Topic 3- Dynamics

Topic 3 Notes Newton’s 3rd Law When body A exerts a force on body B, force on body A is equal in magnitude to force on body B from A. Both forces are in opposite directions and of same kind. Action reaction forces: - act on different bodies - be of the same type - equal magnitude - act in opposite direction Newton’s 1st Law An object continues to be in a state of rest or in motion with constant velocity, unless acted upon by a resultant force. Mass: Property of a body which resists change in motion Weight: Force acting on it due to gravitational field. Linear momentum The product of a body’s mass and velocity Linear Momentum 𝑝 = 𝑚𝑣 p is the linear momentum (kg m s-1) m is the mass of the object (m) v is the velocity of the object (m s-1) Newton’s 2nd Law The rate of change of momentum of a body is directly proportional to the resultant force acting on it, and it takes place in the direction of the resultant force. Newton’s 2nd Law 𝐹𝑛𝑒𝑡 = 𝑑𝑝 𝑑𝑡 = 𝑚𝑎 Fnet is the resultant force (N) p is the linear momentum (kg m s-1) t is the time taken for the object to change momentum (s) m is the mass of the object (m) a is the acceleration of the object (m s-2) Weightlessness = no contact force but there is weight. Weighing scales do not always measure true weight but the contact force acting on the weighing scale. Free Fall As an object falls, its vertical acceleration decreases over time. Initially, its acceleration is 9.81 m s-2. As it increases in velocity, the air resistance will increase with it, but the acceleration decreases. When it reaches terminal velocity, it will fall at constant speed where W=Fdrag. No acceleration. Flowing Mass and Newton’s 2nd Law

e.g. water leaving a hose Newton’s 2nd Law involving Flowing Mass 𝐹𝑛𝑒𝑡 = 𝑚 𝑡 ∆𝑣 Fnet is the resultant force (N) m is the mass of the object (kg) t is the time taken for the amount of mass to flow out (s) v is the velocity (m s-1) Impulse The product of the force and the time duration of the impact. = change in momentum Impulse ∆𝑝 = ∫ 𝐹 𝑑𝑡 Fnet is the resultant force (N) p is the linear momentum (kg m s-1) t is the time taken for the object to change momentum (s) Shown by the area under the force-time curve. Principle of Conservation of Linear Momentum The total linear momentum of a system remains constant provided that no external resultant force acts on the system. Principle of Conservation of Linear Momentum 𝑚1𝑢1 + 𝑚2𝑢2 = 𝑚1𝑣1 + 𝑚2𝑣2 m1 and m2 are the masses of the 2 colliding objects u1 and u2 are the velocities of the objects before collision v1 and v2 are the velocities of the objects after collision Principle of Conservation of Kinetic Energy 1 2 𝑚1𝑢12 + 1 2 𝑚2𝑢22 = 1 2 𝑚1𝑣12 + 1 2 𝑚2𝑣22 m1 and m2 are the masses of the 2 colliding objects u1 and u2 are the velocities of the objects before collision v1 and v2 are the velocities of the objects after collision Relative speed of approach = relative speed of separation 𝑢1 − 𝑢2 = 𝑣2 − 𝑣1 u1 and u2 are the velocities of the objects before collision v1 and v2 are the velocities of the objects after collision Elastic collision: Total kinetic energy of the colliding bodies is conserved. All 3 equations are applicable. Inelastic collision: Collision where kinetic energy is not conserved. A perfectly inelastic collision is a collision where the colliding bodies will stick with one another and move off with the same velocity. Only the principle of conservation of linear momentum is applicable.