Understanding Fundamental Forces and Newton's Laws

Fundamental Forces in Physics

Weight (W)

• Weight is the gravitational force that exists between masses. Specifically, it is the force exerted on an object by a planet's gravity when the object is at the planet's surface.
• It can be calculated using the formula: W = mg
  • Where: m is the mass of the object under study, measured in kilograms (kg) in the SI unit system.
  • g is the acceleration due to gravity at the planet's surface. On Earth, g ≈ 9.81 m/s².
• Weight is directed along the line connecting the object under study with the planet's center, oriented towards the planet's center.

Normal Force (N)

• The Normal Force is a contact force that acts between two surfaces that are touching each other.
• It is often calculated indirectly, as it balances other forces perpendicular to the surface.
• Its direction is perpendicular to the surface of contact between the bodies.
• Its orientation is away from the contact surface, pushing towards the object under study.

Frictional Force (F_r)

• Frictional force is a force that opposes relative motion or the tendency of relative motion between two surfaces in contact.
• It can be calculated by: Fr = μN
  • Where: N is the normal force.
  • μ (mu) is the coefficient of friction. It is a dimensionless number that depends on the nature of the surfaces in contact.
• Its direction and orientation are always opposite to the direction of motion or impending motion.

Tension (T)

• Tension is a contact force transmitted through a cable, rope, string, or similar connector when pulled taut by forces acting from opposite ends.
• It is often calculated indirectly by analyzing the forces acting on the system.
• Its direction is along the length of the cable or rope.
• Its orientation is always away from the object to which the cable or rope is attached.

Elastic Force (F_e)

• Elastic force is the restoring force that arises in elastic materials when they are deformed from their equilibrium shape. This force acts to return the material to its original state.
• It follows Hooke's Law, which states: Fe = -k∆l (The negative sign indicates it's a restoring force).
  • Where: ∆l (delta l) is the change in length (elongation or compression) of the elastic body from its original length.
  • k is the elastic constant (or spring constant), which depends on the material and geometry of the elastic body. It is measured in Newtons per meter (N/m) in the SI unit system.

Newton's Laws of Motion

Newton's First Law: Law of Inertia

Newton's First Law states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.

• When the net force (resultant force) acting on an object is zero, the object will maintain its state of motion.
• If an object is initially at rest, it will remain at rest.
• If an object is initially in motion, it will continue to move with uniform rectilinear motion (constant velocity).

Newton's Second Law: Fundamental Law of Dynamics

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The acceleration is in the direction of the net force.

• When the net force acting on an object is not zero, the object accelerates. This acceleration is in the same direction and orientation as the net force.
• This relationship is expressed by the formula: Fnet = ma
  • Where: Fnet is the resultant (net) force applied to the object.
  • m is the inertial mass of the body.
  • a is the acceleration acquired by the object.
• The inertial mass of a body is a measure of the resistance the body offers to a change in its state of rest or motion.
• This law is also used to define the SI unit of force: One Newton (N) is the force that produces an acceleration of 1 m/s² in the same direction and orientation as the force, when acting on an object that has a mass of 1 kg.