RSS FEED IDEMS: PHYSICSGOEASY
- Galileo Biograpgy
Galileo Galilei (1564-1642)
Galileo's experiments into gravity refuted Aristotle Galileo was a hugely influential Italian astronomer, physicist and philosopher.
Galileo Galilei was born on 15 February 1564 near Pisa, the son of a musician. He began to study medicine at the University of Pisa but changed to philosophy and mathematics. In 1589, he became professor of mathematics at Pisa. In 1592, he moved to become mathematics professor at the University of Padua, a position he held until 1610. During this time he worked on a variety of experiments, including the speed at which different objects fall, mechanics and pendulums.
In 1609, Galileo heard about the invention of the telescope in Holland. Without having seen an example, he constructed a superior version and made many astronomical discoveries. These included mountains and valleys on the surface of the moon, sunspots, the four largest moons of the planet Jupiter and the phases of the planet Venus. His work on astronomy made him famous and he was appointed court mathematician in Florence.
In 1614, Galileo was accused of heresy for his support of the Copernican theory that the sun was at the centre of the solar system. This was revolutionary at a time when most people believed the Earth was in this central position. In 1616, he was forbidden by the church from teaching or advocating these theories.
In 1632, he was again condemned for heresy after his book 'Dialogue Concerning the Two Chief World Systems' was published. This set out the arguments for and against the Copernican theory in the form of a discussion between two men. Galileo was summoned to appear before the Inquisition in Rome. He was convicted and sentenced to life imprisonment, later reduced to permanent house arrest at his villa in Arcetri, south of Florence. He was also forced to publicly withdraw his support for Copernican theory.
Although he was now going blind he continued to write. In 1638, his 'Discourses Concerning Two New Sciences' was published with Galileo's ideas on the laws of motion and the principles of mechanics. Galileo died in Arcetri on 8 January 1642.
Thu, 17 Apr 2008 18:30:00 +0000
- Waves and Oscillation Index
Waves and Oscillation
SHM concept Part 1
SHM concept Part 2
Conceptaul Question for SHM
Subjective questions for SHM
objective Question for SHM
Waves Concept part 1
Waves Concept part 2
Thu, 17 Apr 2008 18:21:00 +0000
- Mechanics Index
Mechanics Index
Gravitation Concept
Conceptaul Question for Gravitation
Motion in a Plane
Conceptaul Question for Motion in a plane
objective Question for kinematics
Subjective Question for kinematics
Relative Velocity Concept
Conceptaul Question for relative velocty
Graphical Question for Motion in a Plane
Newton's law of Motion Concept
Conceptaul Question for Newton law of motion
Note: solution are available at the bottom of posts
Thu, 17 Apr 2008 18:14:00 +0000
- Thermal Index
Thermodynamics Index.
Thermal Expansion
Study Tips Part 1
Study Tips Part 2
Thermo Quick Recap
Conceptual Questions Part 1
Conceptual Questions Part 2
Conceptual Questions Part 3
Conceptual Questions Part 4
IITJEE Objective Questions part 1
IITJEE Objective Questions Part 2
Thermal Expansion Problems
IITJEE Subjective Questions
Thermo Questions
Note:Solutions are available at the bottom of each post
Thu, 17 Apr 2008 17:52:00 +0000
- Waves Concept
PART2
Interference of waves:-
-From principle of superposition we know that overlaping waves algbrically add togather to produce a net wave without altering the way of each other or the individual waves.
-If two sinusoidal waves of the same amplitude and wavelength travell in the same direction they interfere to produce a resultant sinusoidal wave travelling in that direction.
-The resultant wave due to interference of two sinusoidal waves is given by the relation
y′(x,t)=[2Amcos(υ/2)]sin(ωt-kx+υ/2)where υ is the phase difference between two waves.
-If υ=0n then there would be no phase difference between the travelling waves and the interference would be fully constructive.
-If υ=π then waves would be out of phase and there interference would be distructive.
Reflection of waves:-
-When a apulse or travelling wave encounters any boundary it gets reflected.
-If the boundary is not completely rigid then then a part of wave gets reflected and rest of it's part gets transmitted or refracted.
-A travelling wave at a rigid boundary is reflected with a phase reversal but the reflection at open boundary takes place without phase change.
-if an incident wave is represented by
yi(x,t)=A sin(ωt-kx)then reflected wave at rigid boundary is
yr(x,t)=A sin(ωt+kx+π)
=-Asin(ωt+kx)
and for reflections at open boundary reflected wave is given by
yr(x,t)=Asin(ωt+kx)
Standing waves:-
-The interference of two identical waves moving in opposite directions produces standing waves.
-For a string with fixed ends standing wave is given by
y(x,t)=[2Acos(kx)]sin(ωt)above equation does not represent travelling wave since it does not have characterstic form involving (ωt-kx) or (ωt+kx) in the argument of trignometric function.
