General Science
Chapter 10 Physics
Physics is the study of nature and its laws. The word physics has been derived from a Greek word physis which means nature. Physics is one of the academic disciplines, perhaps the oldest through its inclusion of astronomy.
Units
Measurement of any physical quantity involves comparison with a certain basic arbitrarily chosen and widely accepted reference standard called unit.
SI System
It is based on the following seven basic units and two supplementary units
Basic Units | |
Length | metre |
Mass | kilogram |
Time | second |
Electric current | ampere |
Thermodynamic | kelvin |
temperature | |
Luminous intensity | candela |
Amount of substance | mole |
Supplementary Units | |
Plane angle | radian |
Solid angle | steradian |
Greatest Units
1 light year = 9.46 × 10 m^{15} 1 parsec = 3.086 × 10 m^{16 }= 3.26 ly 1 AU = 1.5 × 10 m^{11} 1 metric tonne = 10^{3 }kg 1 quintal = 10^{2 }kg
Dimensions of Physical Quantities
Dimensions of a physical quantity are the powers, to which the fundamental quantities must be raised to represent that quantity completely. There fore, the dimensional formula of a quantity is expressed in terms of fundamental quantities, commonly mass M, length L and time T. Any physical quantity is either a scalar or a vector. e.g. Force , Density^{}Scalar Quantities
Physical quantities which have magnitude only and no direction are called scalar quantities. e.g. mass, speed, volume, work, time, power, energy etc.
Vector Quantities
Physical quantities which have both magnitude and direction and also obey triangle law of vector addition are called vector quantities. e.g. displacement, velocity, acceleration, force, momentum, torque etc.
Kinematics
It is the branch of mechanics, which deals with the motion of object.
Distance
▸ The length of the actual path covered by a body in a particular time interval is called distance. It is always positive.
▸ It is a scalar quantity.
▸ Its unit is metre.
Displacement
▸ The difference between the final and the initial position of an object is called displacement. It may be positive, negative or zero.
▸ It is a vector quantity. Its unit is metre.
▸ The magnitude of displacement may or may not be equal to the path length traversed by an object. Displacement ≤ Distance
Speed
▸ Speed is the distance covered by a moving body in per unit of time interval.
▸ It is a scalar quantity. It is always equal to or greater than magnitude of the velocity.
▸ The average speed of a particle for a given interval of time is defined as the ratio of total distance travelled to the total time taken. Average speed = Total distance travelled /Total time taken
▸ If the body covers first half distance with speed v_{1 }and next half with speed v_{2}, then Average speed = (2v_{1} v_{2})/(v_{1} + v_{2})
Velocity
The rate of change of displacement of a body is called velocity. Velocity = Displacement/Time
▸ Velocity is a vector quantity.
▸ It may be positive or negative.
▸ Average velocity = Total displacement/Total time
▸ If the body covers first half distance with velocity v_{1 }and next half with velocity v_{2}, then
Average velocity = (2v_{1} v_{2})/(v_{1} + v_{2})
▸ If a body travels with uniform velocity v_{1 }for time t_{1 }and with uniform velocity v_{2 }for time t_{2}, then
Average velocity = (v_{1}t_{1} + v_{2}t_{2})/(t_{1} + t_{2})
▸ If a body is moving on a circular path, then after completing one complete cycle, its average velocity is zero.
UniformVelocity
An object is said to be moving with uniform velocity if it undergoes equal displacements in equal intervals of time.
Non-UniformVelocity
An object is said to be moving with nonuniform or variable velocity if it undergoes unequal displacements in equal intervals of time.
Relative Velocity
When two bodies aremoving in the straight line, the speed (or velocity) of one with respect to another is known as its relative speed (or velocity). vAB = velocity of A with respect to B = va – vb^{}Acceleration
▸ It is the rate of change of velocity. Its SI unit ism/ s^{2}. It is a vector quantity.
▸ When the velocity of a body increases with time then its acceleration is positive and if velocity decreases with time then its acceleration is negative and is called retardation or deceleration.
▸ Acceleration of an object is zero, if it is at rest or moving with uniform velocity. Average acceleration, = ( _{2} – _{1})/Δ = Δv/Δt
Motion/Rest
If the position of a body or a system of bodies does not change with time, it is said to be at rest. On the other hand, if the position change with time, it is said to be in motion. A particle in rest does not have the speed and acceleration, while a particle in the motion has its speed and also may have some acceleration, if the speed changes with respect to time.
