One Dimensional Motion
Mechanics is an area of science concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle and Archimedes.
Mechanics is the branch of Physics dealing with the study of motion.
No matter what your interest in science or engineering, mechanics will be important for you - motion is a fundamental idea in all of science.
Mechanics can be divided into 2 areas
Kinematics, dealing with describing motions, and dynamics, dealing with the causes of motion.
In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics.
Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces.
The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. It is also widely known as Newtonian mechanics.
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies.
Besides this, many specializations within the subject deal with solids, liquids and gases and other specific sub-topics. Classical mechanics also provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.
When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules.
When both quantum mechanics and classical mechanics cannot apply, such as at the quantum level with high speeds, quantum field theory (QFT) becomes applicable.
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Motion
In physics, motion is a change in position of an object over time.
Motion is described in terms of displacement, distance, velocity, acceleration, time and speed.
Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame.
Figure 1 – 1: Types of motion
For the concept of motion in one direction, consider a motion of a body along a straight track.
The subject of motion in physics is called a, "body".
One dimensional motion is motion along a straight line.
Reference Frame
In physics, a frame of reference (or reference frame) may be defined as a coordinate system or set of axes within which position, orientation and other properties of objects can be measured.
a framework that is used for the observation and mathematical description of physical phenomena and the formulation of physical laws, usually consisting of an observer, a coordinate system, and a clock or clocks assigning times at positions with respect to the coordinate system.
Distance and Displacement
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
A displacement is a vector whose length is the shortest distance from the initial to the final point of position.
Speed
Speed is the rate of change of distance with time.
In order to calculate the speed of an object we must know how far it's gone and how long it took to get there.
Mathematically
Let's say you drove a car from New York to Boston. The distance by road is roughly . If the trip takes four hours, what was your speed?
Velocity
Velocity is defined as the rate of which displacement changes over time.
It is a vector quantity i.e. it requires both magnitude and direction. In terms of mathematics, the most general definition of velocity is, . What this means is that velocity is the derivative of displacement (x) with respect to time.
Average Velocity
Average velocity is the displacement divided by the time.
For the special case of straight line motion in the x direction, the average velocity takes the form
Acceleration
Acceleration, in physics, is the rate of change of velocity of an object with respect to time.
A body with a positive acceleration is gaining velocity over time. A body with a negative acceleration is losing velocity over time. It is denoted by .
Mathematically
This car is travelling at a speed of −1
This car is travelling at a speed of −1 east
Newton’s Laws of Motion
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces.
First Law
Objects at rest remain at rest and objects in motion remain in motion in a straight line unless acted upon by an unbalanced force.
Second Law
“The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.”
Third Law
“To every action there is always an equal and opposite reaction.”
Force
Force is defined as that, external agency that changes or tends to change the state of rest or uniform motion of a body in a straight line.
Momentum
The momentum of a particle is defined as the product of its mass times its velocity. It is a vector quantity.
The momentum of a system is the vector sum of the momenta of the objects which make up the system. Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude:
Figure shows an object of mass moving with velocity has momentum
Principle of Conservation of Linear Momentum
In physics, the term conservation refers to something which doesn't change. This means that the variable in an equation which represents a conserved quantity is constant over time. It has the same value both before and after an event.
To prove this principle, we consider a collision between two spheres A and B having masses of 1 and respectively. Let 1 and be the velocities of the spheres before collision such that 1 and moving on the same straight line as shown in the figure.
After collision, let their velocities be 1 and on the same line. We can write Rate of change of momentum of the first particle (A)
= −
Rate of change of momentum of the second particle (B)
= −
If they collide with each other for a short time interval , each sphere exerts a force on the other sphere. According to Newton’s third law
Applied Force = - Reaction Force FAB = - FBA
− = - −
1 1 1 1
Initial momentum of the two particles = Final momentum of the particles.
Impulse
Impulse is defined as the product of force acting on an object and the time during which the force acts.
The symbol for impulse is . So, according to the definition of impulse
Suppose, a force is applied to a boulder for . What will be the impulse of this force?
Inertia
Inertia is the resistance of any physical object to any change in its state of motion (this includes changes to its speed, direction or state of rest).
