In this post we will discuss about the graph , and how graphs makes to understand the physics easily ?
Graph-
As we know it is not easy to study or understand the physics. Students who is taking interest in physics and want to understand the physics, it is necessary to improve your mathematics and most importantly graph, students who can’t solve the graphical questions will face lot of difficulties. So I am trying to provide some information/ knowledge for the students, so that students can understand the graphical questions easily. Now these days questions based on graph is important for every topics of physics specially the students who is appearing in the JEE/ NEET examination. Graph makes the calculation easier and it makes the topic to understand more easy. So every students must have to understand the graph and solve the questions based on it.
MOTION , THERE DIFFERENT TYPES, AND EQUATIONS OF MOTION .
MOTION OF AN OBJECT
Motion –
Rest and Motion -An object is said to be in rest , if body does not change its position with time , with respect to surroundings . An object is said to be in motion , if body changes its position with time , with respect to surroundings .
Motion of the body can be of following type –
Rectilinear / Translatory motion – In rectilinear motion a point mass body moves along a straight line . but in translator motion a body which is not a point mass moves in a straight line path.
Circular or rotatory motion – In circular motion a point mass object moves on a circular path. But in rotatory motion a body which is not a point mass moves on a circular path .
Oscillatory or vibratory motion– oscillatory motion is a type of motion in which a body moves to and fro or back and forth repeatedly about a fixed point. If in the oscillatory motion, amplitude is very small then the motion of the body is said to be in vibratory motion.
Motion in one , two and three dimensions-
One dimensional motion– The motion of a body is said to be in one dimensional if only one co-ordinate specify the position of the object in the given time. In such a motion body moves along a straight line
Two dimensional motion– The motion of a body is said to be in two dimensional if any two coordinate specify the motion of the body.
Three dimensional motion – The motion of a body said to be in three dimensional if all three coordinates specify the motion of the body . in such kind of motion body may cover a specific motion or irregular motion.
UNIFORM AND NON-UNIFORM MOTION-
Uniform motion – If a body covers equal distance in equal interval of time then it is said the motion of a body is uniform .
Some important features of the uniform motion is following-
(a) For a uniform motion along a straight line in a given direction , the distance and magnitude of the displacement remain the same .
(b) The velocity in uniform motion doesn’t depend upon the time interval .
(c)There is no need of force for an object to be in uniform motion .
(d) The velocity in uniform motion is in dependent of choice of origin.
(e) The average and instantaneous velocities have value in uniform motion.
If the motion of the object is uniform the following formula is used to find the
different– different physical quantities .
Distance = speed x time ; speed = distance / time
Displacement = velocity x time ; Velocity = displacement / time ;
Average speed = total distance covered / total time taken .
Average velocity = total displacement covered / total time taken
V = X2-X1 / t2-t1 .
Non-uniform motion- An object is said to be in non-uniform motion if it covers unequal distance in equal interval of time ,or equal distance in unequal interval of time. The velocity of a body changes with time it may increase ( accelerated ) or decrease (deaccelerate) with time .
Following are the important equations of motion– for uniformly accelerated motion
1st of motion ( it is also known as velocity – time relation)- v = u + at ( Where v=final velocity, u= initial velocity , a= acceleration, t = time taken .)
2nd of motion (it also known as distance – time relation ) – S=ut+1/2 at2 (where s=displacement ; u = initial velocity ; a= acceleration ; t = time taken .)
3rd of motion (it is also known as the velocity- position relation) – V2-U2=2aS (where – S= displacement ; V= final velocity ; U= initial velocity ; a= acceleration .)
4th of motion ( distance covered by the body in nth second ) Snth = u+ a(2n-1)/2 . (where Snth = distance covered in nth second ; a= acceleration ; n= given time ; u= initial velocity .)
ADDITION OF VECTOR – Vectors can not be added by simple laws of algebra.
Rules of geometric addition of vectors –
For the addition of two vectors– For the addition of two vectors represent these two vectors by arrowed lines using the same scale . Displace the second vector as its coincide with the head of first vector , then the single vector drawn from the tail of the first vector to the head of the second vector represent their resultant ( addition) vector.
the addition of two vectors can be obtained using Triangle law or parallelogram law of vector addition
For the addition of three or more vectors – Represent these vectors by arrowed lines using the same scale . Displace these vectors such that the head of the first vector coincide with the tail of the second vector and head of second coincide with the tail of third vector and so on , then the single vector drawn from the tail of the first to the head of the last represent their resultant vector. The addition of three or more vectors can be found using polygon law of vector addition.
Triangle law of vector addition- It states that if two vectors acting on a particle represented by two sides of a triangle in same order , then the third side in opposite order gives the resultant vector.
What do you mean by the term vector quantity? what are the uses of vector quantity? Explain different types of vector.
VECTORS-
Physical quantity having both magnitude and direction called vector quantity . And the physical quantity having magnitude only called scalar quantity . E.X.- suppose a man move 10 km , now in that case I am discussing about its distance only i.e. it has magnitude only but there is no any information about its direction hence it is a scalar quantity, if we say man is moving 10 km towards East(or any other direction ) so we can say we are discussing about its displacement i.e. it has both magnitude and direction. A vector quantity is represented as an arrow on its top ex;- ? ⃗
Vectors can be divided into two ways –
Polar vector- a vector which has a starting point or a point of application. E. X .- displacement , force etc.
