Distance - Time Graph for Uniform Motion
A public transport bus is traveling from terminus P to terminus Q. The following observation was recorded by a passenger in the bus.. Observations
Distance in km
0
10
20
30
40
50
60
Time
10.00 am
10.10 am
10.20 am
10.30 am
10.40 am
10.50 am
11.00 am
From the above table it is clear that the bus is covering equal distances in equal intervals of more...
Introduction
In everyday life we always come across some objects which are at rest and some objects in motion. The branch of Physics, which deals with the behavior of moving objects, is known as mechanics. Mechanics is further divided into two sections namely Kinematics and Dynamics. Kinematics deals with the study of motion without taking into account the cause of motion, while Dynamics is concerned with the cause of motion, namely force. This chapter covers only the different aspects of motion without considering the cause of motion.
Motion
A body is said to be in motion if its position changes continuously, with respect to a stationary object, taken as reference point, with the passage of time.
When we are sitting in a moving bus, we observe the continuous changes of position with respect to stationary object like houses, trees, lamp posts, etc. We say that the bus is moving or that the bus is in motion.
Motion and rest are Relative Terms
Suppose you are travelling in a train, which is in motion.
Observe 1: Is there any change in your position with respect to your co passengers? Answer: No
Observe 2: Is there any change of scene you view through the window?
Answer: Yes
Thus, we can say that an object is in, motion, if it changes its position continuously with respect to its surroundings in a given time. Since the position of desk and benches does not changes with time, hence we can say that they are not in motion, i.e. they are stationary. You must have observed sky at night: the position of stars changes with the passage of time, whereas the position of house and our surrounding remains the same. But in reality the earth is also moving, that means all the objects on the surface of the earth are also in motion. Thus, an object which appears to be at rest, may actually be in motion. Therefore, motion and rest are relative terms. Hence, to describe the motion of an object we have to specify how its position changes with respect to a fixed point called the reference point or origin.
Without frame of reference we cannot specify whether an object is in motion or at rest. A frame of reference is another object or scene with respect to which we compare an object's position.
Types of Motion
Translatory motion
Circular motion
Rotatory motion and
Vibratory motion
Translatory Motion
The continuous change of position of an object from one point to another more...
Newton's Laws of Motion
Newton's First Law of Motion
Everybody remains in its state of rest or of uniform motion, unless it is compelled to change its state by an unbalanced force, impressed on it.
\[F=m\times a\]
if, \[F=0\]
\[\Rightarrow \,\,a=0\,\,(m\ne 0)\]
(i) We tend to fall forward when a bus suddenly stops. When bus stops suddenly, we tend to resist the change in our state of motion and hence fall forward.
(ii) We tend to fall backward when a bus suddenly starts.
(iii) We tend to get thrown to one side when a car takes sharp turn.
Martin and Robert are arguing in the cafeteria. Martin says that if he throws the burger with a greater speed it will have a greater inertia. Robert argues that inertia does not depend upon speed, but rather upon mass. With whome do you agree?
(a) Martin
(b) Robert
(c) Both are correct
(d) Both are incorrect
(e) None of these
Answer: (b)
Why it is advised to tie the luggage with a rope on the roof of bus?
(a) Luggage might fall in forward direction
(b) Luggage might fall in backward direction
(c) To prevent fall (in both the directions) of the luggage from the roof of the bus.
(d) All of these
(e) None of these
Answer: (c)
Newton's Second Law of Motion
The rate of change of momentum of a body is directly proportional to the unbalanced force applied and takes place in the direction of the force.
Mathematical expression,
\[F=\frac{dp}{dt}=m\times a\]
\[\Rightarrow \,\,F\alpha \frac{\Delta p}{\Delta t}\]
\[\Rightarrow \,\,F=k\frac{\Delta p}{\Delta t}\]
Where, k is the constant of proportionality.
