Step-by-Step Derivation and Real-Life Applications
Isaac Newton provided us with many laws and discoveries. One of his laws talks about motion and the forces it attains.
Starting with his first law, also known as the law of inertia tells us that if an object is moving or going in a specific direction or a straight line, its state won’t change until and unless an external force acts towards it. Then comes Newton’s second law of motion, which tells us that the time of change of any object is equal to its magnitude as well as its direction of imposition. This law is the most important and most talked-about law of the three laws of motion.
Formula of Newton’s Second Law of Motion
The Newton’s Second Law of Motion’s formula says that the force is equal to the product of the mass of the object and its acceleration.
Going further to Newton's third law, which states that to every reaction, there is
supposed to be an equal and opposite reaction.
Mathematical Formulation of Second Law of Motion
The second law of motion tells us about the relationship between force and acceleration. We can measure a lot of things with this law, including the force related to the mass and acceleration of the object. In simpler terms, this law conveys that any form of acceleration is the result of some form of force acting on or towards it. The force is also considered to be directly proportional to the direction of the object.
Equation describing the Newton’s second law of motion:
F = m*a,
Or a = \[\frac {F(net)}{m}\]
(Here, F = force m = mass a = acceleration)
Where, an ∝ f
And a ∝ \[\frac {1}{m}\]
Newton’s second law of motion is applied when starting with a simple example of the second law of motion if you push a chair and a bed with the same force. The chair will move and the bed might not. Since the chair has lesser volume and weight as compared to the bed, it will tend to attain more Acceleration. We can also take the example of a bicycle. Whenever you push the paddles of a cycle, it tends to move forward. This is a clear result of the second law of motion.
Application of Newton’s Second Law of Motion
An example of Newton’s second law of motion formula is pushing a car and truck by applying the same force. Since the car has a smaller mass, it will gain more acceleration than a truck which has a much larger mass.
Riding a bicycle is another instance of Newton’s Second Law of Motion formula at work. Here, the bike is the mass, and the rider pushing the paddles with his or her leg is the force.
Another instance of Newton’s Second law of motion formula can be observed in the cricket field. A fielder while catching a cricket ball pulls his or her hand back. It is done to delay the momentum of the ball, which is moving at an incredible speed. If the velocity is not reduced, then the ball which is moving at high speed will exert a considerable force on the player’s hand leading to serious injury.
You must have noticed that during athletic sports like long jumps, high jumps, a bed of sand or cushioned bed is placed at the place where the sportsperson is going to land. It is because, when the sportsperson lands after completing a long jump or high jump, his/her momentum becomes zero.
However, when momentum becomes zero very quickly, it results in the creation of a great force that may cause injury to the person, which is why a soft bed or bed of sand is placed to slow down the momentum of the sportsperson to prevent an accident. It is a practical application of Newton’s Second law Formula.
Do It Yourself
A force of 70 Newton was exerted on an object whose mass is equal to 30 kilograms. Calculate the acceleration of the said object according to the second law of motion formula.
An object has a mass of 12 kilograms. After applying force, it accelerates at 15 m/s2. Determine the value of force that was applied using Newton’s 2nd law formula.
Based on your understanding, derive the mathematical formula of the second law of motion.
FAQs on Understand Newton’s Second Law of Motion
1. What is Newton's second law of motion in simple terms?
In simple terms, Newton's second law of motion states that the acceleration of an object is directly related to the net force applied to it and inversely related to its mass. This means that if you push an object, it will speed up, and the harder you push, the more it will accelerate.
2. How is Newton's second law written as a mathematical formula?
The most common mathematical expression for Newton's second law is F = ma. In this formula:
- F represents the net force acting on the object.
- m represents the mass of the object.
- a represents the resulting acceleration.
3. What are some real-world examples of Newton's second law?
A simple real-world example is kicking a football. When you kick the ball, you apply a force to it. The ball, which has a certain mass, accelerates in the direction of the kick. If you kick it harder (more force), it accelerates more and travels faster. This perfectly demonstrates the relationship between force, mass, and acceleration.
4. What is the difference between mass and weight, and why is it important for understanding this law?
Mass is the measure of how much matter is in an object and it remains constant everywhere. Weight, on the other hand, is the force of gravity on that object. This distinction is critical for the second law because the 'm' in F=ma refers to an object's mass, not its weight. An object's mass is the same on Earth and the Moon, but its weight is different.
5. How does the concept of momentum help explain Newton's second law more fully?
While F=ma is very useful, the more complete formulation of Newton's second law states that force is equal to the rate of change of momentum. Momentum (p) is the product of mass and velocity (p = mv). This definition is more powerful because it can be applied to situations where the mass of an object changes, like a rocket that burns fuel and becomes lighter as it accelerates.
6. According to the second law, what happens if there is no net force on an object?
If the net force (F) applied to an object is zero, then according to the formula F=ma, its acceleration (a) must also be zero. This means the object's velocity will not change. It will either remain at rest if it was already still, or it will continue to move at a constant velocity if it was already in motion. This shows how the second law aligns perfectly with Newton's first law of inertia.