Equation of Motion
For motion on a straight line with constant acceleration a
( ) = +
( ) = + 1/2 t^{2}
(iii) ^{2} = ^{2} + 2
Equation of Motion Under Gravity
(a) Downward Direction
( ) v = u + gt ( ) h = ut + 1/2 gt^{2} ( ) v^{2} = u^{2} + 2gh
where, s = displacement travelled h = height, t = time u = initial velocity v = final velocity a = acceleration, g = acceleration due to gravity for retardation awill be replaced by – a
(b) Upward Direction If velocity of a body is decreasing instead of increasing, then equation of motion are
( ) v = u – gt ( ) h = ut – 1/2 gt^{2} ( ) v^{2} = u^{2} – 2gh
(c) Distance travelled by a body in nth second s_{nth} snth = u + (2n – 1) a/2
▸ If the body is thrown upwards, then it will rise until its vertical velocity becomes zero. Then, the maximum height attained is h = u^{2}/2g
Graphical Representation of Motion
Displacement-Time Graph
If a body moves with a uniform velocity then displacement – time graph is a straight line. The slope or gradient of the straight line is speed.
Velocity-Time Graph
1. Constant Acceleration If a body moves with a constant velocity, velocity-time graph is a straight line.
2. Uniformly Accelerated Motion The velocity-time graph is a straight line.
Two Dimensional Motion
In this motion of a body is described in a rectangular co-ordinate axis.
ProjectileMotion
▸ When a particle is projected so that it makes certain angle with horizontal then the motion of the particle is said to be projectile. Path of a projectile is parabolic in nature.
▸ The initial velocity u of the projectile can be resolved into two components (i) u cos θ (horizontal direction) (ii) u sin θ (vertical direction)
For the Projectile Motion Maximum Height It is the maximum vertical distance travelled by a body.
It is given by (H) = (u^{2} sin^{2}θ)/2g
Horizontal Range The distance between projecting and landing point. It is given by (R) = (u^{2} sin2θ)/g
Time of Flight Time taken in reaching the landing point from projecting point. It is given by (T) = (2usinθ)/g
▸ For maximum range θ = 45°. Therefore, a long jumper takes jump at an angle of 45°.
▸ For maximum height θ = 90°.
▸ The horizontal range is the same when the body is projected at θ or (90° – θ).
▸ When a body is dropped freely from the top of the tower and another body is projected horizontally from the same point, both will reach the ground at the same time.
▸ When two balls of different masses are projected horizontally they will reach ground at same time.
CircularMotion
▸ When an object moves along a circular path, then its motion is called circular motion e.g. motion of top etc. If an object moves along a circular path with uniform speed, its motion is called uniform circular motion. It is accelerated even if the speed of the body is constant. The motion of a satellite is an accelerated motion.
▸ The acceleration is directed towards the centre and is given by = v^{2}/r, where v is the speed and r is the radius. This is called centripetal acceleration.
Force
Force is a push or pull which can change the position or direction of a body.
Centripetal Force
A body performing circular motion is acted upon by a force which is always directed towards the centre of the circle. This force is called centripetal force. Any of the forces found in nature (such as frictional force, gravitational force, electrical force, magnetic force etc) may act as a centripetal force.
▸ Cyclist bends his body towards the centre on a turn while turning to obtain the required centripetal force.
▸ Generally, in rain the scooter slips at the turning of a road because the friction between tyre and road is reduced. Due to this, necessary centripetal force is not provided. Roads are banked at turns to provide the required centripetal force for taking a turn.
Centrifugal Force
Pseudo ForceWhen we in a non-inertial frame of reference to apply Newton’s laws, we have to apply a force on the object equal to mass times in opposite direction of acceleration or retardation of the frame. Centrifugal force is such a Pseudo force. It is always equal and opposite to centripetal force. Cream separator, centrifugal drier etc work on the principle of centrifugal force.
Newton’s Laws of Motion
First Law
▸ “Every body retains its state of rest or state of uniform motion, until an external force is applied on it.” This law is also known as law of inertia or law of Galileo.
▸ First law gives the definition of inertia. Inertia is the virtue of a body due to which it tries to retain its state. Inertia is of three types Inertia of rest Inertia of motion Inertia of direction
▸ A person sitting in a moving car falls forward, when the car stops suddenly. This is because the feet of the passenger comes to the rest along with the car, but the upper part of his body, tends to remain in motion due to inertia of motion.
▸ The dust particle come out from a carpet, when it is beaten with a stick due to their inertia of rest.
▸ Inertial FrameWhenever the frame of reference is moving with uniform velocity or is at rest.
