Newton's Laws of Motion | Formula, Examples and Questions
Newton's Laws of Motion, formulated by the renowned English physicist Sir Isaac Newton, are fundamental principles that form the core of classical mechanics. These three laws explain how objects move and interact with forces, shaping our view of everything from everyday movement to the dynamics of complex systems. Whether it's how a car accelerates or predicting the trajectory of a satellite, Newton's Laws are essential in analysing the behaviour of moving objects.
Newton's Laws of Motion in physics are the fundamental laws that describe the relationship between the motion of an object and the forces acting on it. There are three laws under Newton's Law of Motion:
- First Law of Motion
- Second Law of Motion
- Third Law of Motion
First Law of Motion (Law of Inertia)
An object at rest will remain at rest, and an object in motion will continue in a straight line at constant speed, unless acted upon by an external unbalanced force. This is also known as the law of inertia.
- This law introduces the concept of inertia, the resistance of an object to changes in its motion.
- An object’s mass determines its inertia, with heavier objects requiring more force to change their motion.
- In the absence of external forces, such as friction or gravity, an object in motion will continue indefinitely.
- Objects at rest will remain stationary unless a force is applied to move them.
- The law is foundational to other laws of motion and is crucial in explaining real-world scenarios like the motion of vehicles or the trajectory of space objects.
For Example ,
- A car parked on a level surface will remain stationary until an external force, such as a push, is applied, In this picture a person applied a force on car but the car didn’t move.
- A rolling football eventually stops due to the friction force on the ground. ( Change in State: Motion to rest , Force Applied: Friction)
For more, read Newton’s First Law of Motion
Newton's Second Law of Motion
The rate of change of an object’s momentum is directly proportional to the applied unbalanced force and occurs in the direction of the force.
- Newton's Second Law of Motion defines the relationship between force, mass, and acceleration.
- It can be mathematically expressed as F = ma, where "F" is the force applied, "m" is the mass of the object, and "a" is the acceleration produced.
- The law implies that the acceleration of an object depends on the net force acting upon it and its mass.
- The larger the mass of an object, the smaller its acceleration for a given force.
- This law is crucial for calculating the force required to move objects, from everyday activities like pushing a cart to complex calculations in engineering and space missions.
For Example,
- Catching a ball on the cricket field by a fielder is the best example of Newton's second law of motion. When the fielder catches the ball it moves its hands backward to increase the time of the catch resulting in lowering the force by the ball on the hands of the catcher.
- Imagine you’re pushing a shopping cart. The harder you push (more force), the faster it rolls (accelerates), right? That’s the basic idea behind Newton’s Second Law of Motion!
Formula for Newton’s Second Law of Motion
Newton's Second Law of Motion explains how a force affects a body's motion by changing its velocity and acceleration.
Mathematically it is shown as,
Force ∝ (Change in Momentum) / (Time Taken)
F ∝ d(mv)/dt
F = kd(mv)/dt
F = k\{v.dm/dt + m.dv/dt\} As mass is always constant,
\{dm/dt = 0\}
F = km.dv/dt Experimentally, k = 1
F = m.dv/dt
we \ know \ that, \ dv/dt = a F= ma
where,
- F is the Force Applied
- m is the Mass of Object
- a is the Acceleration of Object
For more, read : Newton’s Second Law of Motion
Try it now!
Imagine you're pushing a sled on a smooth surface. If you apply a constant force, how does the acceleration of the sled change if you increase its mass? What happens to the sled's acceleration if you increase the force applied while keeping the mass constant? Conduct an experiment to verify how force and mass affect the sled's acceleration, and record your observations."
Newton’s Third Law of Motion
Newton's third law states that for every action, there is an equal and opposite reaction.
- Forces described by Newton's Third Law always come in pairs, meaning two objects interact through forces that are equal in magnitude but opposite in direction.
- The law helps explain the conservation of momentum in systems where objects collide. The momentum lost by one object is gained by the other, keeping the total momentum constant.
For Example,
- Recoil of the gun when a bullet is fired is an example of Newton's Third Law of Motion.