Taking the limit \[\Delta t\to 0,\] the term \[\frac{\Delta p}{\Delta t}\] becomes the derivative and is denoted by,
\[\frac{dp}{dt}=\frac{d(m\times v)}{dt}=\frac{mdv}{dt}=m\times a\]
\[\Rightarrow \,\,F=\frac{dp}{dt}\,\,\,\,\,\,=m\times a\]
(i) A cricketer gradually pulls hand backwards with the moving ball when he catches the ball. While doing so he increases the time during which the high velocity of the ball is reduces to zero and the acceleration of the ball is also reduced drastically and hence the impact of catching the ball is also reduced and it does not hurt the player.
(ii) A judo champ breaks a pile of bricks in one go. His action is too fast. In this case he needs to increase the force with which he can break the pile, so he decreases the time by fasting his action. more...
Inertia
Inertia is the property of a body due to which the body opposes any change in its state of rest or of uniform motion along a straight line. Inertia is the measure of mass. More mass means more inertia.
Inertia of Rest
A body which is at rest will remain at rest unless or until some external force is applied to it.
It is the inability of a body to move on its own.
Activity
If we give sharp horizontal flick to the card then the card shoots away and the coin falls into the glass.
This happens due to inertia of rest of coin. The coin tends to remain in its state of rest and hence falls into the glass.
Inertia of Motion
It is the inability of a moving body to stop on its own.
Rahul is being chased through the woods by a bull moose which he was attempting to photograph. The enormous mass of the Bull Moose is extremely intimidating. Yet, if Rahul makes a zigzag pattern through the woods he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton's first law of motion.
Solution:
The large mass of the Bull Moose means that the Bull Moose has a large inertia. Thus, Rahul can more easily change his own state of motion make quick changes in direction while the moose has extreme difficulty changing its state of motion.
Inertia of Direction
The tendency of a body by which it resists a change in its direction of motion is called inertia of direction.
Yatin spends most Sunday afternoons at rest on the sofa, watching football games and consuming large quantities of food. What effect (if any) does this practice have upon his inertia?
(a) Increases
(b) Decreases
(c) No effect
(d) All of these
(e) None of these
Answer: (a)
Small droplets of water fall down when you shake a wet piece of cloth due to _____.
(a) Inertia of rest of droplets
(b) Inertia of motion of droplets
(c) Inertia of direction of droplets
(d) None of these
(e) All of these
Answer: (a)
Classification of Forces
Forces may be classified into the following two classes:
Contact forces
Action-at-a-distance
The contact forces arise as a result of physical contact between two bodies, one by which force is exerted and the other on which force is exerted. The force exerted by the wind on us is a contact force. The force of friction is also a contact force. The action-at-a-distance corresponds to the forces, which do not involve any physical contact between the two bodies, but act through the space between them.
The gravitational force, the magnetic force and the electrical force are the examples of the action- at-a-distance force.
Free Body Diagram
A book is at rest on a table top..
A baby is suspended motionless from the ceiling by two ropes.
A motor cycle and a car are moving on a horizontal road with the same velocity. If they are brought to rest by the application of brakes, which provide equal retardation, then
(a) Motor cycle will stop at shorter distance
(b) Car will stop at a shorter distance
(c) Both will stop at the same distance
(d) Nothing can be predicted
(e) None of these
Answer: (c)
The amount of net force required to keep a 5-kg object moving rightward with a constant velocity of 2 m/s is ________.
(a) 0 N
(b) 0.4 N
(c) 2 N
(d) 2.5 N
(e) 5 N
Introduction
The Greek thinker, Aristotle held the view that if a body is moving, something external -is required to keep it moving. The Aristotelian law of motion may be phrased for our purpose here, : An external force is required to keep a body in motion.
Force
Force is that agency which can change the state of rest or of uniform motion or shape or direction of motion of any object. The unit of force in M.K.S. system is newton. It is a vector quantity.
Effects of force
Force is required to change the shape and size of a body.
Force is required to move or stop a body.
Force is required to change the speed or direction of a moving body.
Balanced and Unbalanced Forces
Balanced forces cannot change the speed of a body. They can change the shape of the object. If the resultant of the forces acting on a body is zero, then the forces are said to be balanced.
In tug of war you must have observed balanced forces in action, if the two teams have equal strength, or force, the rope will stay pretty much in the same place.
