1. Understanding Newton’s Second Law of Motion
Newton’s second law explains how force affects the motion of an object. It tells us that the acceleration of an object depends on two things: the force applied and the mass of the object.
In simple words: greater the force, greater the acceleration; greater the mass, lesser the acceleration.
1.1. What the Law States
“The acceleration produced in an object is directly proportional to the force applied and inversely proportional to its mass.”
This means that applying more force makes an object accelerate faster, and objects with more mass require more force to show the same acceleration.
2. Mathematical Form of the Second Law
The law can be expressed using the famous formula:
\( F = ma \)
This formula is one of the most important equations in physics.
2.1. Meaning of Each Term
- \( F \): Force applied on the object (in Newtons)
- \( m \): Mass of the object (in kilograms)
- \( a \): Acceleration produced (in m/s²)
2.2. How Mass Affects Acceleration
For the same force, a heavier object will accelerate less, and a lighter object will accelerate more:
\( a = \dfrac{F}{m} \)
3. Explaining the Law with Everyday Examples
Newton’s second law is easy to understand with real-life situations involving pushing, kicking, throwing, and lifting objects.
3.1. Example 1: Kicking a Ball
A stronger kick (more force) makes a football accelerate more. A heavier ball (more mass) accelerates less even with the same kick.
3.2. Example 2: Pushing Shopping Carts
An empty cart accelerates quickly when pushed, but a filled cart accelerates slowly. Same force, different mass.
3.3. Example 3: Throwing Stones
A small stone accelerates much more than a large stone when the same force is applied.
4. Impulse and Newton’s Second Law
Impulse is the force applied over a short time. The second law explains how impulse changes momentum:
\( F = \dfrac{\Delta p}{\Delta t} \)
where momentum \( p = mv \).
4.1. Impulse–Momentum Relation
When a force acts on an object for a small time, it changes its momentum. This is why:
- A cricketer pulls hands backward while catching a ball.
- Airbags in cars increase the stopping time during accidents.
5. Units of Force and Acceleration
In the SI system:
- Force is measured in Newtons (N)
- Acceleration is measured in m/s²
- Mass is measured in kilograms (kg)
5.1. Definition of 1 Newton
1 Newton is defined as the force needed to give a mass of 1 kg an acceleration of 1 m/s².
\( 1 \text{ N} = 1 \text{ kg·m/s}^2 \)
6. Simple Numerical Example
Let’s apply the formula \( F = ma \) to a simple situation:
6.1. Example
A 10 kg object is pushed with a force of 30 N.
Acceleration:
\( a = \dfrac{F}{m} = \dfrac{30}{10} = 3 \text{ m/s}^2 \)
This means the object’s velocity increases by 3 m/s every second.