Newton's Laws of Motion and Momentum for A Level Physics AS

Newton's Laws of Motion

Newton's three laws of motion lay the foundation for our understanding of forces and motion in classical mechanics. These laws are:

1. Law of Inertia: An object at rest remains at rest, and an object in motion continues to move at a constant velocity, unless acted upon by an external force.
2. Law of Force and Acceleration: The acceleration a of an object is directly proportional to the net force F acting on it and inversely proportional to its mass m. Mathematically, F = ma.
3. Law of Action and Reaction: For every action force, there is an equal and opposite reaction force.

Momentum and Impulse

The linear momentum p of an object with mass m moving at velocity v is given by p = mv. Impulse J is the product of the net force F acting on an object and the time interval Δt for which it acts: J = FΔt.

Worked Example: Collision

Problem: A 2 kg object moving at 5 m/s collides head-on with a 3 kg object initially at rest. If the collision is perfectly elastic, find the final velocities of the two objects.

Solution:

• Initial momentum of 2 kg object = 2 × 5 = 10 kg m/s
• Initial momentum of 3 kg object = 0
• Total initial momentum = 10 kg m/s
• By conservation of momentum, total final momentum = 10 kg m/s
• Let the final velocities be v1 and v2 for the 2 kg and 3 kg objects respectively
• Then 2v1 + 3v2 = 10
• Using conservation of kinetic energy, v1 = -2.5 m/s and v2 = 3.33 m/s

Conservation Principles

Newton's laws and the concepts of momentum and impulse lead to the principles of conservation of momentum and kinetic energy in isolated systems. These principles allow us to analyze collisions, explosions, and other dynamic scenarios involving multiple bodies.

For additional resources, refer to the OCR A Level Physics specification and BBC Bitesize A Level Physics revision guides.