Newton's laws of motion

Newton’s Laws of Motion

  • Overview: Newton's laws deal with force, motion, and acceleration.

Newton's First Law of Motion

  • Statement: Every object continues in its state of rest or uniform motion in a straight line unless acted upon by a net force.

  • Key Concept: Inertia - resistance to a change in motion.

  • Examples: A car being pushed without starting indicates external force without momentum change.

  • Net Force (F_net): Replaces external force (F_applied) when acceleration (a) = 0.

Newton's Second Law of Motion

  • Statement: Net force acting on a body equals the product of its mass and acceleration.

  • Equation: F_net = ma.

  • Component Form: F_net,x = ma_x and F_net,y = ma_y.

  • Implications: Different components affect motion along respective axes.

Vectors

  • Vector Expression: V = Vcos(θ)i + Vsin(θ)j, where θ is the angle with the positive x-axis.

Example of Vector Analysis

  • Angles:

    • V1: θ1 = 0° (along x-axis)

    • V2: θ2 = 90° (along y-axis)

    • V3: θ3 = 205° (180° + 25°)

  • Calculating Components:

    • For V1: V1,x = 10N, V1,y = 0N.

    • For V2: V2,x = 0N, V2,y = 15N.

    • For V3: V3,x = -18.13N, V3,y = -8.45N (from calculations).

Problem Solving with Forces

  1. Net Force Calculation: Net force is the vector sum of forces acting (figures omitted).

  2. Magnitude and Direction: Scale net force F = √(F_x² + F_y²) to determine resultant force.

  3. Application of Second Law: Use F_net = ma to relate forces and mass to acceleration.

Worked Example with Forces

  • Using force magnitudes and angles:

    • F1 = 30N, θ1 = 90°; F2 = 60N, θ2 = 45°; F3 = 40N, θ3 = 0°.

    • Net Force Calculation: F_net = F1 + F2 + F3 = [resultant components calculation]

    • Magnitude and Direction of acceleration can then be found using F_net = ma.

Momentum and Collisions

  • Momentum Change: F = dp/dt, where dp is the change in momentum.

  • Collision Dynamics:

    • Elastic vs. Inelastic Collisions:

      • Elastic: Both momentum and kinetic energy conserved.

      • Inelastic: Momentum conserved; kinetic energy dissipated.

Newton’s Third Law of Motion

  • Statement: Forces between two objects are equal in magnitude and opposite in direction.

  • Vector Form: F_AB = -F_BA.