Projectile motion refers to the curved path an object follows when it is thrown or projected into the air and moves under the influence of gravity. In this motion, the object experiences two independent motions: horizontal motion (along the x-axis) and vertical motion (along the y-axis).
Projectile Motion can be seen in our daily life very easily as from throwing a rock to launching a cannonball are all examples of Projectile Motion. It is one of the fascinating topics in the field of physics which has very wide real-world applications. From sports to military technologies all leverage the understanding of Projectiles and their motion under the force of gravity.
Understanding Projectile motion helps us predict the trajectory, velocity, and range of objects that are thrown, launched, or dropped in the air. In this article, we will learn the key concepts and formulas of projectile motion and use those to solve real-world scenario-based problems.
What is Projectile Motion?
The object which is thrown at some angle with some initial velocity performs the parabolic motion under the influence of the force of gravity and is called the projectile. The path of the projectile is known as the trajectory of the motion. All the objects thrown into the air such as stones by some random child, football kicked by some athlete, cricket balls thrown by the player or hit by the batsman, etc. are all examples of projectiles.
Projectile MotionProjectile Motion Definition
A projectile is any object thrown into space with only gravity acting on it. The primary force acting on a projectile is gravity. This is not to say that other forces do not act on it; rather, their impact is minimal when compared to gravity.
When a particle is thrown obliquely near the earth's surface, it follows a curved path with constant acceleration toward the earth's center (we assume that the particle remains close to the surface of the earth). The path of such a particle is known as a Projectile Path, and its motion is known as Projectile Motion.
The object's horizontal motion is uniform and constant, meaning it moves at a constant speed in a straight line, unaffected by gravity. However, the object's vertical motion is affected by gravity, causing it to accelerate downwards.
As a result of these combined motions, the object follows a curved path known as a parabola. Examples of projectile motion include throwing a ball, launching a rocket, or shooting a cannonball. The path of the projectile depends on its initial velocity, angle of projection, and the force of gravity acting on it.
Properties of Projectile Motion
Projectile motion is one of the most common types of motion in a plane. The only acceleration acting in a projectile motion is the vertical acceleration caused by gravity (g). As a result, equations of motion can be used separately in the X- and Y-axes to determine the unknown parameters.
- The motion of a projectile in two dimensions is divided into two parts:
- Horizontal motion in the x-direction with no acceleration and
- Vertical motion in the y-direction with constant acceleration due to gravity.
- To simplify calculations, projectile motion is typically calculated without accounting for air resistance.
Example of Projectile Motion
Projectile motion is an example of Projectile Motion, as it occurs in a two-dimensional plane. The motion of a projectile i.e., an object performing the projectile motion, is under the influence of gravity due to which in the absence of gravity i.e., space, the objects do not perform the projectile motion. Let's consider examples of projectile motion in the real world.
One familiar example is a ball thrown in the air by some player. When a player throws a ball in the air, the ball follows a projectile motion. The momentum of the player gives the player an advantage by allowing them to adjust the trajectory of the ball. Besides this, other examples of projectile motion include throwing a basketball, a stone into a river, a javelin, an angry bird, kicking a football, or firing a bullet.
All the above-mentioned motions share the common characteristic of being influenced primarily by gravity after release. This means that when an object is thrown into the air, we can predict its duration in the air and the distance it will travel before hitting the ground, assuming we neglect air resistance. In the horizontal direction, there is no acceleration if air resistance is ignored.
Consequently, when an object is thrown near the Earth's surface, its motion can be treated as two-dimensional, with acceleration occurring in one direction.
Projectile MotionTo illustrate this point, let's consider a rolling ball. If the ball follows a specific path, it may seem like it is moving in two dimensions. However, if the ball rolls in a straight line, it becomes the motion in one dimension. The choice of axis does not change the nature of the motion itself.
