Newtonian model of motion — A/L Combined Mathematics

What must I remember about Newtonian model of motion?

• Newton's Laws of Motion: First Law (law of inertia), Second Law (resultant force equals time rate of change of linear momentum: F = dp/dt = m*a for constant mass), Third Law (action and reaction are equal, opposite, and act on different interacting bodies).
• Linear Momentum and Impulse: Linear momentum p = m*v; Impulse of a constant force F over time interval Δt is I = F * Δt; Impulse of variable force I = ∫ F dt = Δp = m*v - m*u (Impulse-Momentum Theorem).
• Work, Energy, and Power: Work done by constant force W = F * d * cos θ; Kinetic Energy E_k = (1/2)m v²; Work-Energy Theorem: Net work done by all forces equals change in kinetic energy: W_net = ΔE_k = (1/2)m v² - (1/2)m u².
• Conservative forces and Mechanical Energy Conservation: For conservative forces (gravity, ideal elastic springs), total mechanical energy E = E_k + E_p remains constant: (1/2)m v1² + m g h1 = (1/2)m v2² + m g h2.
• Power definition: Instantaneous power P = dW/dt = F * v; average power P_avg = Total Work / Total Time; tractive force of an engine F = P / v.

Test yourself (1 minute)

1. Connected particles over a pulley

   Write individual equations of motion F = ma along the direction of acceleration for each body; tension T is internal to the combined system but external to each isolated body.

2. Vehicle on inclined road

   Equation of motion along incline: F - R - mg sin α = m * a, where F = P/v is engine driving force, R is resistive force, and α is inclination angle.

3. Maximum speed condition

   Maximum velocity is attained when acceleration a = 0, so engine driving force equals sum of resistive forces: F_max = R + mg sin α => P = (R + mg sin α) * v_max.

Practise Newtonian model of motion questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 3

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Where does Newtonian model of motion fit in the syllabus?

Year 2 · Term 2