-In standing waves amplitude of waves is different at different points i.e., at nodes amplitude is zero and at antinodes amplitude is maximumwhich is equal to sum of amplitudes of constituting waves.
-At intermediate points amplitude of wave varies between these two limits of maxima and minima
Normal modes of stretched string:--Frequency of transverse motion of stretched string of length L fixed at both the ends is given by
f=nv/2L
where n=1,2,3,4,.......
-The set of frequencies given by above relation are called normal modes of oscillation of the system.
-The mode with n=1 is called the fundamental mode with frequancy
f1=v/2L-Similarly second harmonic is the oscillation mode with n=2 and so on.
-Thus the string has infinite number of possible frequency of viberation which are harmonics of fundamental frequency f1 such that fn=nf1
Thu, 17 Apr 2008 17:31:00 +0000
- Waves concept
-Definition of wave:-
It is a disturbance which travels through the medium due to repeated periodic motion of particles of the medium about their equilibrium position.
-Example of wave motion are sound waves traveling through an intervening mediun, water waves, light waves and many more such examples are there.
-Waves requiring material medium for their propagation are called MECHANICAL WAVES. Mechanical waves are governed by Newton's law of motion.
-Sound waves are mechanical waves in atmosphere between source and the listner and require medium for their propagation.
-Other examples of mechanical waves are sesmic waves and water waves.
-Those waves which does not require material medium for their propagation are called NON MECHANICAL WAVES.
-One familiar example of NON MECHANICAL WAVES is waves associated with light or light waves. Another such examples are radio waves, X-rays, micro waves, UV light, visible light and many more.
-Transverse waves are such waves where the displacements or oscillations are perpandicular to the direction of propagation of wave.
-Longitudinal waves are those waves in which displacement or oscillations in medium are parallel to the direction of propagation of wave for example sound waves.
-At any time t , displacement y of the particle from it's equilibrium position as a function of the coordinate x of the particle is
y(x,t)=A sin(ωt-kx)
where,
A is the amplitude of the wave
k is the wave number
ω is angular frequency of the wave
and (ωt-kx) is the phase.
-Wavelength λ and wave number k are related by the relation
k=2π/λ
-Time period T and frequency f of the wave are related to ω by
ω/2π = f = 1/T
-speed of the wave is given by
v = ω/k = λ/T = λf
-Speed of a transverse wave on a stretched string depends on tension and the linear mass density of the string not on frequency of the wave
i.e,
v=√T/μ
T=Tension in the string
μ=Linear mass density of the string
-Sounds waves are longitudinal mechanical waves that can travel through solids,liquid and gases
-Speed of longitudinal waves in a medium is given by
v=√B/ρ
B=bulk modulus
ρ=Density of the medium
-Speed of longitudinal waves in ideal gas is
v=√γP/ρ
P=Pressure of the gas
ρ=Density of the gas
γ=Cp/CV
Principle of superposition:
When two or more waves traverse thrugh the same medium,the displacement of any particle of the medium is the sum of the displacement that the individual waves would give it.
y=Σyi(x,t)
Tue, 15 Apr 2008 17:20:00 +0000
- Solutions for Conceptual questions of Newton's law
1.sol:- (d) and B are
A body acted uopn by a certain force produces acceleration i.e. it undergoes change in it's velocity. hence choice (d) is correct
2. sol:- (a)
3. sol:-(d)
4. sol:- (b)
since velocity of block when it reaches the ground is given by v=(2gh)1/2 the correct choice will be (b).
5. Solution:A,C
6. sol:- (a)
7. Solution :(c)
8. Solution:(c)
Sat, 12 Apr 2008 17:40:00 +0000
- Solutions for Kinematic Graphical Problem
1. a
2.c
3.c
4.b
5.a
6.a
7.b
8. d
Fri, 11 Apr 2008 17:25:00 +0000
- Subjective Question for SHM
Q1. A mass attached to a spring is free to oscillate , with angular velocity ω , in a frictionless horizontal plane. The mass is displaced from it's equilibrium position by a distance x0 towards the center by pushing it with velocity v0 at time t=0. Find the amplitude of resulting oscillations in terms ofω,x0 and v0 .
Ans. A=√[x02+(v02/ω2)]
Q2. A uniform cylinder of length l and mass m having crosssectional area Ais suspended , with length vertical , from a fixed point by a massless spring , such that it is half submearged in a liquid of density σ at equilibrium position.. When the cylinder is given a small downward push and released , it starts oscillating verticallywith small amplitude . Calculate the frequency of oscillations of cylinder.