Projectile MotionOn the other hand, when a ball is thrown at an angle with some initial velocity, its velocity has components in the x, y, and z directions. It might seem like this motion is three-dimensional. However, a plane can fully describe this type of motion, indicating that it is a two-dimensional motion. Regardless of the projection angle, as long as the body remains close to the Earth's surface and air resistance is negligible, the motion will be two-dimensional. The choice of axes can be rotated to define the ball's motion entirely.
In conclusion, the dimension of an object's motion is determined by the minimum number of coordinates needed to fully describe its motion. Projectile motion occurs in a two-dimensional plane and is applicable to various real-life scenarios.
Terms Related to Projectile Motion
Consider the following example of a ball that is projected at an angle θ from the point O with respect to the horizontal x-axis with an initial velocity u:
Before understanding the derivation of the relation for projectile motion let's first introduce some terms used in it, which are:
Angle of Projection
The angle at which the body is projected with respect to the horizontal is referred to as the angle of projection. In the above diagram, θ is the angle of projection
Velocity of Projection
The velocity with which the body is thrown is referred to as the velocity of projection. Here, u is the initial velocity of the projectile that has vertical and horizontal components as shown in the diagram.
Point of Projection
A point of projection is the point from which the body is projected in the air. In the above diagram, point O is known as the point of projection.
Projectile Trajectory
The path taken by a projectile in the air is referred to as the projectile's trajectory and in the diagram, the path followed by the projectile is the trajectory of a projectile.
Horizontal Range
The horizontal distance travelled by the body performing projectile motion is referred to as the range of the projectile, and in the above-mentioned diagram OB is Horizontal Range.
Equation of Motion for Projectile
We know that the linear equations of motion are:
v = u + at
S = ut + 1/2(at2)
v2 = u2 + 2aS
Applying the above equation for projectile motion the equation will be:
v = u - gt
S = ut - 1/2(gt2)
v2 = u2 - 2gS
Where,
- u is Initial Velocity,
- v is Final Velocity,
- g is Acceleration due to gravity,
- S is Displacement, and
- t is Time.
Projectile Motion Formula
There are various formulas for the Projectile Motion for calculation of various this such as:
- Time of Flight
- Horizontal Range
- Maximum Height
Let's discuss these formulas with various different cases as follows:
Time of Flight of Projectile Motion
Time of flight is the total time taken by the projectile from start to end. We can calculate it as,
In the Y direction total displacement (Sy) = 0
Taking motion in Y direction only,
Sy = uyt - 1/2(gt2)
For object to achive peak height uy = u sinθ and Sy = 0, and t it the time taken by object to achive the peak height.
0 = usinθ - 1/2(gt2)
⇒ t = 2usinθ/g
Time of Flight (2t) = 2usinθ/g
Now there can be various cases of the above-mentioned formula, let's consider the following cases:
Case 1: If θ = 90°
As we can see from the formula of Time of flight, time taken by the projectile is directly proportional to the angle of projection. For any given initial velocity(u) will be constant and g is always constant i.e., g=-9.8 m/s2.
When projectile is projected at an angle of 90° time of flight will be maximum.
tmax = 2usinθ/g = 2u/g
[As sin 90° = 1]
Case 2: If θ = 30°
When the projectile is projected at an angle of 30° time of flight is half of the tmax as sin30° = 1/2.
t = 2usin30°/g = tmax/2
Horizontal Range of Projectile
The horizontal range is the distance covered by the projectile horizontally and it can be calculated by the distance = speed/time formula, where speed is the horizontal component of initial speed or velocity and time is the total time of flight. Thus, the formula for Horizontal Range is given by:
Range (R) = ux × t
And as ux = u cosθ and t = 2usinθ/g
Range (R) = ucosθ × 2usinθ/g
As a result, the Horizontal Range of the projectile is given by (R):
Horizontal Range (R) = u2sin2θ/g
Now there can be various cases of the above-mentioned formula, let's consider the following cases:
Case 1: If θ = 90°
When projectile is projected at an angle of 90° Horizontal range will be zero, because projectile will strike at the same point where the projectile is projected.
