Newton's second law & Law of momentum | POINT classical mechanics

Newton's second law and momentum

In the study of motion, momentum and the relationship between applied forces and changes in motion form the backbone of classical mechanics. Momentum reflects the extent of an object's motion, while the principles connecting forces to momentum changes illuminate how objects accelerate and interact with their surroundings. This exploration delves into the interplay between momentum and the underlying framework that governs the influence of forces, setting the stage for a deeper understanding of the dynamics that shape both everyday phenomena and advanced technological systems.

momentum

You may notice that the ability to stop objects moving under inertia depends on

1- Mass

The greater the mass of the object, the greater its inertia

Therefore, it is difficult to stop a large truck, while it is easy to stop a small car if they have the same speed.

2- Velocity

The greater the speed of the object, the greater its inertia

Therefore, it is difficult to stop a car moving at a high speed, while it is easy to stop it if it is moving at a low speed.

The mass of a body (m) and its velocity (v) are related together by a physical quantity known as momentum (P) and are determined from this equation: P = mv

The unit of measurement of momentum is: kg.m/s

The dimensional formula for momentum is: M.L/T

(1) Momentum is a vector quantity.

Because it is the product of a scalar quantity (mass) and a vector quantity (velocity), and its direction is the same as the direction of the body's velocity.

(2) According to the relationship (P = mv), then:

Momentum: For a stationary body, it is equal to zero, no matter how much its mass increases because the body hasn't velocity (P = m×0 = 0)

and for a moving body, it is not equal to zero, no matter how little its mass because the body has velocity

Newton's second law

- The net force acting on an object is equal to the time rate of change in the momentum of that object.
Or
- If a net force acts on an object, it gives it an acceleration that is directly proportional to the force acting on it and inversely proportional to its mass.

Explanation of Newton's Second Law:

If a force affects an object, its velocity changes and accordingly it acquires acceleration. If:

1- Two different forces affect two equal masses

Then The mass that is affected by a greater force moves with greater acceleration

[The acceleration is directly proportional to the force when the mass is constant (aF)]

2 Two equal forces act on two different masses

The larger mass moves with less acceleration

[Acceleration is inversely proportional to mass when the force is constant (a1/m)]

Mathematical formula for Newton's second law

F = ma

The unit of force is km.m/s², equivalent to the newton, and its dimensional formula is M.L/T²

The Newton: is the amount of force that, if applied to a body with a mass of 1 kg, causes it to accelerate at a rate of 1 m/s² in the same direction as the force.

*Force (F) is a vector quantity:

Because it is the product of a scalar quantity (mass) by a vector quantity (acceleration) and the direction of acceleration is always in the same direction as the resultant force.

Force can be measured using a spring balance

Life applications of Newton's second law:

According to Newton's second law when a moving body collides with another stationary body, the collision force (F):

increase With the increase in the mass of the moving body (m) when other factors are constant, for example, a large truck colliding with an object is more destructive than a small car moving at the same speed.

increase With the increase in the change in the speed of the body (v) when other factors are constant, for example, a car colliding with an object is less destructive than a car with the same mass but moving at a higher speed.

Decreases with the increase in the time of impact, the time of change in the amount of motion (t) when other factors are constant, for example:

(1) A car colliding with a wall is more destructive than a pile of straw.

(2) An egg falling on a pillow does not break, while it breaks when dropped from the same height on Land.

(3) Airbags are used in cars to protect the driver in the event of a collision.

(4) A person falling from a high place into water is less injured than falling to the ground, and the severity of the injury increases with the height from which the person falls.

*If a body moves in a straight line on a horizontal surface under the influence of two forces, one of which is a horizontal pushing force (driving force)[Fd] and the other is a frictional force [Ff] between the surface and the moving body, then the resultant force [Fr] acting on the body is calculated from this equation: Result force = Driving force - Friction force

*If a body is affected by a constant net force (F), it moves with a uniform acceleration (a), and thus the three equations of motion apply to its motion.

to continue to newton's third law and the concepts of mass and weight

Reflecting on the dynamics of momentum and its connection to applied forces offers valuable insights into the behavior of moving objects. The way in which an object's motion is influenced by external forces not only enriches our theoretical understanding but also informs practical approaches in engineering and science. By focusing on these core concepts without delving into explicit definitions, we appreciate how the elegant interplay of momentum and force remains central to deciphering the complexities of motion and continues to inspire advancements in both academic research and real-world applications.