Unbalanced forces can cause the change in speed or direction of motion of the body. If the resultant of the forces acting on the body is not zero, the forces are said to be unbalanced.
The trolley will accelerate if \[T>F\]
When two unbalanced forces are exerted in opposite directions, their combined effect is equal to the difference between the two forces and is exerted in the direction of the larger force.
Resultant Force
When two or more forces act on a body simultaneously, then the single force which produces the same effect as produced by all the forces acting together is known as the resultant force.
Bhor’s Model of Atom
After the drawback found in Rutherford model of an atom, it became necessary to find the reason for the stability of the atom. Bhor put forward his model of an atom and this was found to be acceptable to almost all the scientis of that time. According to Bhor model, an atom consists of nucleus which contains neutron and proton and electron that revolve around the nucleus in the fixed orbit and do not radiate energy. Energy is radiated or absorbed by an atom only when an electron moves from one shell to another. When electrons jumps from lower to higher energy level, it absorbs energy and when it jumps from higher to lower it radiates energy. The energy is always radiated or absorbed in the form of packet called photons. The orbit or the shell in which electrons revolves is called the energy level.
The energy levels are represented by the letters K, L, M, N, —. The maximum number of electrons in first shell called K shell can be 2, in second shell L shell can be 8, in third shell M shell can be 18, and so on. This distribution of electron is called the electronic configuration.
Atomic Numbers
It is defined as the number of proton present in the nucleus of an atom. It is denoted by letter Z.
Mass Number
It is the sum of proton and neutron present in the nucleus of an atom. It is normally denoted by A.
A = Z + n
Where/ n is the number of neutron
A is the mass number
Z is the atomic number.
Valence Electron
The number of electron present in the outermost shell of an atom is called the valence electron.
Valency
The number of electron loosed or gained by an atom to attain the stable electronic configuration is called the valency.
Isotopes
Isotopes of an atom is defined as the atoms of same elements having same atomic number but having different atomic mass. The isotopes is due to the difference in the number of neutron in an atom.
\[^{92}{{U}_{235}}\] and \[^{92}{{U}_{236}}\] are the isotopes of uranium. Apart from this other isotopes are \[^{6}{{U}_{12}}\] and \[^{6}{{C}_{14,}}\] \[^{1}{{H}_{1}},\,{{\,}^{1}}{{H}_{2}},\] and 3.
There are two types of isotopes radioactive and non radioactive isotopes. Uranium is a radioactive isotopes.
Isotopes have got wide application. Some of the applications of isotopes are:
Rutherford's Alpha Particle Scattering Experiment
In his experiment Rutherford bombarded a thin gold foil with the fast moving alpha particles. He took a gold foil about 1000 atoms thick and a doubly charged helium ions.
Observation
In his experiment Rutherford made the following observation:
Most of the \[\alpha \] particles passed straight through the gold foil.
Few of the \[\alpha \] particles were deflected through a small angles as it passes through the gold foil.
Very few a particles bounces back in the same direction from which they came.
Conclusion
On the basis of his experiment and observation he made the following conclusion:
There is large empty space in the atom.
The nucleus of the atom is positively charged.
The nucleus of the atom is densely packed.
Rutherford Model of Atom
On the basis of the above experiment he proposed the following model of an atom. According to him atom consists of positively charged nucleus where the entire mass is supposed to be concentrated. The electron revolve around the nucleus in a well defined orbit and size of the nucleus is very small as compared to the size of the atom.
Drawback of Rutherford Model of Atom
Followings are the drawback of Rutherford model of an atom:
The orbital revolution of the electron is not expected to be stable. Any particle in a circular orbit would undergo acceleration. During acceleration, charged particles would radiate energy. Thus, revolving electrons would lose energy and finally fall into nucleus. If they were so, the atom would be highly unstable and hence matter would not exist in the form that we know. But this does not happen and we know that atoms are quite stable.
