Newton's Second Law Of Motion

What is Newton’s Second Law of Motion?

Newton’s second law states that

The acceleration of an object is dependent on the mass of the particle and force acting on it.

Newton’s Second Law of Motion Formula

F = ma

The acceleration is caused by a force which is directly proportional to the amount of force and is indirectly proportional to the amount of inertia. Following is the equation which is obtained from the statement:

\(\vec{a}=\frac{\vec{F}_{net}}{m}\)

Where,

  • \(\vec{a}\) is the acceleration
  • \(\vec{F_{net}}\) is the net force
  • m is the mass

But we consider only the magnitude of force and acceleration making the equation scalar quantity which is given as:

\(\vec{F_{net}}=ma\)

Component Form of Newton’s Second Law

The vector form of Newton’s second law of motion is obtained from the definition. According to Newton’s second law, the net force of an object is an influence of the environment, acceleration is the object’s response, and the strength of an object is inversely proportional to the mass of the object. So it can be said that larger the mass, smaller is the acceleration.

Following is the vector form of Newton’s second law of motion:

\(\vec{F_{x}}=m\vec{a}_{x}\)

\(\vec{F_{y}}=m\vec{a}_{y}\)

\(\vec{F_{z}}=m\vec{a}_{z}\)

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Application of Second Law

The Second law of motion becomes easy if we know an object’s mass and acceleration so that we can find the net force on the object.

This concept is useful for blocks and rope problems and also for pulley system problems. Also we need to understand that tension is a force so the net tension of an object is the same as the net force.


Newton’s Second Law and Momentum

Newton’s second law in terms of momentum is stated as

The instantaneous rate at which an object’s momentum changes is equal to the net force acting on the body.

Following is the vector equation for Newton’s second law of momentum:

\(\vec{F}_{net}=\frac{d\vec{p}}{dt}\)

Newton described momentum as quantity of motion which is a way of combining velocity of an object and its mass.

Momentum \(\vec{p}\) is defined as the product of the mass of an object and its velocity which is given as:

\(\vec{p}=m\vec{v}\)

Since velocity is a vector quantity, momentum too is a vector quantity.

The value of net force after substituting for momentum is given as:

\(\vec{F}_{net}=m\frac{d(\vec{v})}{dt}=m\vec{a}\)

Therefore, above is the Newton’s second law of motion in terms of momentum.

Newton’s Second Law Examples

Example 1:

If there is a block of mass 2kg, and a force of 5N is acting on it in the positive x-direction, and a force of 3N in the negative x-direction, then what would be its acceleration?

Newton's 2nd Law

To calculate its acceleration, we first have to calculate the net force acting on it.

\(F_{net}\) = 5N – 3N = 2N

Mass = 2kg

∴ Acceleration = \( \frac 22 \)  = 1 m/\(s^2\)

Example 2:

Newton’s second law is applied in daily life to a great extent. For instance, in Formula One racing, the engineers try to keep the mass of cars as low as possible. Low mass will imply more acceleration, and the more the acceleration, the chances to win the race are higher.

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