied: First Condition (Translational Equilibrium): The vector sum of all forces acting on the body must be zero.
Mathematically: $\sum \vec{F} = 0$.
In terms of components: The sum of all forces acting in the horizontal direction must be zero ($\sum F_x = 0$). The sum of all forces acting in the vertical direction must be zero ($\sum F_y = 0$). This ensures that the body has no linear acceleration.
Second Condition (Rotational Equilibrium): The vector sum of all moments (torques) about any arbitrary point must be zero.
Mathematically: $\sum \vec{\tau} = 0$. This implies that the sum of the clockwise moments about any point is equal to the sum of the anti-clockwise moments about the same point (Principle of Moments). This ensures that the body has no angular acceleration.