3.5._Newton_s_Laws_of_Motion_and_Momentum

Newton's Laws of Motion and Momentum

Newton's Three Laws

Universal Laws: Applicable to all objects and motions.

1. First Law: An object will remain at rest or continue to move with constant velocity unless acted upon by a resultant force. This principle is also referred to as the law of inertia, highlighting the resistance of any physical object to change in its state of motion.

2. Second Law: The net force acting on an object is directly proportional to the rate of change of momentum and acts in the same direction. It can be expressed as:

   • Formula: F = k * (∆p/∆t), where k is typically 1. This law emphasizes how acceleration of an object depends not only on the net force acting upon it but also on its mass.

3. Third Law: For every action, there is an equal and opposite reaction. This law states that forces occur in pairs, each acting on a different object, and they are of equal magnitude but in opposite directions. An example is the gravitational force experienced between the Earth and a person.

Fundamental Forces

Four Fundamental Forces:

• Gravitational: The attraction between masses, always attractive and much weaker than the other forces at a fundamental level.

• Electromagnetic: Affects charged particles, can be attractive or repulsive, and is responsible for a variety of physical phenomena, including electricity, magnetism, and light.

• Strong nuclear: Binds protons and neutrons together in an atomic nucleus; it is the strongest of the four forces but acts over a very short range.

• Weak nuclear: Responsible for radioactive decay and neutrino interactions, it operates at a subatomic level.

Linear Momentum

Definition: Linear momentum (p) is the product of mass (m) and velocity (v).

• Formula: p = mv

• Unit: kg·m/s (vector quantity, considers direction).

• Special Case of Second Law: F = ma is applicable when mass remains constant.

• Derived formula: F = (∆p/∆t) = (m(v - u)/t) emphasizes how changes in momentum relate to forces acted over time.

Impulse of a Force

Impulse: Measures change in momentum; defined as the product of force (F) and the time duration (∆t) it acts.

• Formula: Impulse = ∆p = F∆t = m(v - u), linking the impulse to the change in momentum experienced by an object when a force is applied for a duration of time.

Collisions and Conservation of Momentum

Conservation of Momentum:

• During the collision of two or more objects, momentum and kinetic energy may transfer.

• Conserved: Total momentum remains constant if no external forces act upon the system.

• Formula: Total initial momentum = Total final momentum, elaborating how total momentum is maintained pre- and post-collision.

Types of Collisions

• Perfectly Elastic Collision: Total kinetic energy remains constant, and both momentum and kinetic energy are conserved. Examples include ideal gas particle collisions.

• Inelastic Collision: Kinetic energy is transformed into other forms (e.g., heat, sound), while momentum is still conserved. This includes more common scenarios like car crashes.

• Both types conserve total energy and total momentum for one-dimensional and two-dimensional collisions.

One Dimensional Collisions

Conservation Formula:

• m1u1 + m2u2 = m1v1 + m2v2, where m is mass and u/v are initial and final velocities.

• Directionality: Choose one direction as negative; velocities of objects moving in that direction must consider negative signs.

Two Dimensional Collisions

• Conservation of momentum applies separately to x and y directions, allowing a more complex analysis of collisions in a plane.