Sir Frederick John Dealtry Lugard was born on 22 January, 1858. Between 1901 and 1928…

# SIMPLE GUIDANCE FOR YOU IN NEWTON’S LAWS OF MOTION

**Newton’s First Law**

Newton’s First Law, also known as the Law of Inertia, states that an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity in a straight line, unless acted upon by an external force.

There are two types of inertia mentioned in this law: the inertia of rest and the inertia of motion.

The inertia of rest refers to the tendency of an object to resist any change in its state of rest. For example, a book lying on a table will remain at rest until a force is applied to move it.

The inertia of motion, on the other hand, refers to the tendency of an object to resist any change in its state of motion. For example, a moving car will continue to move at a constant velocity in a straight line, unless acted upon by an external force such as friction or a change in direction from the steering wheel.

In both cases, the object will continue to behave according to its current state unless acted upon by an external force. This concept is fundamental to our understanding of motion and is the basis for many of the laws of physics.

**Distinction between inertia mass and weight**

Inertia mass and weight are both physical quantities that are related to the motion of an object, but they are distinct from each other. Here are the main differences between them:

**Definition:**Inertia mass refers to the amount of matter present in an object, which resists any change in its state of motion. Weight, on the other hand, refers to the force exerted on an object due to gravity, which is proportional to its mass.**Units:**Inertia mass is typically measured in kilograms (kg), while weight is measured in newtons (N). One kilogram of mass on Earth weighs about 9.8 newtons due to gravity.**Independence:**Inertia mass is independent of gravity and is an intrinsic property of an object. It remains the same regardless of the object’s location or environment. Weight, however, depends on the object’s location and the strength of the gravitational field it is in.**Measurement:**Inertia mass can be measured by comparing the acceleration of an object to a known force, as in the formula F = ma, where F is the force, m is the mass, and a is the acceleration. Weight can be measured by using a scale, which measures the force exerted by the object due to gravity.**Significance:**Inertia mass is significant in determining an object’s resistance to changes in its state of motion, such as its ability to accelerate or decelerate. Weight, on the other hand, is significant in determining an object’s interaction with other objects in a gravitational field, such as its ability to exert a force on another object.

In summary, inertia mass and weight are both important physical quantities, but they have different definitions, units, independence, measurement methods, and significance.

**Newton’s Second Law**

Newton’s Second Law of Motion states that the force acting on an object is directly proportional to the object’s acceleration, and inversely proportional to its mass. This law can be expressed mathematically as F = ma, where F is the force applied to an object, m is its mass, and a is its acceleration.

**Momentum** is a measure of an object’s motion and is defined as the product of an object’s mass and velocity (p = mv). According to Newton’s Second Law, the rate of change of an object’s momentum is equal to the net force acting on the object (F = dp/dt), where dp/dt represents the time derivative of the object’s momentum.

**Impulse** is the change in an object’s momentum that results from a force acting on it for a period of time. It is defined as the product of the force and the time interval over which it acts (J = Ft). By Newton’s Second Law, the impulse applied to an object is equal to its change in momentum (J = Δp).

**Using Ticker-Timer for Acceleration**

A ticker-timer is a timing device that can be used to measure the motion of an object with constant acceleration. To use a ticker-timer to determine the acceleration of a falling body, you need to set up the experiment as follows:

- Attach a ticker-timer to a vertical surface, such as a wall or a stand, so that it hangs down vertically.
- Attach a strip of ticker-tape to the ticker-timer, making sure it is positioned directly below the timer.
- Attach a small mass, such as a metal ball or a coin, to the end of a string.
- Hold the mass at rest above the ticker-tape and release it.
- The mass will accelerate under the force of gravity, causing the ticker-tape to be marked with a series of dots at equal intervals.
- Measure the time between each dot on the tape using a stopwatch or a timer.
- Calculate the acceleration of the falling object using the formula a = 2s/t^2, where s is the distance between two consecutive dots on the tape and t is the time interval between the dots.

If the force acting on the falling object is constant, such as in the case of gravity, then the acceleration will also be constant. This means that the distance between the dots on the ticker-tape will increase at a constant rate, and the time intervals between the dots will be equal. By measuring the time intervals between the dots and using the formula above, you can determine the acceleration of the falling object.

Overall, the use of a ticker-timer can be an effective method for determining the acceleration of a falling object when the accelerating force is constant.

