Physics Complete

Problems on SHM displacement,velocity and Acceleration

Expansion of Solids and Applications

Physics Waves and Oscillations Complete

noreply@blogger.com (Unknown) — Sat, 28 Mar 2009 23:34:00 -0700

Wave is a periodic disturbance and it carries energy from one place to other with out any permanent displacement of particles of medium.Generally particles vibrates about their mean position and transfer energy form one place to other.

Here is the list of topics about waves and for the completeness simple harmonic motion is added here.

Simple Harmonic Motion

Oscillations and periodic motion
Displacement in SHM
SHM overview
Velocity and Acceleration in SHM
Energy of Particle in SHM
Simple Pendulum
Damped SHM

Waves and Propagation

Resonance
Wave Propagation
Transverse and Longitudinal Waves

Physics and Heat Complete

noreply@blogger.com (Unknown) — Sat, 28 Mar 2009 23:26:00 -0700

Heat is a disordered form of energy which transfers from body of higher temperature to lower.No mechanical work is done during the transfer of hear internal energy of bodies will be transferred between the bodies.

Here is the compilation of all heat topics for the reference sake and this list will be naturally growing as the time passes by.

Heat and temperature
Thermal Expansion
Change of state and latent heat
Heat transfer
Conduction
Convection
Radiation
Thermodynamics
Zeroth law
Internal Energy
Heat engine
Second law of thermodynamics

Temperature and its Measurement

Problems on Expansion of Solids

Expansion of Liquids

Anomalous expansion of water

Expansion of gases and Applications

Applications of Boyle’s law

Thermal Conduction in Transmission of Heat

Newton’s law of cooling

Thermodynamics and First Law of Thermodynamics

Molar Specific Heats of Gas and Relation between Them

Isothermal process and Applications

Adiabatic Process and its Applications

Cyclic Process,Reversible Process and Work Done Graphs

Heat Engine and Second Law of Thermodynamics

Kinetic theory of gases and Expression for Pressure

RMS Velocity of Gas Molecule and Applications

Degree of freedom and Law of the Equipartisien energy

Physics Properties of Matter Complete

noreply@blogger.com (Unknown) — Sat, 28 Mar 2009 23:13:00 -0700

Properties of matter is a vital study in physics which gives us insights about the world around us.Matter exits in different formats like solids,liquids and gases. In each state matter exhibits different properties . Here is the list of compilation of all properties of matter topic wise for the reference sake.

Elasticity

Elastic behavior of solids
Stress and Strain
Stress and strain graph
Young's modulus and its determination
Shear modulus in physics
Bulk Modulus

Hydrodynamics

Fluid Pressure
Pressure variation with depth
Hydraulic Lift
stream line flow of fluids
Blood flow and heart attack
Torricellie's law
Fluid flow and venturi meter
Dynamic lift and Bernoullie's theorem
Viscosity

Surface Tension

What is surface tension
Angle of Contact
Surface Energy and Surface Tension

Mechanical Properties of Solids and Young's Modulus

Problems and Solutions on Young's Modulus of a wire

Rigidity Modulus and Bulk Modulus

Behavior of a Wire under Increasing Load

Breaking Stress and Its Applications

Experimental determination of Young's modulus of the wire

Energy stored in the wire

Problems and Solutions on Elasticity

Physics Mechanics

noreply@blogger.com (Unknown) — Sat, 28 Mar 2009 21:48:00 -0700

Here is the list of all topics of mechanics under suitable heads and this is for the quick browsing of the site in particular about classical mechanics of physics.

Measurements

Units and Dimensions part one and two
Uses and limitations of dimensional formulas
List of dimensional formulas part one and two

Errors and Approximations

What are errors in measuring physical quantities ?
How approximation is made in physics ?
What are significant figures ?
Rounding Off a number for Calculation

Vectors

Vector concepts part one and two
Dot product of vectors
Cross product of vectors
Resolution of vectors

Kinematics

One dimensional motion in physics
Speed and Velocity of Kinematics
Acceleration in physics
Linear motion in detail
Projectile motion

Circular and Rotatory Motion

Uniform Circular motion
Circular motion part two
Motion of a body in vertical circle
Torque
Moment of Inertia

Newton laws of motion

Law of inertia
Momentum
Conservation of momentum
What is a force
Law of force
Common forces in mechanics
Action and Reaction law
Free body diagram and Newton laws

Friction

What is friction ?
Rolling Friction

Work Energy and Power

What is work ?
Work done by a variable force
Work and Energy theorem
Potential energy
Conservation of Energy
Potential energy of a spring

Collisions

Introduction to collisions

Center of Mass

What is center of mass ?

