Slide 1 : PROF. ARDAMAN SIDHU
HKSIS
PRESENTS
LECTURES IN PHYSICS
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Wiziq.com
FORCE : FORCE Force is an external effort in the form of push or pull, which (i) produces or tries to produce motion in a body at rest, or (ii) stops or tries to stop a moving body, or (iii) changes or tries to change the direction of motion of the body.
ARISTOTLE’S FALLACY : ARISTOTLE’S FALLACY The Greek thinker Aristotle (384 B.C. – 322 B.C.), held the view that if a body is moving, some external force is required to keep it moving.
But there is flaw in Aristotle’s argument. A ball rolling on the floor stops because an external force of friction between the ball and the floor and also resistance of air opposes the motion of the ball. If there were no opposing forces, the rolling ball would never stop.
INERTIA : INERTIA This, inherent property of all bodies, by virtue of which they cannot change by themselves their state of rest or of uniform motion along a straight line is called Inertia.
LINEAR MOMENTUM : LINEAR MOMENTUM LINEAR MOMENTUM
The linear momentum of a body is defined as the product of the mass of the body and its velocity i.e.
Linear momentum is a vector quantity.
The SI unit of linear momentum is kg ms-1
NEWTON’S LAWS OF MOTION : NEWTON’S LAWS OF MOTION First Law. According to this law, a body continues to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by some external force to change the state.
NEWTON’S LAWS OF MOTION : NEWTON’S LAWS OF MOTION Second Law. According to this law, the rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place always in the direction of the force applied.
NEWTON’S LAWS OF MOTION : NEWTON’S LAWS OF MOTION Third Law. According to this law, to every action, there is always an equal and opposite reaction i.e. the forces of action and reaction are always equal and opposite.
NEWTON’S FIRST LAW DEFINES FORCE : NEWTON’S FIRST LAW DEFINES FORCE According to Newton’s first law of motion, a body continues to be in a state of rest or of uniform motion along a straight line, unless it is acted upon by an external force.
Hence we define force as an external effort in the form of a push or pull which moves or tries to move a body at rest; stops or tries to stop a body in motion; changes or tries to change the direction of motion of a body.
NEWTON’S FIRST LAW DEFINES INERTIA : NEWTON’S FIRST LAW DEFINES INERTIA This inability of a body to change by itself its state of rest or state of uniform motion along a straight line is called INERTIA of the body.
Quantitatively, inertia of a body is measured by the mass of the body. Heavier the body, greater is the force required to change its state and hence greater is its inertia. The reverse is also true.
THREE TYPES OF INERTIA : THREE TYPES OF INERTIA Inertia of rest.
Inertia of motion.
Inertia of direction.
INERTIA OF REST: : INERTIA OF REST: Inability on part of the body to change by itself its state of rest is called inertia of rest.
Examples of Inertia of Rest
Suppose we are standing in a stationary bus and the driver starts the bus suddenly. We get thrown backward with a jerk.
The dust particles in a carpet fall off when it is beaten with a stick.
When we shake a branch of a mango tree, the mangoes fall down.
THREE TYPES OF INERTIA : THREE TYPES OF INERTIA INERTIA OF MOTION
It is the inability of a body to change by itself its state of uniform motion i.e. a body in uniform motion can neither accelerate nor retard on its own and come to rest. For example:
Suppose we are standing in a moving bus, and the driver stops the bus suddenly. We are thrown forward with a jerk.
A person jumping out of a speeding train may fall forward.
An athelet runs a certain distance before taking a long jump.
THREE TYPES OF INERTIA : THREE TYPES OF INERTIA (c) Inertia of direction
It is the inability of a body to change by itself its direction of motion i.e. a body continues to move along the same straight line unless compelled by some external force to change it.
For example:
When a stone tied to one end of a string is whirled and the string breaks suddenly, the stone flies off along the tangent to the circle.
When a car rounds a curve suddenly, the person sitting inside is thrown outwards.
The rotating wheels of any vehicle throw out mud, if any, tangentially, due to directional inertia.
When a knife is sharpened by pressing it against a grinding stone, the sparks fly off along the tangent to the grinding stone.
EXPLANATION OF NEWTON’S SECOND LAW : EXPLANATION OF NEWTON’S SECOND LAW P = mv
Second law of motion gives us a measure of force.
UNITS OF FORCE : UNITS OF FORCE The units of force are of two types:
ABSOLUTE UNITS AND GRAVITATIONAL UNITS.
Absolute units
The absolute unit of force on SI is Newton
One Newton force is that much force which produces an acceleration of in a body of mass I kg.
UNITS OF FORCE : UNITS OF FORCE Absolute units
(ii) The absolute unit of force in c.g.s. system is dyne.
