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ü        Energy is defined to be the capacity to do work. Energy is a scalar quantity and measured in Joules (J).

Mechanical energy is of two types:

Þ            Kinetic Energy

Þ            Potential Energy

Kinetic energy is the energy which is possessed by a body by virtue of its motion. Kinetic energy of a body is the energy due to its motion. If a body of mass ‘m’ moves with a velocity ‘v’, its kinetic energy is given by

For an unaccelerated body, the resultant force acting on the body is zero. But for an accelerated body, the resultant force is not zero and will do some work. We can relate the work done by this force with the consequent increase in kinetic energy of the body. Consider a body being acted on by various forces

ü        The above equation states that the work done by the resultant external force on a body is equal to the change in the kinetic energy of the body. This relation is called Work-Energy Theorem.

Illustrations

1.      A 50 g bullet strikes a wooden plank and comes to rest after penetrating 10 cm into wood. If wood offers a resistance of 10000 N, what is the velocity with which the bullet strikes the plank?

Sol. Work done by the resistant force, acting on the bullet opposite in the direction of displacement of bullet, is given by

W = 10000 N * (10 * 10²) m

= 1000 J

According to Work-Energy Theorem this should be equal to the change in kinetic energy.

W = K₂K₁

i.e.,                          1000 = 0  K1

(K₂ = 0, because the final velocity of bullet is zero)

K1 = 1/2(mv²) = 1000

where v is the initial velocity of bullet

v² = (2 * 1000 J)/ (5 * 10^-3 kg)

= 4000 (m/s)²

v = 200 m/s

ü        We all know that it is hard work lifting a heavy box from one platform to another in a railway station. Similarly we know that children need lots of energy as they grow up.

ü        We feel tired if we run a hundred meters in twenty seconds, whereas we could walk that distance easily in a couple of minutes.

ü        These are some common sense notions of work and energy which can however be precisely defined and measured in physics.

ü        These definitions are measurements can be used consistently to describe and predict the behaviour of bodies and thus can form very powerful tool for analysis of physical systems.

OBJECTIVE

ü        In the previous chapter we studied the Newton’s laws of motion to understand how objects move under the influence of force acting on them or the relation between the force and the acceleration produced by this force.

ü        In this chapter however, we will study the situation where one is not interested in such an exhaustive study of object’s motion rather desires to relate the final velocity of an object to the forces acting on it without going into the deeper details how the object acquired that velocity. The work-energy theorem solves this purpose.

PRE-REQUISITE

Velocity

ü        Rate of change of position of an object is known as its velocity.

V = dx /dt

Acceleration

ü        Rate of change of velocity of an object is known as its acceleration.

a= dv / dt = d²x / dt²

Force

ü        Force is a push or pull which tends to change the position of the object on which it is applied.

Newton’s first law of motion

ü        It states that every object persists in its natural state of motion i.e. continues to be at rest or moves in a straight line with uniform (constant) velocity. (This is what is meant by natural state of motion); In the absence of a net external force acting (impressed) on it.

Newton’s Second law of motion

Newton’s Third Law of Motion

ü        When ever a body exerts a force on a second body, the second body always exerts a force of equal magnitude but opposite in direction on the first one.

Conservation of Energy

ü        Whenever one form of energy is transformed into other forms, the total amount of energy before transformation is always equal to the amount of energy after transformation, i.e., the total amount of energy remains conserved.