Work, Energy and Power is one of the most application-based chapters in Physics because it combines formulas, derivations, graphs, and numerical problem-solving in the same topic. Questions based on conservation of energy, collisions, work-energy theorem, and power often require both conceptual understanding and calculation accuracy, which can become confusing during revision and exams. Physics Wallah provides complete Work, Energy and Power study material in PDF form, including notes, formula sheets, MCQs, and numerical practice to help you revise concepts and solve questions more effectively.
Work forms the foundation of Work, Energy, and Power in Physics. It explains how applied force causes displacement and transfers energy from one system to another. Whenever a force acts on an object and produces motion, work is said to be done.
Work is a scalar quantity defined as the dot product of force and displacement.
W = F · S = FS cosθ
Where:
F = applied force
S = displacement
θ = angle between force and displacement
Based on the direction of force:
Positive Work: Force acts in the direction of motion
Negative Work: Force opposes motion, such as friction
Zero Work: Force acts perpendicular to displacement
When force changes with displacement, work cannot be calculated using simple multiplication. In such cases, integration is used.
W = ∫xi→xf F(x) dx
The total work done by a variable force is equal to the area under the Force vs Displacement graph.
Moving objects possess kinetic energy due to motion. Momentum and kinetic energy are closely connected and play an important role in mechanics and collisions.
Kinetic energy is the energy possessed by an object because of its motion.
K = ½ mv²
Where:
m = mass of the object
v = velocity of the object
Kinetic energy is always positive and depends on the frame of reference.
Linear momentum is defined as:
p = mv
The relationship between momentum and kinetic energy is:
K = p² / 2m
p = √(2mK)
Important observations:
Bodies with equal momentum do not necessarily have equal kinetic energy
Lighter bodies possess more kinetic energy for the same momentum
Heavier bodies possess greater momentum for the same kinetic energy
The Work Energy Theorem establishes the relationship between work done and change in kinetic energy. It explains how forces directly affect the motion of an object.
According to the theorem, the net work done on an object equals the change in its kinetic energy.
Wnet = ΔK
If positive work is performed, kinetic energy increases, and the object speeds up. If negative work is performed, kinetic energy decreases, and the object slows down.
This theorem helps simplify many mechanics problems without directly using equations of motion.
Forces are classified depending on whether the work done depends on the path followed by the object.
A force is conservative if the work done depends only on the initial and final positions, not on the actual path taken.
Gravitational force is a common example. Whether an object is lifted vertically or moved through an inclined path, the work done against gravity remains the same.
Characteristics of conservative forces:
Work done is path independent
Mechanical energy remains conserved
Potential energy can be associated with the force
A force is non-conservative if the work done depends on the path followed.
Friction is the most common example. A longer path causes greater energy loss due to heat and sound.
Characteristics of non-conservative forces:
Work done depends on the path
Mechanical energy is not conserved completely
Energy is dissipated into the surroundings
Elastic potential energy is the stored energy present in stretched or compressed elastic objects such as springs.
E = ½ kx²
Where:
k = spring constant
x = displacement from equilibrium position
Elastic potential energy depends on deformation and is fully recoverable in ideal elastic systems.
The law of conservation of mechanical energy states that energy cannot be created or destroyed. It only changes from one form into another.
If only conservative forces act within a system, the total mechanical energy remains constant.
K + U = Constant
Where:
K = kinetic energy
U = potential energy
As kinetic energy increases, potential energy decreases, and vice versa, while total energy remains conserved.
A collision is a short-duration interaction between two objects. Collisions are classified based on whether kinetic energy remains conserved.
In a perfectly elastic collision:
Total momentum is conserved
Total kinetic energy is conserved
No energy is lost as heat, sound, or deformation
Elastic collisions are idealised situations commonly used in mechanics and particle physics.
Most real-world collisions are inelastic because some kinetic energy is lost during impact.
In a perfectly inelastic collision, the colliding bodies stick together and move with a common velocity after the collision.
vc = (m1v1 + m2v2) / (m1 + m2)
Where:
m1, m2 = masses of the bodies
v1, v2 = initial velocities
vc = common velocity after collision
In all inelastic collisions:
Momentum remains conserved
Kinetic energy is not conserved completely
Power measures the rate at which work is done or energy is transferred.
Average power over a time interval is given by:
Pavg = W / t
Where:
W = work done
t = time taken
Instantaneous power represents the power delivered at a specific instant of time.
P = dW / dt
It becomes important in systems where force and velocity continuously change, such as engines, turbines, and moving machines.
Understanding Work, Energy and Power requires regular concept revision and numerical practice because questions are often formula-based as well as application-oriented. Physics Wallah provides complete Work, Energy and Power study material in PDF form to help you revise concepts, formulas, and important numerical problems more effectively.
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Work, Energy and Power Study Material |
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Work, Energy and Power is an important Physics topic from which both theoretical and numerical questions are frequently asked in examinations. You can use the PW study material below to strengthen conceptual understanding, revise formulas, and practise numerical problems effectively:
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