Thomson's Model of Atom
Thomson proposed the model of atom before the discovery of neutrons. According to his model, an atom consists of a positively charged sphere and electrons are embedded in it. The positive and negative charge are equal in magnitude that’s why atom is electrically neutral. His model was also known as watermelon model of an atom. Although Thomson's model was electrically neutral, but other scientist could not explain this model and hence was not accepted.
Drawback of Thomsons Model
Some of the drawbacks of Thompson's model of atom were:
Since the weight of an electron is about a thousandth part of a hydrogen atom, it would mean that a single atom, especially of the heavier elements/ would contain many thousand electrons. But J.J. Thomson himself found that the number of electrons in an atom cannot be greatly different from the atomic weight.
According to this model, hydrogen can give rise to only one spectra! line, contrary to the observed fact of several lines.
This model could not explain the large angle scattering of alpha particles by thin metal foils..
Distance - Time Graph for Uniform Motion
A public transport bus is traveling from terminus P to terminus Q. The following observation was recorded by a passenger in the bus..
Observations
Difference between Distance and Displacement
Introduction
In everyday life we always come across some objects which are at rest and some objects in motion. The branch of Physics, which deals with the behavior of moving objects, is known as mechanics. Mechanics is further divided into two sections namely Kinematics and Dynamics. Kinematics deals with the study of motion without taking into account the cause of motion, while Dynamics is concerned with the cause of motion, namely force. This chapter covers only the different aspects of motion without considering the cause of motion.
When we are sitting in a moving bus, we observe the continuous changes of position with respect to stationary object like houses, trees, lamp posts, etc. We say that the bus is moving or that the bus is in motion.
Motion and rest are Relative Terms
Suppose you are travelling in a train, which is in motion.
Observe 1: Is there any change in your position with respect to your co passengers? Answer: No
Observe 2: Is there any change of scene you view through the window?
Answer: Yes
Thus, we can say that an object is in, motion, if it changes its position continuously with respect to its surroundings in a given time. Since the position of desk and benches does not changes with time, hence we can say that they are not in motion, i.e. they are stationary. You must have observed sky at night: the position of stars changes with the passage of time, whereas the position of house and our surrounding remains the same. But in reality the earth is also moving, that means all the objects on the surface of the earth are also in motion. Thus, an object which appears to be at rest, may actually be in motion. Therefore, motion and rest are relative terms. Hence, to describe the motion of an object we have to specify how its position changes with respect to a fixed point called the reference point or origin.
Without frame of reference we cannot specify whether an object is in motion or at rest. A frame of reference is another object or scene with respect to which we compare an object's position.
Newton's Laws of Motion
Newton's First Law of Motion
Everybody remains in its state of rest or of uniform motion, unless it is compelled to change its state by an unbalanced force, impressed on it.
\[F=m\times a\]
if, \[F=0\]
\[\Rightarrow \,\,a=0\,\,(m\ne 0)\]
(i) We tend to fall forward when a bus suddenly stops. When bus stops suddenly, we tend to resist the change in our state of motion and hence fall forward.
(ii) We tend to fall backward when a bus suddenly starts.
(iii) We tend to get thrown to one side when a car takes sharp turn.
Martin and Robert are arguing in the cafeteria. Martin says that if he throws the burger with a greater speed it will have a greater inertia. Robert argues that inertia does not depend upon speed, but rather upon mass. With whome do you agree?
(a) Martin
(b) Robert
(c) Both are correct
(d) Both are incorrect
(e) None of these
Answer: (b)
(i) A cricketer gradually pulls hand backwards with the moving ball when he catches the ball. While doing so he increases the time during which the high velocity of the ball is reduces to zero and the acceleration of the ball is also reduced drastically and hence the impact of catching the ball is also reduced and it does not hurt the player.
(ii) A judo champ breaks a pile of bricks in one go. His action is too fast. In this case he needs to increase the force with which he can break the pile, so he decreases the time by fasting his action. more... 
Inertia
Inertia is the property of a body due to which the body opposes any change in its state of rest or of uniform motion along a straight line. Inertia is the measure of mass. More mass means more inertia.
Inertia of Rest
A body which is at rest will remain at rest unless or until some external force is applied to it.