(IIT 1990)
Ans. f=[(k+(σAg)/m]1/2
Q3. What should be the percentage change of length of pendulum in order that clock have same time period when moved from place where g=9.8 m/s2 to another where g=9.81 m/s2.
Ans. .102%
Q4. A 4 kg particle is moving along x axis under the action of the force F=-(π2/16)x N
when t=2 s the particle passes through origin.If x0 is the amplitude of oscillating particle find the equation of elongation.
Ans. x=x0 cos( πt/8 + π/4)
Q5. Two blocks of masses m1 and m2 are connected by a spring and these masses are free to oscillate along the axis of the spring. Find the angular frequency of oscillation.
Ans.
ω=√[k(m1+m2)/m1m2]
Wed, 09 Apr 2008 18:14:00 +0000
- Objective Question for SHM
Q 1. Total energy of mass spring system in harmonic motion is E=1/2(mω2A2). Consider another system executing SHM with same amplitude having value of spring constant as half the previous one and mass twice as that of previous one. The energy of second oscillator will be
(a) E
(b) 2E
(c) √ 2E
(d) E/2
Q 2. A particle is executing linear SHM of amplitude A. What fraction of total energy is potential when the displacement is 1/4 times amplitude.
(a) 3/2
(b) 1/6
(c) 1/4
(d) 1/2√ 2
Q 3. Fig below shows two spring mass systems. All the springs are identical having spring constant k and are of negligible mass. If m is the mass of block attached to the spring then the ratio of time period of oscillations of both systems is
(a) 1:2√ 2
(b) 1:1/2√ 2
(c) 1:√ 2
(d) √ 2:1
Q 4. Fig below shows two equal masses of mass m joined by a rope passing over a light pully. First mass is attached to a spring and another end of spring is attached to a rigid support. Neglacting frictional forces total energy of the system when spring is extended by a distance x is
(a) mv2+1/2(Kx2)+mgx
(b) mv2-1/2(Kx2)+mgx
(c) mv2-1/2(Kx2)-mgx
(d) mv2+1/2(Kx2)-mgx
where v = dx/dt , the velocity of mass
Q 5. A spring of force constant k is cut into two pieces such that one piece is four times the length of the other. the longer piece will have force constant equal to
(a) 4k/5
(b) 5k/4
(c) 3k/2
(d) 4k
Q 6. In the system shown below frequency of oscillation when mass is displaced slightely is
(a) f=1/2π(k1k2/(k1+k2)m)1/2
(b) f=1/2π((k1+k2)/m)1/2
(c) f=1/2π(m/(k1k2))1/2
(d) f=1/2π((k1+k2)/(k1k2)m)1/2
Q 7. A simple pendulum is displaced from it's mean position o to a position A such that hight of A above O is 0.05m. It is then released it's velocity when it passes mean position is
(a) .1m/s
(b) 5.0m/s
(c) 1m/s
(d) 1.5m/s
Q 8. A particle is executing SHM at mid point of mean position and extreme position . What is it's KE in terms of total energy E.
(a) E/2
(b) 4E/3
(c) √ 2E
(d) 3E/4
Q 9. A solid cylinder of radius r and mass m is connected to a spring of spring constant k and it slips on a frictionless surface without rolling with angular frequency
(a) √(k/mr)
(b) √(kr/m)
(c) √(k/m)
(d) √(2k/m)
Tue, 08 Apr 2008 17:43:00 +0000
- Solutions for Relative velocity conceptual
1. a
2. a
3. b
4.a
5.a
6.a
7.d
8.a
9.b
10 b
Sat, 05 Apr 2008 17:22:00 +0000
- Conceptual Question of SHM
1.To execute SHM system must have
a. Elasticity
b. Moment of Inertia
c. Inertia
d. all the above
2. Angular frequency of system executing SHM depends on
a. mass
b. total energy
c.force constant
d. Amplitude
3.A particle of mass m is attached to a massless string of lenght L and is oscillating in vertical plane with one end of string fixed to rigid support.Tension in the string at a certain instant is T=kmg.Then
a. K can never be equal to 1
b. K can never be greater than 1
c. K can never be greater than 3
d K can never be less than 1
4.The bob A of a simple pendulum is released when the string makes an angle 45 with the verical.Its hit another bob B of the same mateial and same mass kept at rest on the table.If the collsion is elastic
a. B moves first and A follows it with half of its intial velocity
b.A comes to rest and B moves with the velocity of A
c Both A and B moves with same velocity of A
d Both A and B comes to rest at B
5.For a particle executing SHM
a.Acceleration is proportional to the displacement in the direction of the motion
b.Acceleration is proportional to the displacement but in opposite direction of the motion
c. Total energy of particle remains constant
d KE and PE of particle remains constant
6. which one of the following statement is true
a. Maximum value of velocity in SHM is A2ω
b.In SHM velocity of the particle is maximum when displacment is maximum
c.Velocity of the particle is zero in SHM when displacement attains its maximum on either side
d.Velocity in SHM vary periodically with time
7. which one of the following statement is true
a. Amplitude and intial displacement of particle in SHM are always equal
b.Amplitude and intial displacement of particle in SHM are never equal
c. Amplitnude of a particle in SHM can be equal to its initial displacement
d. Amplitnude of a particle in SHM can be greater to its initial displacement
8.The amplitutde and phase of a particle executing SHM depends on
a.The displacemnt of particle at t=0
b.The velocity of particle at t=0
c Both Velocity and displacement at t=0
d Neither velocity and displacemnt at t=0
Fri, 04 Apr 2008 17:56:00 +0000
- Oscillations
PART 2
(1) Some system Executing SHM
a)Oscillations of a Spring mass system
-In this case particle of mass m oscillates under the influence of hooke's law restoring force given by F=-Kx where K is the spring constant
Angular Frequency ω=√(K/m)
Time period T=2π√(m/K)
And frequency is =(1/2π)√(K/m)
Time period of both horizontal ans vertical oscillation are same but spring constant have diffrent value for horizontal and vertical motion
b) Simple pendulum
-Motion of simple pendulum oscillating through small angles is a case of SHM with angular frequency given by
ω=√(g/L)
and Timeperiod
T=2π√(L/g)
Where L is the length of the string.
