Newtons Second Law of Motion and Momentum

The second of Newton’s laws of motion states that specific relations exist between mass, acceleration, and the force affecting the mass body. In other words, whatever mass moves with a certain acceleration has the measure of force which is equal to the product of that mass and acceleration (F = ma). Considered this way, this law also explains the concept of momentum which is mass multiplied by velocity.

What is the Second Law of Motion?

The acceleration of an item is determined by two variables: the net force acting on it and the mass of the object, according to Newton's second law. Therefore, the body's acceleration is proportional to the body's net force and inversely proportional to its mass. This means that the acceleration of an object increases as the force acting on it increases. Similarly, when an object's mass grows, so does its acceleration.

The second law thus reduces to the more common mass-acceleration product:

F = ma

F = mass * acceleration

Keep in mind that this relationship is only valid for things with a fixed mass. This equation states that when an item is subjected to an external force, it will accelerate and that the quantity of acceleration is proportional to the force. The quantity of acceleration is also inversely related to the item's mass; given equal forces, a heavier object will experience less acceleration. A force causes a change in velocity, and a change in velocity produces a force, according to the momentum equation. It's a two-sided equation.

There is a magnitude and a direction associated with velocity, force, acceleration, and momentum. This is referred to as a vector quantity by scientists and mathematicians. The equations presented here are vector equations that can be used in any of the component directions.

Newton's Second Law in Terms of Momentum

The net external force equals the change in momentum of a system divided by the time it changes, according to Newton's second law of motion. In equation form, this law is

$\mathrm{F}_{\text {net }}=\mathrm{dp} / \mathrm{dt}$

Here, p is the momentum of the body.

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For Changing Mass

Let us assume that we have a car at a point ( 0 ) defined by location $X_0$ and time $t_0$. The car has a mass $m_0$ and travels with a velocity $v_0$. After being subjected to a force $F$, the car moves to point 1 which is defined by location $X_1$ and time $t_1$. The mass and velocity of the car change during the travel to values $m_1$ and $v_1$. Newton's second law helps us determine the new values of $m_1$ and $v_1$ if we know the value of the acting force.

Taking the difference between point 1 and point 0, we get an equation for the force acting on the car as follows:

$$
F=\frac{m_1 v_1-m_0 v_0}{t_1-t_0}
$$
Let us assume the mass to be constant. This assumption is good for a car because the only change in mass would be the fuel burned between point " 1 " and point " 0 ". The weight of the fuel is probably small relative to the rest of the car, especially if we only look at small changes in time. Meanwhile, if we were discussing the flight of a bottle rocket, then the mass does not remain constant, and we can only look at changes in momentum.

For Constant Mass

For a constant mass, Newton's second law can be equated as follows:

$$
F=m \frac{v_1-v_0}{t_1-t_0}
$$
We know that acceleration is defined as the change in velocity divided by the change in time.
The second law then reduces to a more familiar form as follows:

$$
F=m a
$$
The above equation tells us that an object will accelerate if it is subjected to an external force. The amount of force is directly proportional to the acceleration and inversely proportional to the object's mass.

Application of Newton's Second Law

The use of Newton's second law of motion can be observed in determining the amount of force required to move or stop an item. Here are a few examples to assist you grasp what we're talking about:

1. Slab of Bricks is broken by a karate player.

In order to smash a slab of bricks, a karate player employs Newton's second law of motion. Because the force is proportional to the acceleration, the player likes to move his or her hands quickly over the brick slab. This aids him in gaining speed and exerting a commensurate amount of power. The amount of force required to break the bricks is sufficient.

2. Kicking a soccer ball

We apply force in a precise direction when we kick a ball, which is the direction in which it will travel. Furthermore, the harder we kick the ball, the more force we apply to it, and the further it will travel.

3. Object launched from a great height

When an object is hurled from a specific height, the earth's gravitational attraction aids acceleration. As the object approaches the Earth, its acceleration increases. Newton's second law of motion states that a body's acceleration is proportional to its force. When an object collides with the ground, the impact force is activated. This is why a brittle object thrown from a tall structure deforms more than one thrown from a lesser height.

4. Driving a vehicle

In simple terms, Newton's second law of motion asserts that any object with mass will produce an equivalent amount of acceleration if force is applied to it. When we turn on the ignition system of a car, for example, the engine creates enough force to allow the automobile to drive with proportionate acceleration.

5. A cart is being pushed.

In a supermarket, pushing an empty cart is easier than pushing one that is loaded. To accelerate, more mass requires more force.

6. Two individuals are walking.

If one of the two people walking is heavier than the other, the heavier person will walk more slowly since the lighter person's acceleration is greater.