It is the inability of a body to move on its own.
Activity
Rahul is being chased through the woods by a bull moose which he was attempting to photograph. The enormous mass of the Bull Moose is extremely intimidating. Yet, if Rahul makes a zigzag pattern through the woods he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton's first law of motion.
Solution:
The large mass of the Bull Moose means that the Bull Moose has a large inertia. Thus, Rahul can more easily change his own state of motion make quick changes in direction while the moose has extreme difficulty changing its state of motion.
Yatin spends most Sunday afternoons at rest on the sofa, watching football games and consuming large quantities of food. What effect (if any) does this practice have upon his inertia?
(a) Increases
(b) Decreases
(c) No effect
(d) All of these
(e) None of these
Answer: (a)
Classification of Forces
Forces may be classified into the following two classes:
Free Body Diagram
A book is at rest on a table top..
A motor cycle and a car are moving on a horizontal road with the same velocity. If they are brought to rest by the application of brakes, which provide equal retardation, then
(a) Motor cycle will stop at shorter distance
(b) Car will stop at a shorter distance
(c) Both will stop at the same distance
(d) Nothing can be predicted
(e) None of these
Answer: (c)
Introduction
The Greek thinker, Aristotle held the view that if a body is moving, something external -is required to keep it moving. The Aristotelian law of motion may be phrased for our purpose here, : An external force is required to keep a body in motion.
Effects of force
In tug of war you must have observed balanced forces in action, if the two teams have equal strength, or force, the rope will stay pretty much in the same place.
Unbalanced forces can cause the change in speed or direction of motion of the body. If the resultant of the forces acting on the body is not zero, the forces are said to be unbalanced.
The trolley will accelerate if \[T>F\]
When two unbalanced forces are exerted in opposite directions, their combined effect is equal to the difference between the two forces and is exerted in the direction of the larger force.
Bhor’s Model of Atom
After the drawback found in Rutherford model of an atom, it became necessary to find the reason for the stability of the atom. Bhor put forward his model of an atom and this was found to be acceptable to almost all the scientis of that time. According to Bhor model, an atom consists of nucleus which contains neutron and proton and electron that revolve around the nucleus in the fixed orbit and do not radiate energy. Energy is radiated or absorbed by an atom only when an electron moves from one shell to another. When electrons jumps from lower to higher energy level, it absorbs energy and when it jumps from higher to lower it radiates energy. The energy is always radiated or absorbed in the form of packet called photons. The orbit or the shell in which electrons revolves is called the energy level.
The energy levels are represented by the letters K, L, M, N, —. The maximum number of electrons in first shell called K shell can be 2, in second shell L shell can be 8, in third shell M shell can be 18, and so on. This distribution of electron is called the electronic configuration.
Atomic Numbers
It is defined as the number of proton present in the nucleus of an atom. It is denoted by letter Z.
\[^{92}{{U}_{235}}\] and \[^{92}{{U}_{236}}\] are the isotopes of uranium. Apart from this other isotopes are \[^{6}{{U}_{12}}\] and \[^{6}{{C}_{14,}}\] \[^{1}{{H}_{1}},\,{{\,}^{1}}{{H}_{2}},\] and 3.
There are two types of isotopes radioactive and non radioactive isotopes. Uranium is a radioactive isotopes.
Isotopes have got wide application. Some of the applications of isotopes are:
Rutherford's Alpha Particle Scattering Experiment
In his experiment Rutherford bombarded a thin gold foil with the fast moving alpha particles. He took a gold foil about 1000 atoms thick and a doubly charged helium ions.
Observation
In his experiment Rutherford made the following observation:
Thomson's Model of Atom
Thomson proposed the model of atom before the discovery of neutrons. According to his model, an atom consists of a positively charged sphere and electrons are embedded in it. The positive and negative charge are equal in magnitude that’s why atom is electrically neutral. His model was also known as watermelon model of an atom. Although Thomson's model was electrically neutral, but other scientist could not explain this model and hence was not accepted.
Drawback of Thomsons Model
Some of the drawbacks of Thompson's model of atom were:
