Module 2 & 3: Work and Kinetic Energy, Potential Energy and Energy Conservation Kannur University Notes KU1DSCPHY101

Access high-quality Kannur University KU1DSCPHY101 Physics notes for Modules 2 and 3, covering Work, Kinetic Energy, Potential Energy, and Energy Conservation as per the FYUGP Semester 1 syllabus (2025). These notes explain core physics concepts like work-energy theorem, power, mechanical energy, gravitational and elastic potential energy, and law of conservation of energy with clarity and precision. Designed for BSc Physics students under the FYUGP (NEP 2020-aligned) framework, the material includes theory, derivations, diagrams, solved problems, and real-life applications to help improve conceptual understanding and exam performance. Perfect for semester exam preparation, internal assessments, and revision, these notes simplify complex principles and highlight important formulas and problem-solving techniques. Whether you’re a student or educator, this is an essential resource to grasp the fundamentals of energy in mechanics. Stay ahead with well-structured, syllabus-based Kannur University Physics study material crafted for academic success.

Topics Covered

Work and Kinetic Energy

Work, Work: Positive, Negative or Zero, Total Work, Kinetic Energy and Work Energy Theorem, The meaning of Kinetic Energy, Work and Kinetic Energy in Composite systems
Work and Energy with varying forces, work done by a varying force, Straight- Line Motion, Work – Energy Theorem for Straight Line Motion, Varying Forces, Work Energy theorem for Motion along a Curve, Power.

Potential Energy and Energy Conservation

Gravitational Potential Energy, Conservation of Mechanical Energy, When Force other than Gravity do Work, Gravitational Potential Energy for Motion along a Curved Path, Elastic Potential Energy, Situations with both Gravitational and Elastic Potential energy
Conservative and Non-Conservative Forces, The Law of Conservation of Energy, Force and Potential Energy, Energy Diagrams

From the textbook: University Physics with Modern Physics – Hugh D Young & Roger A Freedman-14th edition, 2016.

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Work is defined as:

W = \vec{F} \cdot \vec{d} = Fd \cos \theta

where

$F$ = applied force
$d$ = displacement of the object
$\theta$ = angle between the force and displacement

1. Positive Work

Done when the force and displacement are in the same direction.
The force helps the motion.
Example: Pushing a moving cart forward, lifting an object upward.

2. Negative Work

Done when the force and displacement are in opposite directions.
The force opposes the motion.
Example: Friction force acting on a moving object, or a person trying to stop a moving trolley.

3. Zero Work

Happens when either:
- There is no displacement ( $d=0$ ), OR
- The force is perpendicular to displacement ( $\theta = 90^\circ$ ).
Example: A person holding a heavy bag without moving it (no displacement), or the centripetal force in circular motion (perpendicular to displacement).

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COMPLETE NOTES FOR SEMESTER 1 HAS BEEN POSTED IN THIS WEBSITE

Module 1: Notes Module 1: Newton’s Laws of Motion Kannur University Notes KU1DSCPHY101

Module 2: Notes Module 2 & 3: Work and Kinetic Energy, Potential Energy and Energy Conservation Kannur University Notes KU1DSCPHY101

Module 3: Notes Module 2 & 3: Work and Kinetic Energy, Potential Energy and Energy Conservation Kannur University Notes KU1DSCPHY101

Module 4: Notes Module 4 : Momentum, Impulse and Collisions Notes Kannur University KU1DSCPHY101

WORK

Definition: Work is done when a force is applied to a body and the body displaces in the direction of the force component.
Formula (constant force):
$W = \vec{F} \cdot \vec{d} = Fd\cos\theta$
Where $\theta$ is angle between force & displacement.
Units: Joule (J) → 1 J = work done by 1 N force over 1 m.

Positive, Negative, or Zero Work

Positive work: $0^\circ \le \theta < 90^\circ$ → force component in direction of displacement.
(e.g., pushing object forward)
Negative work: $90^\circ < \theta \le 180^\circ$ → force opposes motion.
(e.g., friction on moving body)
Zero work: $\theta = 90^\circ$ → force perpendicular to displacement.
(e.g., centripetal force in circular motion)

TOTAL WORK

If multiple forces act:
$W_{\text{total}} = W_1 + W_2 + W_3 + \dots$
Or use net force: $W_{\text{total}} = F_{\text{net}} \cdot d$ .

