Slide 2 : Lecture by PROF. ARDAMAN SIDHU
HKS INSTITUTE OF SCIENCES
INTRODUCTION : INTRODUCTION The branch of Physics which deals with the study of motion of material objects is called Mechanics.
Statics.
It is a branch of mechanics which deals with the study of material objects at rest.
Slide 4 : Kinematics. It is that branch of mechanics which deals with the study of motion of material objects without taking into account the factors. Dynamics. It is that branch of mechanics which deals with the study of motion of objects taking into account the factors which cause motion.
‘Dynamls’ meaning power. Since the force is the cause of motion, therefore dynamics is based on the concept of force.
OBJECT IN MOTION : OBJECT IN MOTION Rest
An object is said to be at rest if it does not change its position with time, with respect to its surroundings. Motion
An object is said to be in motion if it changes its position with time, with respect to its surroundings
TYPES OF MOTION OF A BODY : TYPES OF MOTION OF A BODY Rectilinear motion.
Rectilinear motion is that motion in which a particle or point mass body is moving along a straight line.
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Translatory Motion
is that motion in which a body which is not a point mass body is moving such that all its constituent particles move simultaneously along parallel straight lines.
Circular or Rotatory motion : Circular or Rotatory motion A circular motion is that motion in which a particle or a point mass body is moving on a circle.
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A rotatory motion is that motion in which a body, which is not a point mass body, is moving such that all its constituent particles moves simultaneously along concentric circles.
CONCEPT OF POINT MASS OBJECT : CONCEPT OF POINT MASS OBJECT Thus an object can be considered as a point object if during motion in a given time, it covers distance much greater than its own size.
For example: A car traveling a few hundred kilometer distance, can be taken as a point object.
FRAME OF REFERENCE : FRAME OF REFERENCE Thus the frame of reference is a system of coordinate axes attached to an observer, with respect to which, the observer can describe position, displacement, acceleration etc. of a moving object.
Inertial frame of reference : Inertial frame of reference is one in which Newton’s first law of motion holds good.. For example, a frame of reference attached to a person in a bus at rest or moving with a uniform velocity along a straight path..
Non-inertial frame of reference : Non-inertial frame of reference is one in which Newton’s first law of motion does not hold good.
For example, a frame of reference attached to a person in a bus moving with variable velocity for moving with acceleration along a straight path.
MOTION IN ONE TWO AND THREE DIMENSIONS : MOTION IN ONE TWO AND THREE DIMENSIONS One dimensional motion.
The motion of an object is said to be one dimensional motion if only one out of the three coordinates specifying the position of the object changes with respect to time.
For example, the motion of train along a straight railway track, an object dropped from a certain height above the ground, a man walking on a level road.
Two dimensional motion. : Two dimensional motion. The motion of an object is said to be two dimensional motion if two out of the three coordinates specifying the position of the object change with respect to time.
In two dimensional motion, the object moves in a plane. For example, an insect crawling , earth revolving around the sun, a billard ball moving over the billard table.
Three dimensional motion : Three dimensional motion The motion of an object is said to be three dimensional motion if all the three coordinates specifying the position of the object change with respect to time.
PATH LENGTH AND DISPLACEMENT : PATH LENGTH AND DISPLACEMENT Path length. The path length of an object in motion in a given time is the length of actual path traversed by the object in the given time.
Displacement. The displacement of an object in motion in a given time is defined as the change in position of the object, i.e., the difference between the final and initial positions of the object in a given time.
DIFFERENCE BETWEEN DISTANCE AND DISPLACEMENT : DIFFERENCE BETWEEN DISTANCE AND DISPLACEMENT Distance 1. It is the actual path traversed by the object in the given time.
2. It is scalar quantity.
3. The distance traveled by an object in a given time is never negative or zero, but is always positive.
4. The distance traveled in a given time is either equal or greater than displacement but never less than displacement.
5. The distance covered by an object between two positions can have many values, depending upon the path followed.
6. The distance traveled by the object between two position tells the type of path followed. Displacement 1. It is the shortest distance between the initial and final positions of the object in the given time.
2. It is a vector quantity.
3. The displacement of an object in a given time can be positive, zero or negative.
4. The displacement of an object in a given time can be equal or less than distance traveled but never greater than distance traveled.
5. The displacement of an object between two positions has a unique value.
6. The displacement of an object between two positions does not tell the type of path followed.
Slide 17 : Speed of an object in motion is defined as the ratio of total path (i.e. actual distance covered) and the corresponding time taken by the object.
Speed = Uniform speed. An object is said to be moving with a uniform speed, if it covers equal distances in equal intervals of time, howsoever small these intervals may be.