Gravitation

Kepler Laws
Universal Gravitational Constant
Gravitational potential energy
Weightlessness

Equations of Motion in One Dimension

Average Speed Average Velocity and Acceleration

Equation of motion in one dimensional motion

Problems on Motion of a Body Along a Straight Line

Acceleration due to gravity and One Dimensional Motion Equations

Projectile Motion Range,Time of Flight and Maximum Height Equations

Velocity of Projectile and Problems on Projectile Motion

Horizontal Projectile, Applications Problems with Solutions

Physics Mechanics transverse longitudinal waves

noreply@blogger.com (Unknown) — Sat, 28 Mar 2009 21:18:00 -0700

As per physics definition a wave is a periodic disturbance which propagates energy from place to other. One of the important type of wave is mechanical wave and it need materiel medium for propagation.

Mechanical waves are further classified depending on the space up to where they propagate.If the wave propagate for infinite distance and never come back then it is called progressive wave.If the wave is confined between any two finite points then it is called stationary wave.

A progressive wave is further classified into two types basing on the vibration of particles and direction of motion of wave.

If the direction of vibration of particles of elastic medium is parallel to direction of wave propagation it is called longitudinal wave and if the vibration of particles is perpendicular to direction of wave motion then the wave is called transverse wave.

The following is the representation of longitudinal progressive wave and we can notice the compressions and rarefactions . A compression is a place where particles are crushed close and rarefaction is a place where particles are bit separated.

The compressions and rarefactions are systematic and they are separated by fixed distance.Two successive compressions and rarefactions are constantly separated by a fixed distance and it is called wave length.

Further we can draw a case of transverse wave as shown below.

In transverse waves, the particle motion is normal to the direction of propagation of the wave. Therefore, as the wave propagates, each element of the medium undergoes a shearing strain. Transverse waves can, therefore, be propagated only in those media which can sustain shearing stress, such as solids and strings, and not in fluids.

Fluids as well as solids can sustain compressive strain; therefore, longitudinal waves can propagate in all elastic media. For example, in medium like a steel bar, both transverse and longitudinal waves can propagate while air can sustain only longitudinal waves.

Related post

How does waves propagate ?

Simple Harmonic Motion Displacement ,Velocity and Acceleration

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum

Progressive Wave Representation and Problems

Waves in Physics Introduction

noreply@blogger.com (Unknown) — Fri, 27 Mar 2009 10:09:00 -0700

A wave is a periodic disturbance. Wave in physics carries different kinds of energies from one place to other. Broadly waves are of two types by the name mechanical and non mechanical waves.Mechanical waves needs a medium for prorogation and non mechanical waves don't need any medium for prorogation. They can travel through vaccum.

For mechanical wave propagation the medium shall have elastic nature and shall contain inertial property.In the case of wave propagation no particle of medium displaces permanently from their mean position and they just vibrate about their mean position.During that process they transfer energy to their next particles and this process continues until the destination is reached.

These patterns of transfer of energy which move without the actual physical transfer or flow of matter as a whole, are called waves.In a wave, information and energy, in the form of signals, propagate from one point to another but no material object makes the journey.

The other kind of waves are matter waves.Matter waves are associated with moving electrons, protons, neutrons and other fundamental particles, and even atoms and molecules.

Wave propagation of sound waves in air is done in the following way: As the wave passes through air, it compresses or expands a small region of air. This causes a change in the density of that region, δρ, this change induces a change in pressure, δp, in that region. Pressure is force per unit area, so there is a restoring force proportional to the disturbance. If a region is compressed, the molecules in that region are packed together, and they tend to move out to the adjoining region, thereby increasing the density or creating compression in the adjoining region.

Consequently, the air in the first region undergoes rarefaction. If a region is comparatively rarefied the surrounding air will rush in making the rarefaction move to the adjoining region. Thus, the compression or rarefaction moves from one region to another, making the propagation of a disturbance possible in air.

SHM related topics

Resonance
Damped simple harmonic motion
Simple Pendulum
What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
Simple Harmonic Motion
Velocity and acceleration of SHM
Energy of particle in SHM

Resonance in Physics

noreply@blogger.com (Unknown) — Thu, 26 Mar 2009 08:41:00 -0700

Every body will have some frequency with which it vibrates and it is called its natural frequency.Under the influence of external force body vibrates with a frequency different from its natural frequency and it is called forced vibration. Resonance is a special case of forced vibration.If the frequency of external force is equal to the frequency of body which is going to be vibrated then the body virates with the maximum frequency and the phenomenon is called Resonance.