R = u2sin2θ/g = 0
[As sin 2θ = sin 180 = 0, at θ = 90°]
Case 2: If θ = 45°
When projectile is projected at 45° Horizontal Range of the projectile is maximum.
Rmax = u2sin2θ/g = u2/g
As sin 90 = 1 and it is the maximum value of the trigonometric ratio sin.
Maximum Height of Projectile
It is the highest point of the particle (point A). When the ball reaches point A, the vertical component of the velocity (Vy) will be zero.
0 = (usinθ)2 - 2gHmax
[ Here, S = Hmax , vy = 0 and uy = u sin θ ]
Therefore, the Maximum Height of the projectile is given by (Hmax):
Maximum Height (Hmax) = u2sin2θ/2g
Now there can be various cases of the above-mentioned formula, let's consider the following cases:
Case 1: if θ = 90°
If we project a projectile at an angle of 90° it achieves maximum height (Hmax).
Hmax = u2sin2θ/2g = u2/2g
[As, sin2 90° = 1 ]
Case 2: if θ = 45°
When the projectile is projected at an angle of 45°, the height of the projectile is half of its maximum height (Hmax) as sin245° = 1/2.
H = u2sin2θ/2g = (1/2)u2/2g = Hmax/2
We can also say that if the projectile angle is 45° than Horizontal range of projectile will be 4 time the height of projectile.
H = u2/4g = R/4
OR
R = 4H
[ As Horizontal range at θ = 45°, R = u2/g ]
Equation of Trajectory of Projectile
The equation of the trajectory is a path followed by the particle during the projectile motion. The equation is:
y = x tanθ - gx2/2u2cos2θ
Derivation of Equation of Trajectory of Projectile
Let's consider a projectile launched at an angle θ to the horizontal with an initial velocity uo. Assuming there is no air resistance, the only force acting on the projectile is the force of gravity, which acts vertically downward.
The equation of motion in the x direction is given by:
x = uo cos θ × t . . .(i)
Where,
- x is the horizontal distance travelled by the projectile,
- t is the time elapsed, and
- uo is the initial velocity, and θ is the angle of launch.
The equation of motion in the y direction is given by:
y = uo sin(θ) × t - 1/2 × g × t2. . .(ii)
Where,
- y is the vertical distance travelled by the projectile,
- g is the acceleration due to gravity (approximately 9.8 m/s^2), and
- t is the time elapsed.
From equation (i), t = x/(uo cos θ), put this in equation (ii)
y = uo sin(θ) × x/(uo cos θ) - 1/2 × g × (x/(uo cos θ))2
OR
y = x tan θ - g x2/(2uo2 cos2 θ)
This is the equation of a parabolic trajectory, which describes the path followed by the projectile.
Parabolic Motion of Projectile
This is the equation of projectile motion it is similar to the parabola (y = ax + bx2) as a = tan θ and b = g/(2uo2 cos2 θ). So, we can say that projectile motion is always parabolic in nature.
Application of Projectile Motion
There are various applications of Projectile Motion, some of which are as follows:
Sports: In many sports such as football, cricket, archery, shooting, rugby, etc. athletes need to have a good understanding of projectiles and their motion as this can help them predict the movement in the game and help them have an upper edge on their opponent team.
Military: In many Military Technologies advanced projectiles such as missiles, tanks, aerial shell bombing, etc. and to make this technological advancement in the military understanding of advanced projectile motion is much needed.
Photography: In many scenarios, the photographer needs to take a photo of a moving object such as sports or any other creative curiosity of the photographer. To click that perfect picture there, the photographer needs to have some understanding of the projectile motion so that he can predict the position of the object which needs to be photographed.
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Sample Questions on Projectile Motion
Question 1: What is a projectile? Prove that the path of a projectile is parabolic.
Solution:
Projectile: A projectile is any object thrown into space with only gravity acting on it is called a projectile.
We know that the equation of projectile is, y = x tan θ - gx2/2u2cos2θ comparing the equation with y = ax + bx2
Here,
The above equation of trajectory is similar to the equation of a parabola.
Hence, the path of a projectile is parabolic.
