3.1 Momentum and Newton's Laws of Motion:
3.1.1 Mass and resistance to change in motion:
- Mass is the property of an object that resists changes in its motion.
- Objects with larger mass require more force to produce a given acceleration.
3.1.2 Newton's second law of motion (F = ma):
- The force acting on an object is equal to its mass multiplied by its acceleration.
- The direction of acceleration and resultant force is always the same.
3.1.3 Linear momentum:
- Linear momentum (p) is the product of an object's mass and velocity.
- Linear momentum = mass × velocity (p = mv).
3.1.4 Force as the rate of change of momentum:
- Force can be defined as the rate of change of momentum.
- F = Δp/Δt (Force = change in momentum / change in time).
3.1.5 Newton's laws of motion:
- Newton's first law (law of inertia): An object at rest or in motion will continue to remain in that state unless acted upon by an external force.
- Newton's second law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
- Newton's third law: For every action, there is an equal and opposite reaction.
3.1.6 Weight:
- Weight is the force experienced by an object due to a gravitational field.
- Weight = mass × acceleration due to gravity (W = mg).
3.2 Non-uniform motion:
3.2.1 Frictional forces and drag forces:
- Frictional forces oppose the motion of objects in contact with each other.
- Drag forces (including air resistance) act on objects moving through a fluid and increase with speed.
3.2.2 Motion in a uniform gravitational field with air resistance:
- Objects in a uniform gravitational field experience a downward force (weight) and may also experience an upward force due to air resistance.
- The interplay of these forces affects the motion of objects.
3.2.3 Terminal velocity:
- Objects moving against a resistive force (e.g., air resistance) may reach a terminal velocity.
- Terminal velocity is a constant velocity achieved when the resistive force equals the driving force, resulting in zero net acceleration.
3.3 Linear momentum and its conservation:
3.3.1 Conservation of momentum:
- The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it.
3.3.2 Applications of conservation of momentum:
- Conservation of momentum can be applied to solve problems involving interactions between objects.
- Elastic and inelastic collisions in one or two dimensions can be analyzed using the principle of conservation of momentum.
3.3.3 Perfectly elastic collisions:
- In a perfectly elastic collision, the relative speed of approach between objects is equal to the relative speed of separation.
3.3.4 Change in kinetic energy:
- While momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place due to external forces or internal energy transformations.