Lesson Notes By Weeks and Term v4 - SHS 3

Lesson Video

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Performance objectives

• Define heat and temperature and explain their differences.
• Describe the three modes of heat transfer.
• Calculate heat transfer using the specific heat capacity formula.
• Apply heat transfer principles to real-life situations in Ghana.

Lesson summary

This lesson explores the deep connection between two fundamental principles of mechanics: Newton's Third Law of Motion and the Principle of Conservation of Linear Momentum. We often hear Newton's Third Law as "action and reaction are equal and opposite," but what does this truly mean in the real world of moving objects? We will see how this law governs every interaction, from a simple handshake to the collision of two vehicles on the Accra-Kumasi highway. By analysing the change in momentum of colliding objects, we can mathematically prove and verify Newton's Third Law, gaining a more profound understanding of the forces that shape our world.

Lesson notes

A. Review of Foundational Concepts Linear Momentum (p): This is the "quantity of motion" an object has. It is a vector quantity, meaning it has both magnitude and direction. Formula: `p = mv` Where: `p` = momentum (in kg m/s), `m` = mass (in kg), `v` = velocity (in m/s). *Ghanaian Context:* A fully loaded 'trotro' moving at 40 km/h has far more momentum than an 'okada' motorcycle at the same speed because the trotro's mass is much greater. Newton's Third Law of Motion: For every action, there is an equal and opposite reaction. More precisely: If object A exerts a force on object B (`F_AB`), then object B simultaneously exerts a force on object A (`F_BA`) that is equal in magnitude and opposite in direction. Formula: `F_AB = - F_BA` Impulse (J): This is the change in momentum of an object. It is also defined as the product of the net force acting on the object and the time over which the force acts. Impulse is what connects Force (Newton's Laws) to Momentum. Formula: `J = FΔt = Δp = m(v - u)` Where: `F` = Force (N), `Δt` = time interval (s), `Δp` = change in momentum (kg m/s). B. The Core Connection: Verifying Newton's Third Law with Momentum

This is the central idea of our lesson. Let's consider a simple, isolated system of two objects, A and B, colliding with each other. An "isolated system" means there are no external forces acting on them (like friction or air resistance). The Interaction: During the brief time of the collision, `Δt`, object A exerts a force `F_AB` on object B. According to Newton's Third Law, object B must exert an equal and opposite force `F_BA` on object A. `F_AB = - F_BA` (Equation 1) Introducing Time: The forces act for the same amount of time, `Δt`. Let's multiply both sides of Equation 1 by `Δt`: `F_AB * Δt = - (F_BA * Δt)` (Equation 2) Connecting to Impulse and Momentum: We know that Impulse `J = FΔt` and also that Impulse equals the change in momentum `J = Δp`. The term `F_AB * Δt` is the impulse on object B, which causes its momentum to change (`Δp_B`). The term `F_BA * Δt` is the impulse on object A, which causes its momentum to change (`Δp_A`). The Result: Substituting these into Equation 2, we get: `Δp_B = - Δp_A`

This powerful result is the mathematical verification of Newton's Third Law using momentum. It states that in any collision within an isolated system, the change in momentum experienced by one object is exactly equal in magnitude and opposite in direction to the change in momentum experienced by the other object. C. From Newton's Third Law to Conservation of Momentum

We can take our result one step further. Starting from `Δp_A + Δp_B = 0` Let `u_A` and `u_B` be the initial velocities, and `v_A` and `v_B` be the final velocities. `Δp_A = p_A(final) - p_A(initial) = m_A*v_A - m_A*u_A` `Δp_B = p_B(final) - p_B(initial) = m_B*v_B - m_B*u_B` Substituting these into our equation: `(m_A*v_A - m_A*u_A) + (m_B*v_B - m_B*u_B) = 0` Rearranging the terms: `m_A*u_A + m_B*u_B = m_A*v_A + m_B*v_B` Total Initial Momentum = Total Final Momentum

Evaluation guide

• Verify Newton's third law of motion from momentum change.
• Enquiry learning: Let learners verify Newton's third law of motion by comparing the
• momentum change of one body to another body following from elastic collision.
• under standing