▸ Non-Inertial Frame Whenever the frame of reference is accelerating or retarding or rotating is called noninertial frame of reference.
Second Law
▸ ‘‘The force applied on a body is equal to the product of mass of the body and the acceleration produced in it e.g. F = ma.’’
▸ The second law of motion gives the definition of force.
▸ A force is any influence that causes an object to undergo a certain change, either concerning its movement, direction and geometrical structure.
▸ SI unit of force is Newton (N).
Linear Momentum
▸ The product of the mass and the velocity of a body is called the linear momentum of the body.
▸ It is a vector quantity. Its unit is kg-m/s. ∴Linear momentum = Mass × Velocity
▸ A heavier body has a larger linear momentum than a lighter body moving with the same velocity.
▸ In the absence of external forces, the total linear momentum of the system remains conserved.
Application of Conservation of LinearMomentum
▸ When a man jumps from a boat to the shore, the boat slightly moves away from the shore. Rocket works on the principle of conservation of momentum.
▸ When a bullet is fired from a gun, the gun recoils or gives a sharp pull in backward direction.
Impulse
▸ If a force acts on a body for a very short time Δt, then the product of force and time is called the impulse.
▸ Impulse = Change in momentum = Force × Time interval
▸ Its SI unit is N-s or kg-m/s.
Concept of Impulse
▸ A cricketer moves his hands backwards while catching a ball.
▸ A person jumping from a height on a ‘concrete’ floor receives more injury than when jumping on a spongy floor.
▸ Vehicles like cars, buses and scooters are provided with shockers.
▸ Bogies of the trains are provided with buffers to avoid severe jerks during shunting of trains. Buffers increase the time-duration of jerks during shunting. This reduces the force with which bogies push or pull each other and thus severe jerks are avoided.
Third Law
▸ “Every action have equal and opposite reaction.” Action and reaction always act on the different bodies.
▸ On firing the bullet, the gunner is pushed in backward direction.
▸ When the boatman is jumped from the boat, the boat is pushed back.
▸ In a rocket, gases are ejected with a great speed from the rocket backwards and rocket is pushed forwards.
▸ While swimming, a person pushes the water backwards (action). The water pushes the swimmer forward with the same force (reaction).
Equilibrium
▸ If the resultant of all the forces acting on a body is zero, then the body is said to be in equilibrium. If a body is in equilibrium, it will be either at rest or in uniform motion. If it is at rest, the equilibrium is called static, otherwise dynamic.
▸ Static equilibrium is of the following two types (i) Stable Equilibrium If on slight displacement from equilibrium position a body has tendency to regain its original position, it is said to be in stable equilibrium. (ii) Unstable Equilibrium If on a slight displacement from equilibrium position, a body moves in the direction of displacement and does not regain its original position, the equilibriumis said to be unstable equilibrium. In this equilibrium, the centre of gravity of the body is at the highest position.
Neutral Equilibrium
If on slight displacement from equilibrium position a body has no tendency to come back to its original position or to move in the direction of displacement, it is said to be in neutral equilibrium.
▸ In neutral equilibrium, the centre of gravity always remains at the same height.
Condition for Stable Equilibrium
For stable equilibrium of a body, the following two conditions should be fulfilled (i) The centre of gravity of the body should be at the minimum height. (ii) The vertical line passing through the centre of gravity of the body should pass through the base of the body. Centre of Mass Centre of mass of a body (system of particles) is a point where the entire mass of the body is supposed to be concentrated.We can define position of centre ofmass r by X
= (m_{1} r_{1} + m_{2} r_{2} + ……. + mn rn)/(m_{1} + m_{2} + ……. + mn)
Friction
▸ If we slide or try to slide a body over a surface, the motion is resisted by a bonding between the body and the surface. This resistance is called frictional force.
▸ The opposite force that comes into play when one body tends to move over the surface of another body but actually motion has yet not started is called static friction.
▸ The maximum value of the static frictional force which comes into play when a body just begins to slide over the surface of another body is called limiting frictional force.
▸ When two bodies actually roll on each other (as in case of ball bearing), the rolling friction comes into play.
▸ When two bodies actually slide over each other, sliding friction comes into play.
▸ When a body moves over the other body, then the force of friction acting between two surfaces in contact in relative motion is called Kinetic Friction.
▸ > > here , μκμr are called coefficient of static, kinetic and rolling friction respectively.
Advantages and Disadvantages of Friction
▸ Walking is possible due to friction.
▸ The transfer of motion from one part of a machine to other part through belts is possible by friction.