Variable speed. An object is said to be moving with a variable speed if it covers equal distances in unequal intervals of time or unequal distances in equal intervals of time, howsoever small these intervals may be.
Slide 18 : Average speed of the object is that constant speed with which the object covers the same distance in a given time as it does while moving with variable speed during the given time.
Average speed = If a particle travels distances S1,S2,S3 etc. with speeds v1, v2 , v3 etc. respectively, in same direction then
Average speed =
AVERAGE SPEED : AVERAGE SPEED If S1 = S2 = S ; i.e. the body covers equal distances with different speeds then
Vav = (ii) If a particle travels with speeds v1, v2, v3, etc. during time intervals t1, t2, t3, etc. respectively
Vav =
Instantaneous speed. : Instantaneous speed. The speed of an object at a given instant of time is called its instantaneous speed.
Instantaneous speed of an object at an instant of time t is defined as the limit of the average speed as the time interval t at the given instant of time becomes infinitesimally small.
Instantaneous speed =
: Velocity of an object in motion is defined as the ratio of displacement and the corresponding time interval taken by object.
Uniform velocity is that velocity of object with which, it undergoes equal displacements in equal intervals of time howsoever small these intervals may be
POSITION-TIME GRAPH FOR A MOVING OBJECT : POSITION-TIME GRAPH FOR A MOVING OBJECT if an object is at rest or stationary. If an object is in uniform motion along a straight line, starting from, the origin O.
SLOPE OF POSITION-TIME GRAPH. : SLOPE OF POSITION-TIME GRAPH. THE IMPORTANCE OF THE POSITION-TIME GRAPH OF UNIFORM MOTION LIES IN THE FACT THAT ITS SLOPE GIVES US VELOCITY OF THE OBJECT. Velocity of the object
v = = slope of position-time graph.
VELOCITY-TIME GRAPH IN UNIFORM MOTION : VELOCITY-TIME GRAPH IN UNIFORM MOTION VELOCITY-TIME GRAPH OF UNIFORM MOTION HELPS US TO MEASURE THE DISPLACEMENT UNDERGONE BY AN OBJECT IN A GIVEN TIME AS THE AREA ENCLOSED BY VELOCITY-TIME GRAPH WITH TIME AXIS.
IN VELOCITY-TIME GRAPH, THE POSITIVE AREA ENCLOSED WITH TIME AXIS GIVES POSITIVE DISPLACEMENT AND THE NEGATIVE AREA ENCLOSED WITH TIME AXIS GIVES NEGATIVE DISPLACEMENT.
DISPLACEMENT OF A BODY IN A GIVEN INTERVAL OF TIME IS EQUAL TO TOTAL AREA OF VELOCITY-TIME GRAPH, WHICH IS TO BE ADDED WITH PROPER SIGN.
4. DISTANCE TRAVELED BY A BODY IN A GIVEN INTERVAL OF TIME IS EQUAL TO TOTAL AREA OF VELOCITY-TIME GRAPH, WITHOUT CONSIDERING SIGN.
Slide 26 : I. If v – t graph is parallel to time axis, then a) body is moving with uniform velocity. b) its acceleration is zero. c) its displacement can be found out by finding the area of graph. 2. If v – t graph is a straight line, but not parallel to time axis, it has uniform acceleration, which can
be found by slope of the graph. Displacement can be found, by
finding area under v – t graph. Velocity – time graph – conclusions If velocity is plotted on Y–axis & time along X–axis, then such a graph is known as velocity time (v – t) graph.
UNIFORMLY ACCELERATED MOTION : UNIFORMLY ACCELERATED MOTION ACCELERATION
Acceleration of an object in motion is defined as the ratio of change in velocity and the corresponding time taken by the object.
Acceleration =
UNIFORM ACCELERATION. An object is said to be moving with a uniform acceleration if its velocity changes by equal amounts in equal intervals of time.
UNIFORMLY ACCELERATED MOTION : UNIFORMLY ACCELERATED MOTION VARIABLE ACCELERATION. An object is said to be moving with a variable acceleration if its velocity changes by unequal amounts in equal intervals of time.
AVERAGE ACCELERATION. When an object is moving with a variable acceleration, then the average acceleration of the object for the given motion is defined as the ratio of the total change in velocity of the object during motion to the total time taken
INSTANTANEOUS ACCELERATION. The acceleration of the object at a given instant of time or at a given point of motion, is called its instantaneous acceleration.