A person swinging in a swing without anyone pushing it or a simple pendulum, displaced and released, are examples of free oscillations. In both the cases, the amplitude of swing will gradually decrease and the system would, ultimately, come to a halt. Because of the ever present dissipative forces, the free oscillations cannot be sustained in practice.

However, while swinging in a swing if you apply a push periodically by pressing your feet against the ground, you find that not only the oscillations can now be maintained but the amplitude can also be increased. Under this condition the swing has forced, or driven, oscillations.

The maximum possible amplitude for a given driving frequency is governed by the driving frequency and the damping, and is never infinity. The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the oscillator is called resonance.

Example for Resonance

Consider a set of five simple pendulums of assorted lengths suspended from a common rope as shown in figure. The pendulums 1 and 4 have the same lengths and the others have different lengths. Now let us set pendulum 1 into motion. The energy from this pendulum gets transferred to other pendulums through the connecting rope and they start oscillating. The driving force is provided through the connecting rope. The frequency of this force is the frequency with which pendulum 1 oscillates. If we observe the response of pendulums 2, 3 and 5, they first start oscillating with their natural frequencies of oscillations and different amplitudes, but this motion is gradually damped and not sustained.

Their frequencies of oscillation gradually change and ultimately they oscillate with the frequency of pendulum 1, i.e. the frequency of the driving force but with different amplitudes. They oscillate with small amplitudes. The response of pendulum 4 is in contrast to this set of pendulums. It oscillates with the same frequency as that of pendulum 1 and its amplitude gradually picks up and becomes very large. A resonance-like response is seen. This happens because in this the condition for resonance is satisfied, i.e. the natural frequency of the system coincides with that of the driving force.

SHM related topics

Damped simple harmonic motion
Simple Pendulum
What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
Simple Harmonic Motion
Velocity and acceleration of SHM
Energy of particle in SHM

Wave Motion an introduction

Frequency of Stationary wave in a stretched String

Stretched String Problems and Solutions

Vibrations of Sound in Closed Pipe and Open Pipe

Beats and Its Applications

Doppler Effect and Its Applications

Simple Hormonic Motion Damped

noreply@blogger.com (Unknown) — Wed, 25 Mar 2009 04:57:00 -0700

The motion of a simple pendulum, swinging in air, dies out eventually.This is because the air drag and the friction at the support oppose the motion of the pendulum and dissipate its energy gradually. The pendulum is said to execute damped oscillations.

In damped oscillations, although the energy of the system is continuously dissipated, the oscillations remain apparently periodic. The dissipating forces are generally the frictional forces. To understand the effect of such external forces on the motion of an oscillator,let us consider a system as shown in figure where a block of mass m oscillates vertically on a spring with spring constant k.

The block is connected to a vane through a rod . The vane is submerged in a liquid. As the block oscillates up and down, the vane also moves along with it in the liquid. The up and down motion of the vane displaces the liquid, which in turn, exerts an inhibiting drag force (viscous drag) on it and thus on the entire oscillating system. With time, the mechanical energy of the block spring system decreases, as energy is transferred to the thermal energy of the liquid and vane.

Let the damping force exerted by the liquid on the system be Fd. Its magnitude is proportional to the velocity v of the vane or the block. The force acts in a direction opposite to the direction of v. This assumption is valid only when the vane moves slowly. Then for the motion along the x-axis Fd = –b v

where b is a damping constant that depends on the characteristics of the liquid and the vane. The negative sign makes it clear that the force is opposite to the velocity at every moment.

When the mass m is attached to the spring and released, the spring will elongate a little and the mass will settle at some height. This position is the equilibrium position of the mass. If the mass is pulled down or pushed up a little, the restoring force on the block due to the spring is

FS = –kx, where x is the displacement of the mass from its equilibrium position. Thus the total force actingon the mass at any time t is F = –k x –b v.

If a(t) is the acceleration of the mass at time t, then by Newton’s second law of motion for force components along the x-axis, we have m a(t) = –k x(t) – b v(t)

If the oscillator is damped, the mechanical energy is not constant but decreases with time.

SHM related topics

Simple Pendulum
What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
Simple Harmonic Motion
Velocity and acceleration of SHM
Energy of particle in SHM

Wave Motion an introduction

Progressive Wave Representation and Problems

Frequency of Stationary wave in a stretched String

Stretched String Problems and Solutions

Vibrations of Sound in Closed Pipe and Open Pipe

Beats and Its Applications

Doppler Effect and Its Applications

Simple Pendulum and SHM

noreply@blogger.com (Unknown) — Tue, 24 Mar 2009 00:46:00 -0700

A point sized heavy mass suspended with a inextensible string from a rigid support is called simple pendulum. For less angle of oscillation it executes simple harmonic motion.