-Here we notice that period of oscillation is independent of the mass m of the pendulum
c) Compound Pendulum
- Compound pendulum is a rigid body of any shape,capable of oscillating about the horizontal axis passing through it.
-Such a pendulum swinging with small angle executes SHM with the timeperiod
T=2π√(I/mgL)
Where I =Moment of inertia of pendulum about the axis of suspension
L is the lenght of the pendulum
(2) Damped Oscillation
-SHM which continues indefinitely without the loss of the amplitude are called free oscillation or undamped and it is not a real case
- In real physical systems energy of the oscillator gradually decreases with time and oscillator will eventually come to rest.This happens because in acutal physical systems,friction(or damping ) is always present
-The reduction in amplitude or energy of the oscilaltor is called damping and oscillation are call damped
(3) Forced Oscillations and Resonance.
- Oscillations of a system under the influence of an external periodic force are called forced oscillations
- If frequency of externally applied driving force is equal to the natural frequency of the oscillator resonance is said to occur
Thu, 03 Apr 2008 17:44:00 +0000
- Oscillations
PART I
-If a particle moves such that it retraces its path regularly after regular interval of time,its motion is said to be periodic Ex-Motion of earth around Sun
-If a body in periodic motion moves back and forth over the same path then the motion is said to be oscillatory motion
-Simple harmonic motion is simplest form of oscillatory motion
-SHM is a kind of motion in which the restoring force is propotional to the displacement from the mean position and opposes its increase.Mathematically restoring force is
F=-Kx
Where K=Force constant
x=displacement of the system from its mean or equilibrium position
Diffrential Equation of SHM is
d2x/dt2 + ω2x=0
Solutions of this equation can both be sine or cosine functions .We conveniently choose
x=Acos(ωt+φ) where A,ω and φ all are constants
-Quantity A is known as amplitude of SHM which is the magnitude of maximum value of displacement on either sides from the equilibrium position
-Time period (T) of SHM the time during which oscillation repeats itself i.e, repeats its one cycle of motion and it is given by
T=2π/ω where ω is the angular frequency
-Frequency of the SHM is the number of the complete oscillation per unit time i.e, frequency is reciprocal of the time period
f=1/T
Thus angular frequncy
ω=2πf
-Velocity of a system executing SHM as a function of time is
v=-ωAsin(ωt+φ)
-Acceleration of particle executing SHM is
a=-ω2Acos(ωt+φ)
So a=-ω2x
This shows that acceleration is proportional to the displacement but in opposite direction
-At any time t KE of system in SHM is
KE=(1/2)mv2
=(1/2)mω2A2sin2(ωt+φ)
which is a function varying periodically in time
-PE of system in SHM at any time t is
PE=(1/2)Kx2
=(1/2)mω2A2cos2(ωt+φ)
-Total Energy in SHM
E=KE+PE
=(1/2)mω2A2
and it remain constant in absense of dissapative forces like frictional forces
Wed, 02 Apr 2008 17:44:00 +0000
- Solutions for Kinematics objective
1 a,c,d
Hint:Eliminating t from both the equation,you got trajotory and diffrentiating gives velocity y
x=2t y=2t2 So eliminating gives y=x2/2
2.d
3.d
4.c
5.b,c
6.a,b
7.b
8.b
9.a
10.d
Tue, 01 Apr 2008 08:49:00 +0000
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