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Physics Notes Class 11 CHAPTER 6 WORK,
ENERGY AND POWER
Work
When a force acts on an object and the object actually moves in the direction of force, then the
work is said to be done by the force
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If under a constant force F the object displaced through a distance s, then work done by the
force
W = F * s = F s cos θ
where a is the smaller angle between F and s
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∴ 1 joule = 107 erg
Its dimensional formula is [ML2T-2]
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e
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e
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Work done by a force is negative if angle between F and s is obtuse angle
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Work done in different conditions
(i) Work done by a variable force is given by
W = ∫ F * ds
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It is equal to the area under the force-displacement graph along with proper sign
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(iii) In equilibrium (static or dynamic), the resultant force is zero therefore resultant work done
is zero
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


Gravitational force, electrostatic force, magnetic force, etc are conservative forces
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Frictional force, viscous force, etc are non-conservative forces
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(vi) Work done in compressing or stretching a spring is given by
W = 1 / 2 kx2
where k is spring constant and x is displacement from mean position
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power
The time rate of work done by a body is called its power
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ncerthelp
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∴ P = F * v = F v cos θ
where θ is the smaller angle between F and v
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Its S1 unit is watt and its dimensional formula is [ML2T-3]
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It is a scalar quantity
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Its dimensional formula is [ML3T-3]
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Mechanical Energy
The sum of kinetic and potential energies at any point remains constant throughout the motion
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This is known as law of conservation of mechanical energy
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Kinetic Energy
The energy possessed by any object by virtue of its motion is called its kinetic energy
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ncerthelp
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2
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There are three important types of potential energies:
(i) Gravitational Potential Energy If a body of mass m is raised through a height h against
gravity, then its gravitational potential energy = mgh,

(ii) Elastic Potential Energy If a spring of spring constant k is stretched through a distance x
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2 kx2
The variation of potential energy with distance is shown in figure
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It does not exist for non-conservative
forces
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(iii) Electric Potential Energy The electric potential energy of two point charges ql and q’l
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0 * 1010 N-m2 / C2 constant
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where, Ki = initial kinetic energy
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and Kf = final kinetic energy
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e
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(ii) This theorem can be applied to non-inertial frames also
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Mass-Energy Equivalence
According to Einstein, the mass can be transformed into energy and vice – versa
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mass disappears, then produced energy
E = Δmc2
where c is the speed of light in vacuum
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Principle of Conservation of Mechanical Energy
For conservative forces the sum of kinetic and potential energies of any object remains constant
throughout the motion
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Collisions
Collision between two or more particles is the interaction for a short interval of time in which
they apply relatively strong forces on each other
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rrhere are two types of collisions:
1
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In an elastic collision all the involved forces are conservative forces
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2
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In an inelastic collision some or all the involved forces are non-conservative forces
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If after the collision two bodies stick to each other, then the collision is said to be perfectly
inelastic
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It is represented by e and it depends upon the material of the collidingI bodies
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Inelastic One Dimensional Collision
Applying Newton’s experimental law, we have

Velocities after collision
v1 = (m1 – m2) u1 + 2m2u2 / (m1 + m2)
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and v2 = (m2 – m1) u2 + 2m1u1 / (m1 + m2)
When masses of two colliding bodies are equal, then after the collision, the bodies exchange
their velocities
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v1 = 0 and v2 = u1
If a light body of mass m1 collides with a very heavy body of mass m2 at rest, then after
collision
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If a very heavy body of mass m1 collides with a light body of mass m2(m1 > > m21) at rest, then
after collision
v1 = u1 and v2 = 2u1
In Inelastic One Dimensional Collision
Loss of kinetic energy
ΔE = m1m2 / 2(m1 + m2) (u1 – u2)2 (1 – e2)
In Perfectly Inelastic One Dimensional Collision
Velocity of separation after collision = 0
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ncerthelp
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In horizontal direction,
m1u1 cos α1 + m2u2 cos α2= m1v1 cos β1 + m2v2 cos β2

In vertical direction
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ncerthelp
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ncerthelp

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