▸ Brake works on the basis of friction.
▸ Friction causes wear and tear of the parts of machinery in contact. Thus, their lifetime gets reduced.
Methods of Reducing Friction
▸ By polishing, by lubrication, by proper selection of material and by using ball bearing friction can be reduced to some extent.
Work, Energy and Power
Work
When a body is displaced by applying a force on it, then work is said to be done. If a body is displaced by a distance s on applying a force F on it, then work done W = F × s = Fs cos θ, where ‘θ’ is the angle between the force and the direction of displacement. It is a scalar quantity. Its unit is joule (J).
Positive Work Done
▸ Positive work means that force is applied along the direction of displacement. e.g. when a horse pulls a cart on a level road, when a body falls freely under gravitational pull.
Negative Work Done
Negative work means that force is opposite to displacement. e.g. when a positive charge is moved towards another positive charge, when a body is made to slide over a rough surface.
Zero Work Done
If the force is perpendicular to the displacement and if either the force or the displacement is zero, work done is zero. e.g. when a body is moved along a circular path with the help of a string, when a coolie travels on a platform with a load on his head and when a person does not move fromhis position but hemay be holding any amount of heavy load.
Energy
▸ It is defined as capacity of doing work. Its unit is joule in SI and erg in CGS system.
▸ Mechanical energy is in two forms; kinetic energy and potential energy.
Kinetic Energy
▸ It is the energy possessed by a body by virtue of its motion.
▸ If a body of mass m is moving with velocity v, then kinetic energy
KE = 1/2 ^{2} = p^{2}/2m where, p is the linear momentum.
▸ When momentum is doubled, kinetic energy becomes four times.
▸ Kinetic energy of air is used to run wind mills.
▸ Kinetic energy of running water is used to run the water mills.
▸ A bullet fired from a gun can pierce a target due to its kinetic energy.
▸ If a body is moving in horizontal circle then its kinetic energy is same at all points, but if it is moving in vertical circle, then the kinetic energy is different at different points.
Potential Energy
▸ It is the energy possessed by a body by virtue of its position.
▸ Suppose a body is raised to a height h above the surface of the earth, then potential energy of the body = mgh.
▸ When a body is falling downwards, then its potential energy goes on changing to kinetic energy.
▸ The potential energy of the wound spring of a clock is used to drive the hands of the clock.
▸ The potential energy of water in dams is used to run turbines in order to produce electric energy using the generators.
Conservative and Non-conservative Forces
A non-dissipative force is known as conservative force e.g. gravitational force, electrostatic force. Non-conservative forces are dissipative forces e.g. frictional forces, viscous force.
Law of Conservation of Energy
▸ According to the law of conservation of energy, ‘‘Energy can neither be created nor be destroyed but it can only be transformed from one form to another.”
▸ The sum of all kinds of energies in an isolated system remains constant at all times.
Transformation of Energy
▸ In a heat engine, heat energy changes into mechanical energy.
▸ In the electric bulb, the electric energy is converted into light energy.
▸ In burning coil, oil etc., the chemical energy changes into heat energy.
▸ In solar cell, solar energy changes into electrical energy.
▸ In playing sitar, mechanical energy changes into sound energy.
▸ In microphone, sound energy changes into electrical energy.
▸ In loud speaker, electrical energy changes into sound energy.
▸ In battery, chemical energy changes into mechanical energy.
▸ In electric motor, electrical energy changes into mechanical energy.
▸ In candle, chemical energy changes into light and heat energy.
Power
▸ Rate of doing work by a body is called power. i.e. Power = Work done/Time taken
▸ SI unit of power is watt (W) or joule per second and it is a scalar quantity. 1 W = 1 J/s 1 kW = 10^{3 }W 1 MW = 10^{6 }W 1 Horse Power (HP) = 746W 1 watt/second (W-s) = 1J 1 watt/hour (W-h) = 3600 J 1 kilowatt hour (kW-h) = 3.6 × 10^{6 }J
Torque
▸ The turning effect of a force on a body is known as the moment of the force or torque. Torque is a vector quantity. i.e. Torque, Z = F. d Where, F = force d = perpendicular distance of force from the axis of rotation.
Simple Machines
▸ It is based on moment of force.
▸ Lever, inclined plane, screw guage etc. are simple machine.
▸ Scissors, sea saw, brakes of cycle, hand pump, plass are lever of first kind.
▸ Nut cracker and waste carrying machine are lever of second kind.
▸ Tong, man’s hand and tiller are lever of third kind.