**Linear Momentum Conservation**

Linear momentum is a physical quantity that describes the motion of an object in a straight line. It is defined as the product of an object’s mass and velocity, and it has both magnitude and direction. Mathematically, linear momentum is represented as:

p = m*v

where p is the linear momentum, m is the mass of the object, and v is the velocity of the object.

The conservation of linear momentum is a fundamental principle of physics that states that the total linear momentum of a closed system remains constant, provided there are no external forces acting on the system. This means that the sum of the linear momenta of all the objects in the system remains constant, even if the objects collide or interact with each other. This principle is a consequence of the law of conservation of energy and is applicable in various physical systems, including collisions between particles, rockets, and planets. The conservation of linear momentum is a powerful tool for analyzing and predicting the motion of objects in various physical situations.

**Elastic Collision Dynamics**

When two elastic bodies collide in a straight line, the collision can be classified as either elastic or inelastic.

In an elastic collision, the total kinetic energy of the two bodies is conserved. That is, the bodies bounce off each other and no energy is lost to deformation or heat. In this case, the relative velocity of the two bodies before the collision is equal and opposite to their relative velocity after the collision. The conservation of momentum and kinetic energy can be expressed as follows:

m1v1i + m2v2i = m1v1f + m2v2f (Conservation of momentum) 1/2m1v1i^2 + 1/2m2v2i^2 = 1/2m1v1f^2 + 1/2m2v2f^2 (Conservation of kinetic energy)

where m1 and m2 are the masses of the two bodies, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities.

In an inelastic collision, the two bodies stick together after the collision, and some energy is lost to deformation or heat. In this case, the conservation of momentum is still valid, but the conservation of kinetic energy is not. The velocity of the combined mass after the collision can be calculated using the following equation:

(m1v1i + m2v2i)/(m1 + m2) = vf

where vf is the final velocity of the combined mass.

The coefficient of restitution (e) is a measure of the elasticity of the collision and is defined as the ratio of the relative velocity of the bodies after the collision to the relative velocity before the collision. In an elastic collision, e = 1, while in an inelastic collision, 0 < e < 1.

The behavior of elastic bodies in a collision is important in many fields, including physics, engineering, and sports. Understanding the dynamics of collisions can help design safer cars, improve sports equipment, and even model the behavior of particles in a gas.

**Newton’s Third Law**

Newton’s Third Law states that for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on another object, the second object will exert an equal but opposite force back on the first object. In other words, the forces always come in pairs.

This law applies to all interactions between objects, whether they are solid, liquid, or gaseous. It is important to note that the forces in the action-reaction pair always act on different objects, and they have the same magnitude but opposite directions.

For example, when you push on a wall, the wall pushes back on you with an equal and opposite force. When a rocket expels exhaust gases out the back, the force of the gases pushing out is equal and opposite to the force of the rocket moving forward.

Understanding and applying Newton’s Third Law is crucial in many fields, including physics, engineering, and mechanics, as it helps predict the motion and behavior of objects and systems under various conditions.

**Applications**

Newton’s laws of motion are fundamental principles in classical mechanics that describe the motion of objects.

**Recoil of a gun:**According to Newton’s third law of motion, for every action, there is an equal and opposite reaction. When a gun fires a bullet, the bullet exerts a force on the gun that is equal in magnitude and opposite in direction to the force exerted on the bullet by the gun. This causes the gun to recoil in the opposite direction to the bullet.**Jet propulsion:**Newton’s second law of motion states that the force acting on an object is equal to its mass times its acceleration. In the case of a jet engine, fuel is burned to produce a high-speed exhaust stream that propels the airplane forward. By Newton’s second law, the force of the exhaust stream is equal to the mass of the fuel being burned times the acceleration of the exhaust stream.**Rocket propulsion:**Rocket propulsion also relies on Newton’s third law of motion. The rocket expels exhaust gases out of the back of the rocket at high speeds, which produces a force that propels the rocket forward. The force of the exhaust gases is equal and opposite to the force propelling the rocket forward, as required by Newton’s third law. The greater the velocity of the exhaust gases, the greater the force produced and the faster the rocket will travel.

In summary, Newton’s laws of motion are essential for understanding the physics behind the motion of objects and have many practical applications in engineering and technology, including the recoil of guns, and jet and rocket propulsion.