One dyne force is that much force which produces an acceleration of 1 cm s-2 in a body of mass one gram.
1 dyne = 1 g x 1 cm s-2 = 1 g cm s-2
1 newton = dyne
UNITS OF FORCE : UNITS OF FORCE Gravitational units
The gravitational unit of force
in SI is 1 kilogram weight (kg.wt) or 1 kilogram force (kg f).
It is that much force which produces an acceleration of 9.8 ms-2 in a body of mass 1 kg. Thus
1 kg wt. Or 1 kg f = 1 kg x 9.8 ms-2 = 9.8 N
UNITS OF FORCE : UNITS OF FORCE (ii) The gravitational unit of force on c.g.s. system is 1 gram weight ( g wt.) or 1 gram force (1 g f).
It is that much force which produces an acceleration of 980 cm s-2 in a body of mass 1 gram.
CONSEQUENCES OF NEWTON’S SECOND LAW OF MOTION : CONSEQUENCES OF NEWTON’S SECOND LAW OF MOTION No force is required to move a body uniformly along a straight line.
Accelerated motion is always due to an external force.
Second law helps to Measure force
The second law of motion is a vector law.
CONSEQUENCES OF NEWTON’S SECOND LAW OF MOTION : CONSEQUENCES OF NEWTON’S SECOND LAW OF MOTION Force changes only the component of velocity along the direction of force.
The second law of motion is applicable to a single point particle.
However, the law in the same form can be applied to a rigid body.
Any internal force in the system are not to be included in
CONSEQUENCES OF NEWTON’S SECOND LAW OF MOTION : CONSEQUENCES OF NEWTON’S SECOND LAW OF MOTION Concept of INERTIAL MASS. F = ma
A mass which accounts for linear inertia of the body is called inertial mass of the body.
We may define inertial mass of a body as the force required to produce unit acceleration in the body.
IMPULSE : IMPULSE IMPULSE
Impulse of a force is a measure of total effect of the force acting on a body for short interval of time
Impulse = average force x time
i.e. Impulse,
Impulse is measured by the total change in linear momentum produced during the impact.
Impulse is a vector quantity.
The dimensional formula [M1 L1 T-1]
IMPULSE : IMPULSE If we plot a graph between average force and time, the area under the curve and time axis gives the value of impulse.
APPLICATIONS OF THE CONCEPT OF IMPULSE
A cricket player lowers his hands while catching a cricket ball.
When a person falls from a certain height he gets hurt on a cemented floor, the floor does not yield.
China wares and glasswares are wrapped in paper or straw pieces.
The vehicles like scooter, car, bus, truck etc. are provided with shockers.
Bogies of a train are provided with the buffers.
It is difficult to catch a cricket ball than to catch a tennis ball.
An athlete is advised to come to stop slowly.
EXPLANATION OF NEWTON’S THIRD LAW OF MOTION : EXPLANATION OF NEWTON’S THIRD LAW OF MOTION According to Newton’s third law, to every action, there is always an equal and opposite reaction.
Important Notes
Forces always occur in pairs. Force on a body A by B is equal and opposite to the force on body B by A.
Forces of action and reaction act always on different bodies. Hence they never cancel each other.
EXPLANATION OF NEWTON’S THIRD LAW OF MOTION : EXPLANATION OF NEWTON’S THIRD LAW OF MOTION Important Notes
The forces of action and reaction may appear due to actual physical contact of the two bodies or even from a distance.
Newton’s third law is applicable whether the bodies are at rest or they are in motion.
The third law applies to all types of forces e.g. gravitational, electric or magnetic forces etc.
EXPLANATION OF NEWTON’S THIRD LAW OF MOTION : EXPLANATION OF NEWTON’S THIRD LAW OF MOTION ILLUSTRATIONS OF NEWTON’S THIRD LAW
Book kept on a table.
Walking
Swimming
Firing from a gun.
Flight of jet planes and rockets
Rebounding of a rubber ball.
It is difficult to walk on sand or ice
APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR : APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR The actual weight of the person = mg. This acts on the weighing machine which offers a reaction R given by the reading of the weighing machine. This reaction exerted by the surface of contact on the person is the apparent weight of the person.
(i) When the elevator is at rest
Acceleration of the person = 0
Net force on the person f = 0
R – mg = 0
R = mg
APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR : APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR When elevator is accelerating upward.
Let acceleration be a
Then net weight of man is
R= m (g+ a)
Apparent weight becomes greater than the actual weight.
APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR : APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR (ii) When the elevator is accelerating downwards
Suppose uniform downward acceleration of the person in the lift = a
Net downward force on the person,
f = ma
f = mg – R2
R2 = mg – f = mg – ma = m (g – a)
Thus R2 < mg
Hence apparent weight of the person becomes less than the actual weight when the elevator is accelerating downwards.
APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR : APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR (iii) In free fall of a body under gravity, a = g
from (ii) , R2 = m ( g – g) = 0
i.e. apparent weight of the body becomes zero or the body becomes weightless.
Note that weightlessness is felt only because the force of reaction between the person and the plane with which he is in contact vanishes.
APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR : APPARENT WEIGHT OF A MAN IN A LIFT/ELEVATOR (iv) When downward acceleration is greater than g
i.e. a > g, then from (ii), R2 = m ( g – a), R2 becomes negative i.e. apparent weight of the person becomes negative. In that event, the person will rise from the floor of the lift and stick to the ceiling of the lift.
PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM : PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM According to this principle, in an isolated system, the vector sum of the linear momenta of all the bodies of the system is conserved and is not affected due to their mutual action and reaction.
PRACTICAL APPLICATIONS OF THE PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM
1. Recoiling of gun =0
2. While firing, the gun must be held tightly to the shoulder.
APPLICATIONS OF THE PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM : APPLICATIONS OF THE PRINCIPLE OF CONSERVATION OF LINEAR MOMENTUM 3. Flight of rockets and jet planes.
As a result of it, the escaping gases acquire a large backward momentum. This in turn, imparts an equal forward momentum to the rocket in according with the law of conservation of linear momentum.
4. When a man jumps out of a boat to the shore, the boat is pushed slightly away from the shore. The momentum of the boat is equal and opposite.
5. Explosion of bomb.
When bomb explodes, its pieces are scattered horizontally in different directions so that the vector sum of momenta of these pieces becomes zero in accordance with the law of conservation of linear momentum.
6. A person left on a frictionless surface can get away from it by blowing air out of his mouth or by throwing some object in a direction opposite to the direction in which he wants to move.
SECOND LAW IS THE REAL LAW OF MOTION : SECOND LAW IS THE REAL LAW OF MOTION (a) the first law is contained in the second law, and
(b) the third law is contained in the second law.
(a) First law is contained in the second law.
According to Newton’s second law of motion,
F= ma
If no external force is applied on a body,
F = 0
ma = 0
As 0, therefore, a = 0
Thus there will be no acceleration in the body if no external force is applied. This means that a body at rest will remain at rest and a body in uniform motion will continue moving uniformly along the same straight line in the absence of an external force. This is what is stated by first law of motion. Hence the first law is contained in the second law.
(b) THIRD LAW IS CONTAINED IN THE SECOND LAW.
CONNECTED MOTION : CONNECTED MOTION Acceleration of system.
Tension =
SYSTEMS WITH VARIABLE MASS : A ROCKET : SYSTEMS WITH VARIABLE MASS : A ROCKET Consider the flight of a rocket directed vertically upwards from the surface of earth. At t = 0, suppose
m0 = initial mass of the rocket including that of the fuel,
v0 = initial velocity of the rocket,
SYSTEMS WITH VARIABLE MASS : A ROCKET : SYSTEMS WITH VARIABLE MASS : A ROCKET At any time t, suppose
m = mass of the rocket left.
v = velocity acquired by the rocket
As the exhaust gases are escaping
m < m0 and v > v0
In a small interval of time dt,
suppose dm = a small decrease in mass of the rocket = mass of the exhaust gases that escape
dv = corresponding small increase in velocity of the rocket.
vg = velocity of exhaust gases w.r.t. earth.
SYSTEMS WITH VARIABLE MASS : A ROCKET : SYSTEMS WITH VARIABLE MASS : A ROCKET Velocity of rocket v at any time
For numerical problems, we may rewrite eqn.
SYSTEMS WITH VARIABLE MASS : A ROCKET : SYSTEMS WITH VARIABLE MASS : A ROCKET Burnt out Speed of the rocket is the speed attained by the rocket when the whole of fuel of rocket has been burnt.
The rocket is equal to mass of empty container of the fuel. mr
SYSTEMS WITH VARIABLE MASS : A ROCKET : SYSTEMS WITH VARIABLE MASS : A ROCKET Trust on the rocket
The negative sign indicates that thrust on the rocket is in a direction opposite to the direction of escaping gases.
NUMERICALS : NUMERICALS A body of mass 5 kg is acted upon by the perpendicular forces 8N and 6N Give the magnitude and direction of acceleration of the body.
Ans:
NUMERICALS : NUMERICALS Based on Impulse
A rubber ball of mass 50 gm falls from a height of 1 m and rebounds to a height of 0.5 m. Find the impulse and average force between the ball and the ground. If for 0.1 sec time they are in contact
Ans. Impulse = 0.377 N
F = 3.77 N
Slide 45 : For all your Physics Problems
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