Question 2: At what angle projectile should be projected so that the height and Range of the projectile will be equal?
Solution:
If height and horizontal range will be equal,
H = R.
⇒ u2sin2θ/2g = u2sin2θ/g
⇒ sin2θ = sin2θ [Here, sin2θ = 2 sinθ cosθ and tanθ = sinθ/cosθ]
⇒ tan θ = 4
So, θ = tan-1(4)
Question 3: Define horizontal range and find the range of a projectile thrown at 98 m/s with an angle of 30 degrees from horizontal. (use g = 9.8 m/s2)
Solution:
Horizontal Range: The horizontal distance travelled by the body performing projectile motion is referred to as the range of the projectile.
Horizontal Range, R = u2sin2θ/g
⇒ R = (98)2 × (60°) / 9.8
⇒ R = 490√3 m
Question 4: Name the physical quantities which will remain unchanged during the projectile motion.
Solution:
The physical quantities that remain unchanged during the projectile motion are,
- Horizontal component of Velocity
- Horizontal component of Momentum
- Acceleration
- Total Energy
Question 5: What is the maximum height attained by a ball of mass 100 g projected at an angle of 30° from the ground with an initial velocity of 11 m/s and an acceleration due to gravity of g = 10 m/s2?
Solution:
We know that the formula for maximum height is,
H = (usinθ)2/2g
Given: u = 11 m/s, θ = 30°, g = 10 m/s2
Hence, Putting the values we get,
H = 1.5125 m
Question 6: A Football is launched at a 45° angle from the ground with an initial velocity of 10 m/s; the gravity acceleration is g = 10 m/s2. What is the time of the flight?
Solution:
We know that the formula for calculating the time of flight is,
t = 2(usinθ/g)
Given: θ = 45°, u = 10m/s, g = 10m/s2
Putting the values we get,
t = 1.4142 s
Question 7: A projectile is projected from point O at an angle of 30° with an initial velocity of 30 m/s. The projectile hits the ground at point M. (Consider acceleration of gravity g = 10m/s2) Find the following:
- What is the total time of the flight?
- What is the Horizontal Range of the projectile (OM)?
- What is the maximum height of the projectile?
Solution:
Given:
- Initial velocity u = 30m/s.
- Angle of projection, θ = 30°.
1. Time of Flight
We know that the total time of flight by the projectile is given by-
t = 2usinθ/g
Putting the given values,
t = 2 × 30 sin30°/10
⇒ t = 3 s
2. Horizontal Range
We know the formula for the horizontal range is:
R = u2sin2θ/g.
Putting the values we get,
R = (30)2 sin60° /10
⇒ R = 45 √3 m.
3. Maximum Height
Maximum height of the projectile is given by the formula:
Hmax = u2sin2θ/2g
Putting the values we get,
Hmax = (30)2sin230°/2 × 10
⇒ Hmax = 11.25 m.
