Work, Energy and Power — Part 2: Mechanical energy and its conservation: visual lesson, ICSE Class 10 Physics (Science Paper 1)

Lesson

Stored and moving energy

Part 2 — a raised hammer stores energy because of its position; a moving hammer has energy because of its motion. Energy changes form, but the total stays the same.

In this lesson you will

Derive U = mgh and K = ½mv²
Solve problems on potential and kinetic energy
Identify energy conversions in everyday devices
Show that U + K is constant for a freely falling body and describe a pendulum’s energy changes

Table of four objects and their main form of mechanical energy
Object	Main form of mechanical energy
Water held behind a dam	Potential energy
A moving cricket ball	Kinetic energy
A wound spring of a toy car	Potential (elastic) energy
A swinging pendulum	Changes between both

Concept

Potential energy: U = mgh

Potential energy is the energy a body has because of its position or configuration (a raised stone, a stretched bow). Gravitational potential energy of a mass $m$ at height $h$ : the work done to raise it against its weight $mg$ is $W = F \times s = mg \times h$ , and this work is stored, so $U = mgh$ . It is measured from a chosen reference level (usually the ground).

Table of three masses at different heights and their gravitational potential energies
Mass	Height	U = mgh (g = 10 m s⁻²)
2 kg	5 m	100 J
0.5 kg	20 m	100 J
60 kg	3 m	1800 J

Concept

Kinetic energy: K = ½mv²

Kinetic energy is the energy of a body due to its motion. Derivation: a force $F$ accelerates a mass $m$ from rest to speed $v$ over distance $s$ . From $v^{2} = u^{2} + 2as$ with $u = 0$ : $s = \dfrac{v^{2}}{2a}$ . Work done $W = F s = ma \times \dfrac{v^{2}}{2a} = \tfrac{1}{2}mv^{2}$ , stored as $K = \tfrac{1}{2}mv^{2}$ . Doubling $v$ makes $K$ four times as large. Forms: translational (moving along), rotational (spinning wheel), vibrational (atoms in a solid).

Table of how kinetic energy changes when mass or speed changes
Change	Effect on K
Mass doubled	K doubled
Speed doubled	K × 4
Speed halved	K ÷ 4

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