KINETIC ENERGY (KE)

Meaning: Energy due to motion.
Formula:
$KE = \frac12 mv^2$
Unit: Joule (J).

WORK–ENERGY THEOREM

Statement: Net work done on a particle = change in its kinetic energy.
$W_{\text{net}} = \Delta KE = KE_f - KE_i$
Applies to all motion types (straight or curved).

WORK & KINETIC ENERGY IN COMPOSITE SYSTEMS

For multiple particles: total work done by external forces = total change in KE of the system.
Internal forces (action-reaction pairs) cancel in total work calculation.

WORK WITH VARYING FORCES

Straight-line motion:
$W = \int_{x_i}^{x_f} F(x) \, dx$
If F–x graph given: Work = area under curve.

WORK–ENERGY THEOREM FOR STRAIGHT-LINE MOTION

Same as general theorem, but with force only along the motion direction.
$\int_{x_i}^{x_f} F(x) \, dx = \frac12 m v_f^2 - \frac12 m v_i^2$

WORK–ENERGY THEOREM FOR MOTION ALONG A CURVE

Use displacement along the path:
$W = \int_{\text{path}} \vec{F} \cdot d\vec{s}$

POWER

Definition: Rate of doing work.
$P = \frac{dW}{dt}$
For constant force & velocity:
$P = \vec{F} \cdot \vec{v}$
Units: Watt (W) → 1 W = 1 J/s.
Instantaneous power → at a specific moment; average power → over time interval.

Here’s a perfect, exam-focused set of notes for your Gravitational & Potential Energy topics — compact enough to revise quickly, but detailed enough to score full marks.

GRAVITATIONAL POTENTIAL ENERGY (GPE)

Definition: Energy stored due to position in a gravitational field.
Formula:
$U_g = mgh$
(for constant $g$ , reference level where $U = 0$ ).
Unit: Joule (J).
Change in GPE: $\Delta U_g = mg(h_2 - h_1)$ .

CONSERVATION OF MECHANICAL ENERGY

For only gravity (no non-conservative forces):
$E_{\text{mech}} = KE + U_g = \text{constant}$
Example: Falling object → KE increases, GPE decreases by equal amount.

WHEN FORCES OTHER THAN GRAVITY DO WORK

Mechanical energy is not conserved.
Work done by non-conservative forces changes total mechanical energy:
$W_{\text{non-conservative}} = \Delta KE + \Delta U$

GPE FOR MOTION ALONG A CURVED PATH

Only vertical displacement matters for change in GPE:
$\Delta U_g = mg(y_f - y_i)$
Path shape does not affect GPE change.

ELASTIC POTENTIAL ENERGY (EPE)

Energy stored in a stretched or compressed spring:
$U_s = \frac12 kx^2$
where $k$ = spring constant, $x$ = stretch/compression from natural length.

SITUATIONS WITH BOTH GPE & EPE

Total potential energy:
$U_{\text{total}} = U_g + U_s$
Mechanical energy:
$E_{\text{mech}} = KE + U_g + U_s$

CONSERVATIVE & NON-CONSERVATIVE FORCES

Conservative: Work done depends only on initial & final positions, not path. (Gravity, spring force) → mechanical energy conserved.
Non-conservative: Work done depends on path; mechanical energy changes. (Friction, air resistance).

LAW OF CONSERVATION OF ENERGY

Energy cannot be created or destroyed; it changes form.
Total energy of an isolated system is constant:
$E_{\text{total}} = \text{constant}$

FORCE & POTENTIAL ENERGY

Force is the negative gradient of potential energy:
$F_x = -\frac{dU}{dx}$
(Force acts in direction of decreasing potential energy).

ENERGY DIAGRAMS

Graph of $U$ vs. position.
Equilibrium points:
- Stable: $U$ is minimum.
- Unstable: $U$ is maximum.
Total energy line shows allowed motion regions ( $KE = E_{\text{total}} - U$ ).

Module 2 & 3: Work and Kinetic Energy, Potential Energy and Energy Conservation Kannur University Notes KU1DSCPHY101 | BSc Physics Kannur University Notes