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Modulus of RigidityModulus of rigidity also known as shear modulus, is used to measure the rigidity of a given body. It is the ratio of shear stress to shear strain and is denoted by G or sometimes by S or μ. The modulus of rigidity of a material is directly proportional to its elastic modulus which depends on the mat
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Young's ModulusYoung's Modulus is the ratio of stress and strain. It is named after the famous British physicist Thomas Young. Young's Modulus provides a relation between stress and strain in any object. Â When a certain load is added to a rigid material, it deforms. When the weight is withdrawn from an elastic mat
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Bulk Modulus FormulaFor every material, the bulk modulus is defined as the proportion of volumetric stress to volumetric strain. The bulk modulus, in simpler terms, is a numerical constant that is used to quantify and explain the elastic characteristics of a solid or fluid when pressure is applied. We'll go over the bu
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Shear Modulus and Bulk ModulusA rigid body model is an idealised representation of an item that does not deform when subjected to external forces. It is extremely beneficial for evaluating mechanical systems—and many physical items are quite stiff. The degree to which an item may be regarded as stiff is determined by the physica
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Poisson's RatioPoisson's Ratio is the negative ratio of transversal strain or lateral strain to the longitudinal strain of a material under stress. When a material particularly a rubber-like material undergoes stress the deformation is not limited to only one direction, rather it happens along both transversal and
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Stress, Strain and Elastic Potential EnergyElasticity, this term always reminds of objects like Rubber bands, etc. However, if the question arises, which one is more elastic- A rubber or an Iron piece? The answer will be an Iron piece. Why? The answer lies in the definition of Elasticity, elasticity is known to be the ability of the object t
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Thermodynamics
Basics Concepts of ThermodynamicsThermodynamics is concerned with the ideas of heat and temperature, as well as the exchange of heat and other forms of energy. The branch of science that is known as thermodynamics is related to the study of various kinds of energy and its interconversion. The behaviour of these quantities is govern
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Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics states that when two bodies are in thermal equilibrium with another third body than the two bodies are also in thermal equilibrium with each other. Ralph H. Fowler developed this law in the 1930s, many years after the first, second, and third laws of thermodynamics had a
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First Law of ThermodynamicsFirst Law of Thermodynamics adaptation of the Law of Conservation of Energy differentiates between three types of energy transfer: Heat, Thermodynamic Work, and Energy associated with matter transfer. It also relates each type of energy transfer to a property of a body's Internal Energy. The First L
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Second Law of ThermodynamicsSecond Law of Thermodynamics defines that heat cannot move from a reservoir of lower temperature to a reservoir of higher temperature in a cyclic process. The second law of thermodynamics deals with transferring heat naturally from a hotter body to a colder body. Second Law of Thermodynamics is one
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Thermodynamic CyclesThermodynamic cycles are used to explain how heat engines, which convert heat into work, operate. A thermodynamic cycle is used to accomplish this. The application determines the kind of cycle that is employed in the engine. The thermodynamic cycle consists of a series of interrelated thermodynamic
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Thermodynamic State Variables and Equation of StateThe branch of thermodynamics deals with the process of heat exchange by the gas or the temperature of the system of the gas. This branch also deals with the flow of heat from one part of the system to another part of the system. For systems that are present in the real world, there are some paramete
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Enthalpy: Definition, Formula and ReactionsEnthalpy is the measurement of heat or energy in the thermodynamic system. It is the most fundamental concept in the branch of thermodynamics. It is denoted by the symbol H. In other words, we can say, Enthalpy is the total heat of the system. Let's know more about Enthalpy in detail below.Enthalpy
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State FunctionsState Functions are the functions that are independent of the path of the function i.e. they are concerned about the final state and not how the state is achieved. State Functions are most used in thermodynamics. In this article, we will learn the definition of state function, what are the state fun
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Carnot EngineA Carnot motor is a hypothetical motor that works on the Carnot cycle. Nicolas Leonard Sadi Carnot fostered the fundamental model for this motor in 1824. In this unmistakable article, you will find out about the Carnot cycle and Carnot Theorem exhaustively. The Carnot motor is a hypothetical thermod
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Heat Engine - Definition, Working, PV Diagram, Efficiency, TypesHeat engines are devices that turn heat energy into motion or mechanical work. Heat engines are based on the principles of thermodynamics, specifically the conversion of heat into work according to the first and second laws of thermodynamics. They are found everywhere, from our cars, power plants to
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Wave and Oscillation
Introduction to Waves - Definition, Types, PropertiesA wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables o
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Wave MotionWave Motion refers to the transfer of energy and momentum from one point to another in a medium without actually transporting matter between the two points. Wave motion is a kind of disturbance from place to place. Wave can travel in solid medium, liquid medium, gas medium, and in a vacuum. Sound wa
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OscillationOscillations are defined as the process of repeating vibrations of any quantity about its equilibrium position. The word “oscillation†originates from the Latin verb, which means to swing. An object oscillates whenever a force pushes or pulls it back toward its central point after displacement. This
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Oscillatory Motion FormulaOscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
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Amplitude FormulaThe largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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