Given,
Angle of inclination $(\theta)$ = 30°
Coefficient of Friction $(\mu)$ = 0.25
Downward Acceleration $(a)$ = ?
The downward force $= mg\;Sin\;\theta$
The frictional force = $\mu\;R = \mu\;mg\;Cos\theta$
Net downward force along the plane is,
$F = mg\;Sin\theta - \mu\;mg\;Cos\theta = mg\;(Sin\;30 - 0.25 \; *\;Cos\;30) = mg\;*\; 0.283$
Then acceleration $a$ is given by,
$F = ma$ ⇒ $a = $$\frac{F}{m}$ = $\frac{mg\;*\;0.283}{m}$ = $10 * 0.283 = 2.83 \; m/s^2$
Return to Main Menu
Energy is a central concept in Physics. It can be defined as the capacity for doing work. But, it is important to understand that just because energy exists, not necessarily available to do work.
Energy can not be create or destroyed, but it can change from one form to another form.
There are many types of energy such as: Mechanical energy, chemical energy, light energy, thermal energy, electrical energy etc. Mechanical energy further divided into two parts called: Kinetic Energy and Potential Energy. Here, we mainly focused on these two energy.
Kinetic Energy:
Kinetic energy is the energy of motion. It is a capacity of doing work due to its motion. There are many forms of kinetic energy - vibrational (energy due to vibrational motion), rotational (energy due to motion in circle) and translation (energy due to motion in straight line). Here, we will focus upon translation kinetic energy to keep matters simple.
In classical mechanics, the kinetic energy of an (translation) object has depends upon mass (m) and velocity (v) of an object. i.e.
$K.E. = \frac{1}{2}mv^2$
In relativistic mechanics, this is a good approximation only when $v$ is much less than the speed of light.
The amount of kinetic energy an object has depends on the mass and speed of the object.
All moving object have the kinetic energy. The faster object has more speed and has more kinetic energy.
» Calculation of Kinetic Energy:
Consider a body of mass $m$ lying on a horizontal surface. After applying a force $F$, the body travel a distance $d$ with a moving velocity $v$.
As we know from the definition of work:
W = force * distance = $F * d$ .......... (i)
From the Newton's law of motion:
$F = ma$ .......... (ii)
And from the Kinematics, we know the formula:
$v^2 = u^2 + 2ad$ .......... (iii)
If the initial velocity of a body is at rest, so the initial velocity is zero ($u = 0$), then equation (iii) becomes,
$ad = \frac{v^2}{2}$ .......... (iv)
From equation (i), (ii) and (iii), we have
$W = F * d = ma *d $
$= m * ad = m * \frac{v^2}{2}$
Thus,
∴ $W = K.E. = \frac{1}{2}mv^2$ .......... (v)
Where, m - mass and v = velocity of a body.
This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means, for a two fold increase in speed, the kinetic energy will increase by the factor four and so on.
Return to Main Menu
"I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."
~ Sir Isaac Newton
Sir Isaac Newton (1642-1726): A Mathematician, Astronomer and Physicist was born at Wollsthrope in England. He worked in many area of Mathematics and Physics.
He developed the theories of gravitation in 1666, when he was only 23 years old. After some year later, he presented his three laws of motion in the book: "Principa Mathematica Philosophiae Naturalis" in 1687.Click here for: Vedic Laws of Motion
#1. Newton's $1^{st}$ Law:
"A body remains in the state of rest or in the state of uniform velocity if no net force is acting on it."
It is also known as law of Inertia.
(If the net force is zero: Object at rest, stay at rest. And Object in motion, continue to move).
This means that, there is a natural tendency of objects to keep on doing what they're doing. There is no change in the state (rest or motion) without an external force acting. That is, a force is an agent that produces a change in state of a body.
#2. Newton's $2^{nd}$ Law:
"The rate of change of momentum of a body with respect to time is directly proportional to the net external force acting on the body."
However, Newton's second law gives us an exact relationship between force, mass and acceleration. Mathematically,
$F_{net} = ma$
i.e. net force on object = mass of object * acceleration
If we exert the same force on two objects of different mass, we'll get different acceleration (change in motion).The heavier objects require more force to move than the lighter objects.
Note: In equation, $F = ma$; if net force acting on a mass is zero then, $a=0$.This means that, if the net force acting on a body is zero, it moves with constant velocity or it will be rest. Which is the statement of the Newton's $1^{st}$ law.
#3. Newton's $3^{rd}$ Law:
"To every action there is always an equal and opposite reaction."
This means that, for every action there is equal and opposite reaction. It dose not matter which force we call action and which we call reaction.
All forces always occur in pair. For example: During the simplest act of walking, we push against the road surface with our shoes and road pushes back with an equal force but in opposite direction. It is the force the road exerts on us that causes us to move forward.
Similarly, at the swimming time a swimmer moves through the water only because he pushes water backward and the water pushes the swimmer forwards.
Again, Let's understand how a rocket works. The rocket's action is to push down on the ground with the force of its powerful engines, and the reaction is that the ground pushes the rocket upwards with an equal force.
Return to Main Menu
As there is no absolute frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be moving (wikipedia).
In previous chapter, we have studied motion in terms of their position, velocity and acceleration. Variation of these quantities with time is called Kinematics.
In this chapter, we will discuss the cause of Motion due to the force (i.e. force acting in moving objects). This aspect of motion is called Dynamics.
In Physics, Motion is a change in position of an object over time. Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame (wikipedia). If the position of a body is not changing with respect to a given frame of reference, the body is said to be rest (motionless).
Motion is a very common experience in our daily life. For Example: walking of people, flow of water, flying of aeroplane, running of bus etc. In physics, Motion of all large scale (i.e. Projectiles, Cells, Humans, Planets, Universe) are described by Classical Mechanics, where as motion of very small scale (i.e. atomic and subatomic objects) are described by Quantum Mechanics
Types of Motions:
- Simple Harmonic Motion (Example: Pendulum), Anharmonic Motion, Periodic Motion, Circular Motion (Example: Moon and Earth), Linear Motion, Reciprocal Motion, Random Motion, Rotary Motion, Brownian Motion,Curvilinear Motion, Rotational Motion, Rolling Motion, Oscillation, Vibrational Motion, Projectile Motion, etc........
» Force and Inertia
» Newton's Laws of Motion
» Linear Momentum and Conservation laws
» Impulse of force
» Solid friction
» Application of Newton's Laws.
Return to Main Menu
