Lesson Notes By Weeks and Term v4 - SHS 3
HEAT
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HEAT
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Subject: Physics
Class: SHS 3
Term: 1st Term
Week: 15
Grade code: 3.1.3.LI.1
Strand code: 2
Sub-strand code: 1
Content standard code: 3.1.2.CS.1
Indicator code: 3.1.3.LI.1
Theme: ENERGY
Subtheme: HEAT
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In our daily lives in Ghana, we see forces and motion everywhere. From a tro-tro moving on the N1 highway to footballers clashing for a ball at the Baba Yara Stadium, the principles of physics are in action. Today, we will explore a deep connection between two fundamental ideas we have studied: the conservation of momentum during collisions and Newton's famous Third Law of Motion. We will see that these are not separate ideas but are two ways of describing the same reality. Understanding this link helps engineers design safer cars and helps us understand everything from the recoil of a fisherman's speargun to the movement of rockets.
This lesson connects two powerful ideas. Let's review them before we link them. Concept 1: Momentum and Its Conservation Momentum (p): This is the "quantity of motion" an object has. It is the product of an object's mass (m) and its velocity (v). Formula: `p = m * v` Unit: kilogram-metre per second (kg m/s) Momentum is a vector quantity; it has both magnitude and direction. Principle of Conservation of Linear Momentum: This principle states that for a system of interacting objects, the total linear momentum remains constant, provided no external forces (like friction or air resistance) are acting on the system. Such a system is called an isolated system. In simpler terms: Total momentum before collision = Total momentum after collision. For two bodies (A and B) colliding: `m_A * u_A + m_B * u_B = m_A * v_A + m_B * v_B` `m_A`, `m_B` = masses of bodies A and B `u_A`, `u_B` = initial velocities of bodies A and B `v_A`, `v_B` = final velocities of bodies A and B Concept 2: Newton's Third Law of Motion This law describes the nature of forces. It states that: "For every action, there is an equal and opposite reaction." This means that forces always occur in pairs. If body A exerts a force on body B (`F_AB`), then body B simultaneously exerts a force on body A (`F_BA`) that is equal in magnitude and opposite in direction. Formula: `F_AB = -F_BA` The negative sign indicates the opposite direction. The Main Task: Verifying Newton's Third Law from Momentum Change
Now, let's use the Principle of Conservation of Momentum to prove Newton's Third Law. This is the core of our lesson.
Step-by-Step Derivation: Start with the Conservation of Momentum equation for a collision between two bodies, A and B, in an isolated system. `m_A * u_A + m_B * u_B = m_A * v_A + m_B * v_B` Rearrange the equation. Let's group all the terms for body A on one side and all the terms for body B on the other side. `m_A * v_A - m_A * u_A = m_B * u_B - m_B * v_B` Factor out the masses. `m_A * (v_A - u_A) = - [m_B * (v_B - u_B)]` *(Notice we factored out a negative sign on the right side to get the standard 'final - initial' form.)* Recognise the terms. The term `m * (v - u)` represents `m * Δv`, which is the change in momentum (Δp). `m_A * (v_A - u_A)` is the change in momentum of body A (`Δp_A`). `m_B * (v_B - u_B)` is the change in momentum of body B (`Δp_B`). Substitute these into our rearranged equation. `Δp_A = -Δp_B` This is a powerful statement! It means that during a collision, the momentum gained by one body is equal to the momentum lost by the other. Their changes in momentum are equal and opposite. Introduce Time and Force. From Newton's Second Law, we know that the net force acting on an object is equal to the rate of change of its momentum. `F = Δp / Δt` Divide both sides of our momentum-change equation by the time of impact (Δt). The time of impact is the same for both bodies. `Δp_A / Δt = - (Δp_B / Δt)` Identify the forces. `Δp_A / Δt` is the force exerted on body A by body B (`F_AB`). `Δp_B / Δt` is the force exerted on body B by body A (`F_BA`). Final Result. By substituting the forces into the equation, we get: `F_AB = -F_BA` This is precisely Newton's Third Law of Motion. We have successfully verified it using the principle of momentum conservation.