⁛ This means that whenever one object exerts a force on a second object, the second object exerts a force of equal magnitude but in the opposite direction on the first object.
This law is also explained as, when an object "A" applies a force of "F1" on object "B" then "B" applies a force of "F2" on the object such that,
F1 = -F2
Third Law of Motion by Newton is also called the Law of Action and Reaction.
- When you push off the boat to jump onto the dock, the force you apply to the boat causes a reaction where the boat pushes back on you with an equal and opposite force. This mutual interaction causes the boat to move backward as you move forward.
For more, read Newton’s Third Law of Motion
Solved Examples on Newton's Laws of Motion
Question 1. Find out how much net force will be needed to accelerate a 2500 kg truck at 5.50 m/s2.
Given,
- Acceleration (a) = 5.50 m/s2
- Mass of the Truck (m)= 2500 kg
Hence,
Force = Mass × Acceleration
F = 2500 × 5.5
F = 13750 N
Net force will be needed to accelerate a 2500 kg truck at 5.50 m/s2 is 13750 N.
Question 2. What will happen If a net force of 6 N is applied on 0.5 kg object. Calculate the acceleration of the material.
Given,
- Force (F) = 6 N
- Mass (m) = 0.5 kg
Acceleration (a) = ?
Force = Mass × Acceleration
F = m × a
a = F/m
a = 6/0.5
a = 12 m/s2
The acceleration of the object is 12 m/s2
Question 3. If a racing car driver is on the race track in order to overtake accelerates his racing car first at the rate of 8 m/s2 and then at the rate of 16 m/s2. Find the ratio of the forces exerted by the engine for the acceleration change.
Given,
- a1 = 8 m/s2
- a2 = 16 m/s2
We have to find the ratio of F1/F2
F1/F2 = ma1/ma2
Mass of the racing car is same in both the cases,
F1/F2 = a1/a2
F1/F2 = 8/16
F1/F2 = 1/2 = 1:2
Question 4: When a bullet of mass 20 gm is shot from a gun that has an initial velocity of 40 m/s the mass of the gun is 5 kg. What is the initial recoil velocity of the gun?
Given,
- Mass of Bullet (m1) = 20 gm or 0.02 kg
- Mass of Gun (m2) = 5 kg
- Initial velocity = 40 m/s
Let final velocity is v m/s
By Law of Conservation of Momentum,
0 = 0.02 × 40 + 5 × v
5 × v = -0.8
v = -0.8 / 5
v = -0.16 m/s
Practice Questions on Newton's Laws of Motion
Problem 1: A book is placed on a table. Describe what happens to the book when:
a) No force is applied to it.
b) A gentle horizontal force is applied to the book.
c) A vertical force is applied to the book.
Problem 2: What will happen to a stationary soccer ball if no external forces are applied to it?
Problem 3: A bicycle is moving on a flat road. What force causes it to eventually stop if no one keeps pedaling? How does this relate to the first law?
Problem 4: An object with a mass of 5 kg is subjected to a net force of 20 N. Calculate the acceleration of the object.
Problem 5: A force of 10 N is applied to a 2 kg object. What is the object’s acceleration?
(Hint: Use the formula F=ma)
Problem 6: If a force of 15 N causes an object to accelerate at 3 m/s², what is the mass of the object?
Problem 7: When you jump off a boat, the boat moves backward. Explain this observation using Newton's third law.
Problem 8: When a rocket launches, it expels gas downwards, yet it moves upwards. How does this demonstrate Newton's third law?
Problem 9: Two ice skaters, one with a mass of 60 kg and the other with a mass of 80 kg, push off each other on an ice rink. If the 60 kg skater exerts a force of 200 N on the 80 kg skater, what force does the 80 kg skater exert on the 60 kg skater?
Conclusion
Newton's laws of motion explain how forces affect the movement of objects. These principles are essential to classical mechanics and offer a foundation for understanding the behavior and interactions of objects. They help us predict how objects will move in response to various forces and are crucial for fields like engineering and physics. By applying these laws, we can analyze everything from the motion of everyday objects to complex systems in space.