EQUATIONS OF UNIFORMLY ACCELERATED MOTION : EQUATIONS OF UNIFORMLY ACCELERATED MOTION . v2 – u2 = 2aS DISTANCE TRAVELLED IN NTH SECOND OF UNIFORMLY ACCELERATED MOTION Dn = u + (2n – 1)
Slide 30 : If acceleration is plotted on Y–axis & time along X–axis, then such a graph is known as acceleration time (a – t) graph. From figure, it is clear that acceleration does not change. Area covered under a – t graph gives change in velocity. 2 4 6 8 10 1 2 3 4 5 O 6 t ? ?
a B X A Y Acceleration – time graph
Slide 31 : The acceleration of a freely falling body under the action of gravity of Earth is called acceleration due to gravity. The value of g on Earth is 9.8m/s2. Whenever a body is thrown (projected) vertically upwards or dropped towards the ground then acceleration is replaced by acceleration due to gravity. Definition : It is denoted by g. Acceleration due to gravity Let us study body projected upwards and freely falling bodies… Measuring instrument: The value of g is measured with Gravity meter Ex: The Boliden Gravity meter and the
Gulf Gravity meter
Slide 32 : Freely falling body: Then the value of g is taken as –9.8m/s2. The value of g on moon is 1/ 6th of that on the Earth. Let us study the notations we use in Kinematics… +g Then the value of g is taken as +9.8m/s2. When a body is falling towards the Earth under the influence of gravity of Earth is called freely falling body. Body projected upwards: When a body is projected upwards away from the Earth under the influence of gravity of Earth is called body projected upwards. +g Freely falling body and body projected upwards
Slide 33 : HINTS FOR THE PROBLEMS 1. If a body starts from rest, u = 0 2. If a body is brought to rest, v = 0 3. If a body moves with uniform velocity, a = 0 4. For a body thrown upwards, at the highest point, v = 0 5. If a body is dropped from certain height u = 0 6. If a body moves vertically upwards from the earth, a = –g. 7. If a body moves vertically downwards a = + g
Slide 34 : 1. Slope of s – t graph gives VELOCITY 2. Slope of v – t graph gives ACCELERATION 3. Area covered under v – t graph gives DISTANCE Area covered under a – t graph gives CHANGE IN VELOCITY Summary Let us solve few problems using the graphs . . .
Slide 35 : 1) v–t graph is as follows :Then a) plot S–t and a–t graph
b)find displacement of the body after 50 s and velocity of the body after 10 s. a = acceleration Replace t by x as it is plotted on X – axis & S by y as it is plotted on y – axis. The relation ship between S & t is of the form of ? S– t graph is a parabola. y=kx2
(parabola) = slope of v–t graph = tan ? Let’s solve the next bit… Sol:
Slide 36 : • • • a–t graph is the straight line parallel to x – axis or time axis. Acceleration is constant with respect to time. 1 3 • 2 b) S50=? V10=? 10 0 Let’s solve the next problem… 1) V–t graph is as follows :Then a) plot S–t and a–t graph
b)find displacement of the body after 50 s and velocity of the body after 10 s. Sol:
Slide 37 : 2 A car starting from rest travels with uniform acceleration x and then comes to rest with uniform retardation y. If the total time of travel is t second, then the maximum velocity of the car is ______ . Case 1(OA) u1 = 0 v1 = v a1 = x t = t1 Case 2(AB) u2 = v = v2 = 0 a2 = –y t = t2 v = u + at v = 0 + xt1 v = xt1 t1 0 = v – yt2 v = yt2 t2 t = t1 + t2 v t O A B x y vmax vmax=? t = t vmax = ? Let’s solve the next problem… Sol: Formula: Applying for both the cases we get, To get total time add 1 and 2 we get,
Slide 38 : 3) A body is dropped from a height of 20m above the ground. If gravity disappears 1 second after the start, the time it takes to hit the ground is ( assume acceleration due to gravity = 10 m/s2) tAC = 1sec gCB =0 C tAB=tAC + tCB =? Case–1
AC Case–2
CB t AC = 1s t CB = t =? gAC=10m/s2 gCB= 0 SAC = x SCB =20– x u1 = 0 u2 = vC Substituting (1) in (2) we have tAB =tAC+t CB = ? vC= Final velocity of phase AC = u1 + a1t1 = 0 + 10? 1 = 10 m/s Let’s solve the next problem… Sol: Formula: Applying for both the cases we get,
Slide 39 : 4) v–t graph of a Rocket is as follows . Find the maximum height reached and distance covered during Retardation phase. Maximum height = Displacement = Area under v–t Graph = Area of triangle OAB =12500m v = 0 v = 100m/s Acceleration phase Retardation phase A B b} distance travelled during retardation phase = ? vA= u vB = v tAB = =100m/s = 0 250–100 = 150 s tA= tB =250s 100s Sol:
Slide 40 : For all your Physics Problems
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