The forces acting on the bob are the force T, tension in the string and the gravitational force Fg (= m g), as shown in figure. The string makes an angle θ with the vertical. We resolve the force Fg into a radial component Fg cos θ and a tangential component Fg sin θ.

The radial component is canceled by the tension, since there is no motion along the length of the string. The tangential component produces a restoring torque about the pendulum’s pivot point. This torque always acts opposite to the displacement of the bob so as to bring it back towards its central location. The central location is called the equilibrium position ( θ = 0), because at this position the pendulum would be at rest if it were not swinging.

The restoring torque τ is τ = –L (Fg sin θ) where the negative sign indicates that the torque acts to reduce θ, and L is the length of the moment arm of the force Fg sin θ about the pivot point. For rotational motion , τ = I α where I is the pendulum’s rotational inertia about the pivot point and α is its angular acceleration about that point.

and further we can prove that time period of a pendulum is 2(pi) square root of (L/g).

SHM related topics

Simple Harmonic Motion Displacement ,Velocity and Acceleration

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum

Simple Harmonic Motion Displacement ,Velocity and Acceleration

What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
Simple Harmonic Motion
Velocity and acceleration of SHM
Energy of particle in SHM

Topics of Heat and Thermodynamics

Heat engine
Internal Energy
Zeroth law of thermodynamics
Thermodynamics Introduction

Energy of Simple Hormonic Motion

noreply@blogger.com (Unknown) — Mon, 23 Mar 2009 00:11:00 -0700

According to law of conservation of energy total energy of a system always remains constant and the particle in simple harmonic motion is not a exception from it.

A particle executing simple harmonic motion has kinetic and potential energies, both varying between the limits, zero and maximum. Here we will use the equations of a particle's displacement and velocity in SHM.

The velocity of a particle executing SHM, is a periodic function of time. It is zero at the extreme positions of displacement. Therefore, the kinetic energy (K) of such a particle, which is defined as
is also a periodic function of time, being zero when the displacement is maximum and maximum when the particle is at the mean position.Since the sign of v is immaterial in K, the period of K is T/2.
The spring force F = –kx is a conservative force, with associated potential energy U = 1/2 K x^2.
Hence the potential energy of a particle executing simple harmonic motion is,
Thus the potential energy of a particle executing simple harmonic motion is also periodic, with period T/2, being zero at the mean position and maximum at the extreme displacements.

Total Energy

The total mechanical energy of a harmonic oscillator is thus independent of time as expected for motion under any conservative force. The time and displacement dependence of the potential and kinetic energies of a linear simple harmonic oscillator are shown in figure.
In a linear harmonic oscillator, all energies are positive and peak twice during every period. For x = 0, the energy is all kinetic and for x = ± A it is all potential.

In between these extreme positions, the potential energy increases at the expense of kinetic energy. The former stores its potential energy and the latter stores its kinetic energy.
SHM related topics

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum

Simple Harmonic Motion Displacement ,Velocity and Acceleration

What is periodic and Oscillatory Motion is ?
Displacement in Oscillatory motion
Simple Harmonic Motion
Velocity and acceleration of SHM

Topics of Heat and Thermodynamics

Heat engine
Internal Energy
Zeroth law of thermodynamics
Thermodynamics Introduction

Velocity and Acceleation of SHM

noreply@blogger.com (Unknown) — Sat, 21 Mar 2009 22:23:00 -0700

A body in oscillatory motion whose acceleration is directly proportional to displacement and is always directed towards mean position is called simple harmonic motion. Here we are going to derive equations for velocity and acceleration of body in SHM.

Simple harmonic motion is the projection of uniform circular motion on a diameter of the circle in which the latter motion takes place.

A particle in SHM will have a displacement y represented as y = a cos(wt) whose initial phase is equal to zero. Here the particle is in horizontal circular motion. If it is in vertical circular motion instead of sin function we have to use cosine function.By differentiating the above equation we will get velocity and by differentiating once again we will get the equation for acceleration.