(ii) Axial vector – Vectors which represent rotational effects and acts along the axis of rotation in accordance with right hand screw rule.
What is dimensions of a physical quantity?What are the uses of dimensions ?
DIMENSIONS– The dimension of a physical quantity as the power to which the fundamental units have to raised to represent a derived units of the quantity.
As we know that derived units of the physical quantities can be obtained from fundamental units of mass , length and time . Fundamental unit of mass is represented as [M], length is represented as [L] , and time as [T] . If we have to derive the dimension of velocity , then it may be written as
Velocity V = distance / time = [L] / [T] = [M0L1T-1] . Similarly we can find the dimensions of all physical quantities .
The dimensions of the physical quantity is an expression which tells us : (i) The dimensional units on which the quantity depends and (ii) The nature of the dependence .
The dimensional formula of a physical quantity can be obtained by defining there relation with other physical quantities , whose dimensions in mass, length and time are already known .
When a physical quantity is equated to its dimensional formula , what we obtained is the dimensional equation of the physical quantity.
Uses of dimensional equations : –
Checking the accuracy of formula ; Whether the given equations are correct or not can be checked on the basis of principle of homogeneity . according to this principle , the given formula is correct if dimension of left hand side of the equation is equal to the dimension of right hand side of a physical quantity.
Conversion of one system of units into another ; – This is based on the fact that the magnitude of a physical quantity remains the same , whatever the system of its measurement. Q= n1u1 = n2u2. For to do that , we have to use the formula
Which is given as , n2=n1 [M1/M2]a [L1/L2]b [T1/T2]c .
Derivation of formula or to find the actual relationship between given physical quantities. Using the same principle of homogeneity of dimensions , we can derive the formula of physical quantity , provided we know the factors on which the physical quantity depends.
generally it is seen the measured value of a quantity is different from its actual value . this difference in the measured value and and the true value of a quantity is called error of measurement.
Errors of measurement can be divided into following types-
Systematic errors -Those errors whose causes are known and it can be corrected ( or , can be minimised). Like Instrumental errors, personal errors ,Error due to imperfection and errors due to external causes.
Random errors-These errors may arise due to large variety of factors . some time it is also called ‘ chance error’ . random errors can be minimised by repeating the observation.
Gross errors– These errors arises due to carelessness of the observer during the measurement of the values.
Absolute errors– Absolute errors in the measurement is the difference between true value and measured value of the quantities . The absolute errors sometime may be positive and sometime negative .
Mean absolute error-It is the arithmetic mean of magnitudes of absolute errors.
Relative errors /Fractional errors-It is the ratio of mean absolute errors to the mean value or true value of the quantities measured.
Permissible errors-It is the errors which arises due to limitations on the measuring abilities of various instruments use in the experiment.
Accuracy– It is the extent to which a measurement approaches the true value of the quantities measured.
Precision– It describes the limitations of the measuring instruments . It is the degree of correctness of a measurement.
In this topic we will discuss what is a significant figure ? how can we find the significant figure in the given values and what are the rules for counting significant figure ?
Significant figure – It is the measured value of a physical quantity tell the number of digit in which we are confident . ( Larger the value of significant figure greater will be the accuracy and vice versa ).
Number of significant figure in a physical quantity depends upon the least count of the instrument used for its measurement.
Rules for counting significant figure –
All non zero digits are significant figure , and all zeros occurring between the two non zero digits are significant.
In a number less than 1 , all zeros to the right of decimal point and to the left of a nonzero digit are not significant . But all the zeros on the right of the last non zero digit in the decimal part are significant.
All zeros on the right of non zero digits are not significant . but all zeros on the right of the last non zero becomes significant when they come from a measurement.
(Note- change in the unit of measurement of a quantity does not change the number of significant figures .)
– Parallax method has been used for measuring distance of stars which are less than 100 light years away.(parallax is the name given to change in the position of an object with respect to the back ground , when the object is seen from the two different positions .)
PARALLAX METHOD FIGURE
The diameter AB of earth’s orbit around the sun is chosen as the base line as shown in the fig. . N is the nearby star whose distance (d) from the earth is to be measured . F is a far off star whose direction is taken practically the same at all position of earth in its orbital motion .
Suppose A is the position of earth in its orbital motion at any time . using an astronomical telescope we measure <FAN = θ1 , between the directions of light from distant star F and nearby star N . As it clear from the figure <FAN = <ANS =θ1 .
After six months earth is at B which is directly opposite to the point A , let < FBN =θ2, between the direction of light from distant star F and nearby star N is measured again <FBN = <BNS = θ2
Clearly , <ANB = <ANS +<BNS = θ1 + θ2 .
As we know , angle = arc/ radius
Therefore , θ1 + θ2 = AB/AN
Or AN = AB / θ1 + θ2 .
Clearly AB= 2AS = 2AU
If θ1 and θ2 is known then AN can be calculated.
( Note – the parallax method is used for measuring distance of nearby stars only. And parallax method is also used for determining distance of moon from earth ).
