Solving your problem

Hello,
I would like to convey to all the users visiting my blog specially students to contact me for live help for topics related to physics and maths.
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An Invitation

Hi,
I would like to invite all type of queries and question from all of you. I will try my best to solve the problem as soon as possible. It's really about connecting and sharing each others experiences and knowledge.
Thank you!

How to solve problems of physics? (iv)

Hello, once again continuing with my mission to provide online reference for solving practical physics problem, today i would like to take up the discussion of vectors.

The concept of vectors is instrumental in solving problems of maths, physics and engineering. Therefore it is more than just important to understand the underlying concept of vectors before trying to solve confidently the problems of the above mentioned areas.

We can define a vector, simply as a physical quantity that has magnitude as well as direction. Examples of vector quantities are Displacement, Velocity, Force, Acceleration etc. Another way of defining a vector can be, the quantities that follow the vector law of addition.

Laws of vector addition:
There are 2 laws of vector addition.
1) Triangle Law of vector addition: "It states that if 2 vectors AB and AC represent two sides of the triangle in order, then the sum of the two vectors is given by the third closing side BC of the triangle in reverse order."

2) Parallelogram law of vector addition: "It states that if the two vectors OA and OB represent the two sides of a parallelogram then the resultant of these two vector is given by the diagonal OC."

How to sovle problems of physics? (iii)

Now, let us discuss a problem related to Newton's first law of motion so that we understand the application of the equations of motions which are
(i) v = u + at
(ii) s = ut + 1/2 at^2
(iii) v^2 = u^2 + 2as
These are the three basic equations of motion which can be used to solve problems of kinematics if the acceleration is constant.
If you are seeking a more general form then you have to use the basic differential form of these
equations
(i) v = ds /dt
(ii) a = dv/dt
(iii) a = vdv/ds
Using these equations it is possible to solve any problem of kinematics.
Example: A car traveling at a velocity of 10 m/s is stopped by the driver by applying brakes when he is at distance of 30 m from a wall. The maximum retardation possible is 2m/s^2?
Will the driver be able to avoid collision?

Solution:
Given in the problem that initial velocity = 10 m/s
final velocity = 0 m/s (since the car will be at rest)
The maximum retardation is given as 2m/s^2
We can use the equation
v^2 = u^2 + 2as
u = 10 m/s
a = -2m/s^2
v = 0 m/s
Putting these values in the equation we get
0 = 10^2 + 2.(-2).s
4s = 100
s = 25 m
Luckily the driver will manage to avoid the collision!
I will be back with more interesting problems for all you physics enthusiast.

How to solve problems of physics? (ii)

What is the force required to produce an acceleration of 2 m/s^2 in a body of mass 5kg?
Answer: Here is the solution to this simple question
From the previous discussion we came to know that
F = ma
Here in the question it is given that
mass = m =5Kg
acceleration = a = 2m/s^2
therefore force F = ma = 5 x 2 = 10 N
I hope this elementary simple example would have helped you understand the application of newton's second law to some extent.

NOTE: The discussion made above are meant only to assist you in getting familiarized with the concepts and in no way can be used as reference for you classroom work. You should always refer to standard text books available.

I will be coming up with a little more complex problem the next time.

How to solve problems of physics? (i)

In this part of the discussion we will be dealing in general about solving problems based on newton's second law. Newton's second law states that the force exerted on the body is directly proportional to the rate of change of momentum and this change takes place in the direction of the force.
Now, let us try to formulate the law in a more mathematical way.
F is proportional to rate of change of momentum
or F = K. mv(final) - mv(initial) /time
or F = K. m(v(final) -v(initial))/time
We know that acceleration of a body is defined as the rate of change of velocity
or a = v(final) -v(initial)/time
Therefore we have the mathematical form of newton's second law as
F = ma
Although the equation looks simple but let me tell you it is one of the most important equation that has ever been formulated. Almost every problem of mechanics can be solved using this equation.

Since, now you must have had a fair bit of understanding of what the law states. Lets begin with one example which will help you understand the approach to solve problems related to newton's second law.
Here are the meanings of the symbols used in the equations
F= force (S.I units N(newton)
a= acceleration (S.I unit m/s^2)
m= mass of the body (S.I unit Kg)
v(initial) = initial velocity of the body (S.I unit m/s)
v(final) = final velocity of the body (S.I unit m/s)
t= time (seconds)

Solution to the problem