Acceleration can be determined further with equation – ω^2 A cos ( ωt + φ) or – ω^2 (t)

Its graphical method we can represent displacement ,velocity and acceleration as shown below.
SHM related topics

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum

Simple Harmonic Motion Displacement ,Velocity and Acceleration

What is periodic and Oscillatory Motion is ?
Displacement in Oscillatory motion
Simple Harmonic Motion

Topics of Heat and Thermodynamics

Heat engine
Internal Energy
Zeroth law of thermodynamics
Thermodynamics Introduction
Heat transfer by radiation
Heat transfer by convection
Heat transfer and conduction
Heat and Temperature

Simple Hormonic Motion

noreply@blogger.com (Unknown) — Fri, 20 Mar 2009 07:03:00 -0700

For a body to be in simple harmonic motion it shall satisfy some conditions.They are

1.The motion shall be oscillatory.
2.Acceleration of motion shall be directly proportional to displacement.
3.Acceleration shall be always directed to words its mean position.

If this three conditions are met then the oscillatory motion is said to be in simple harmonic motion.

Example :

Let us consider a particle vibrating back and forth about the origin of an x-axis between the limits +A and –A . In between these extreme positions the particle moves in such a manner that its speed is maximum when it is at the origin and zero when it is at ± A. The time t is chosen to be zero when the particle is at +A and it returns to +A at t = T.

Let us record its positions as a function of time by taking ‘snapshots’ at regular intervals of time.The position of the particle with reference to the origin gives its displacement at any instant of time. For such a motion the displacement x(t ) of the particle from a certain chosen origin is found to vary with time as,

x (t) = A cos ( ωt + φ) in which A, ω, and φ are constants.

The motion represented by equation is called simple harmonic motion (SHM); a term that means the periodic motion is a sinusoidal function of time. Equation in which the sinusoidal function is a cosine function.

The previous post is about What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum

Simple Harmonic Motion Displacement ,Velocity and Acceleration

Topics of Heat and Thermodynamics

Heat engine
Internal Energy
Zeroth law of thermodynamics
Thermodynamics Introduction
Heat transfer by radiation
Heat transfer by convection
Heat transfer and conduction
Heat and Temperature

Displacement in Oscillatory Motion

noreply@blogger.com (Unknown) — Thu, 19 Mar 2009 22:05:00 -0700

Displacement of a particle as the change in its position vector. It refers to change with time of any physical property under consideration. For example, in case of rectilinear motion of a steel ball on a surface, the distance from the starting point as a function of time is its position displacement. The choice of origin is a matter of convenience. Consider a block attached to a spring, the other end of which is fixed to a rigid wall as shown in figure below.

It is convenient to measure displacement of the body from its equilibrium position. For an oscillating simple pendulum, the angle from the vertical as a function of time may be regarded as a displacement variable as shown in figure below. The term displacement is not always to be referred in the context of position only.

The displacement can be represented by a 0mathematical function of time. In case of periodic motion, this function is periodic in time. One of the simplest periodic functions is given by

f (t) = A cos ωt

Any periodic function can be expressed as a superposition of sine and cosine functions of different time periods with suitable coefficients.

The previous post is about What is periodic and Oscillatory Motion is ?

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum

Simple Harmonic Motion Displacement ,Velocity and Acceleration

Periodic and Oscillatory Motion

noreply@blogger.com (Unknown) — Thu, 19 Mar 2009 08:45:00 -0700

Oscillatory motion is a to and fro motion about a mean position and periodic motion repeats at regular intervals of time. All oscillatory motions are periodic and all periodic motions are not oscillatory.

If the body is given a small displacement from the position, a force comes into play which tries to bring the body back to the equilibrium point, giving rise to oscillations or vibrations. For example, a ball placed in a bowl will be in equilibrium at the bottom. If displaced a little from the point, it will perform oscillations in the bowl. Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Circular motion is a periodic motion, but it is not oscillatory.

When the frequency is small, we call it oscillation (like the oscillation of a branch of a tree), while when the frequency is high, we call it vibration (like the vibration of a string of a musical instrument). Simple harmonic motion is the simplest form of oscillatory motion. This motion arises when the force on the oscillating body is directly proportional to its displacement from the mean position, which is also the equilibrium position. At any point in its oscillation, this force is directed towards the mean position.

A motion that repeats itself at regular intervals of time is called periodic motion.The following are the examples of periodic motion.

In practice, oscillating bodies eventually come to rest at their equilibrium positions, because of the damping due to friction and other dissipative causes. However, they can be forced to remain oscillating by means of some external periodic agency.

Any material medium can be pictured as a collection of a large number of coupled oscillators. The collective oscillations of the constituents of a medium manifest themselves as waves. Examples of waves include water waves, seismic waves, electromagnetic waves.

Topics of Heat and Thermodynamics

Problems on SHM displacement,velocity and Acceleration

Time Period of Simple pendulum