Mechanics & Properties of Matter - Part 1

MECHANICS & PROPERTIES OF MATTER - PART 1

The branch of Physics dealing with the behavior of matter under the action of forces is called Dynamics and Statics are the two branches of mechanics.

•    The mathematical and physical study of the behavior of bodies under the action of forces that produce changes of motion in them is known as dynamics.
•    Statics deals with the cases where no motion is produced in the bodies under the action of forces.
•    Objects have transnational motion, rotational motion and vibrational motion.
•    The motion of wheels, blades of fan, planets around sun and electrons around the nucleus of atoms are some examples of rotational motion.
•    Elasticity, surface tension and viscosity are a few important physical properties of matter.
•    These properties can be explained on the basis of forces between molecules of matter.
•    A thorough knowledge of properties of matter is essential in identifying different materials available with us.
•    This is useful in choosing proper materials for different applications.
•    This study is made use in the branch of physics called Properties of matter.
•    The basic concepts of Projectile motion, circular motion, gravitation,
•    planetary motion, surface tension, viscosity,
•    Bernoulli’s theorem and their applications.

MOTION OF FREELY FALLING BODIES AND PROJECTILE MOTION

FREELY FALLING BODIES
•    When an object falls towards the earth under gravity in the absence of air resistance, it is called a freely falling body.
•    All objects in free fall near the earth have the same acceleration called the acceleration due to gravity (g).
•    The gravitational force acting on an object of mass ( m) near the earth is its weight W = mg.
•    The acceleration of an object in free fall is independent of its mass. As air resistance normally acts on a falling body and opposes its motion, the object falls at a slower rate than in free fall.
•    Coin and feather experiment : Drop a coin and a feather simultaneously in a tube. Evacuate air from the tube and repeat the same dropping.
•    Observe that in the first case the coin which is heavier than the feather reaches the bottom of the tube more rapidly while the feather flutters down slowly.
•    But in the second case the coin and the feather to fall together.
•    From this experiment we understand that air resistance affects the motion of a falling
•    body. The air resistance on a falling body depends on its shape, size and speed.

Examples
•    A skydiver with an unopened parachute falls quite rapidly and when the chute opens due to the shape and size of the body the air resistance increases and the descent is slowed.
•    This is how the skydiving gives pleasure.
•    Automobiles are now streamlined in shape to reduce air resistance and improve fuel consumption.
•    When a body falls, it accelerates due to gravity and the retarding force of air resistance increases with speed. This continues till the force of air resistance equals the weight of the object. Now the object no longer accelerates but falls with a constant speed called the terminal velocity. The terminal velocity is about 200 km/hr for a skydiver with an unopened parachute.
•    While falling the skydivers use a “spread-eagle” position to increase the air resistance and prolong the time of fall. When the parachute is opened, the fall is slowed by the additional resistive force.

PROJECTILE MOTION
•    Any object which follows a path determined by the gravitational force and air resistance
•    when an initial velocity is given, is called a projectile.
•    A bullet shot from a rifle, a rocket after its fuel is exhausted, a javelin thrown by an
•    athlete and a thrown cricket ball are examples of projectile.
•    The path followed by a projectile is called its trajectory.

VERTICAL PROJECTION
•    We often throw or toss things directly upward and this is a vertical projection. The initial velocity of the object is upward but the acceleration due to gravity is downward.
•    Hence a vertically projected object at its maximum height stops instantaneously and changes its direction.
•    Now it becomes a dropped object in free fall.

MAXIMUM HEIGHT ATTAINED (h)
Let a body be projected vertically upwards with an initial velocity u. As it moves upwards its acceleration is taken as – g.

As the body goes up its velocity decreases and finally becomes zero ( v = 0) when it reaches maximum height.

The maximum height attained by a body is directly proportional to the square of its initial velocity u.

TIME OF ASCENT (t1)

•    The time taken by a body thrown up to reach maximum height is called its time of ascent.
•    Let t1 be the time of ascent. At the maximum height its velocity v = 0.

TIME OF DESCENT (t2)
•    After reaching the maximum height, the body begins to travel downwards like a freely falling body.
•    The time taken by a freely falling body to reach the ground is called the time of descent (t2). In this case u = 0 and g is positive.
•    It is an interesting fact that the time of ascent is equal to the time of descent in the case of bodies moving under gravity.

TIME OF FLIGHT
•    The time of flight is the time taken by a body to remain in air and is given by the sum of the time of ascent (t1) and the time of descent ( t2).

VELOCITY ON REACHING THE GROUND
•    When a body is dropped from a height h its initial velocity u is zero. Let the final velocity on reaching the ground be v.
•    From equations (8) and (9) we conclude that the velocity of the body falling from a height h on reaching the ground is equal to the velocity with which it is projected vertically upwards to reach the same height h.
•    Hence the upward velocity at any point in its flight is the same as its downward velocity at that point.
•    The value of g at a place can be determined by noting the time taken ( t) to cover a vertical height (h) in free fall

CIRCULAR MOTION :
•    Relation between Linear velocity and angular velocity
•    When a particle moves in a circle with a constant speed then the motion is known as uniform circular motion.
•    Consider an object moving in a circle with a uniform speed a round a fixed point O as centre.
•    If the object moves from A to B so that the radius OA moves through an angle q, its angular velocity (w) about O is defined as the rate at which the radius vector sweeps. If t is the time taken by the object to move from A to B then, The unit of the angular velocity is rad s-1.
•    The time taken T by the object to describe the circle once is called the period of circular motion. This is the relation connecting the linear velocity and the angular velocity of the object in circular motion.