Potential energy

Potential energy (PE) is energy stored in a body by virtue of its position (relative to a reference level) or its state (compressed, stretched). ICSE Class 10 restricts the quantitative treatment to one form only: gravitational PE, the energy a raised body holds because of its height.

• Raising a body of mass $m$ through a height $h$ requires doing work against gravity. That work does not disappear — it is stored in the body as potential energy, which it can later give back.
• The stored energy equals the work done in the lift, $W = mgh$, so the formula for gravitational potential energy follows directly:

where: $m$ is the mass of the body (kg), $g$ is the acceleration due to gravity ($9.8\ \text{m/s}^2$), $h$ is the height above the chosen reference level (m), and $PE$ comes out in joules (J), the SI unit of all forms of energy.

• PE is never an absolute number — it is always measured relative to a reference level that you choose (the floor, a table top, the lowest point of a swing). Move the reference and every PE value shifts by a constant; only changes in PE usually carry physical meaning.
• PE is zero at the reference level and grows with height above it. A body below the reference level (in a pit, say) has negative PE relative to that level — a subtlety worth knowing even though ICSE problems rarely test it directly.
• Mechanical energy ties potential energy to the earlier idea of kinetic energy: $E_{mech} = KE + PE$. Ignoring friction and air resistance, mechanical energy stays constant even while KE and PE trade places — the falling hammer loses PE and gains an equal amount of KE.

Other forms of energy — chemical, heat, electrical, nuclear, sound, light, solar, wind, hydro, geothermal — appear in this ICSE chapter only qualitatively, through familiar conversions (chemical energy in fuel becoming heat and light in a flame; electrical energy becoming light in a bulb). Gravitational PE remains the only form given a formula at this level, which is exactly why it deserves careful, formula-level practice.

A pile driver's hammer of mass 200 kg is raised 5 m above a pile and released. (a) Find its potential energy at the top, relative to the pile. (b) Find its kinetic energy just before it strikes the pile.

Step 1. List the knowns: $m = 200$ kg, $h = 5$ m, $g = 9.8\ \text{m/s}^2$.

Step 2. Apply $PE = mgh$ at the top:

The hammer has 9800 J of potential energy relative to the pile when raised.

Step 3. Find the kinetic energy just before impact. Ignoring air resistance, mechanical energy is conserved: $KE + PE = \text{constant}$. At the top, $KE = 0$ and $PE = 9800$ J, so $E_{mech} = 9800$ J. Just before striking the pile, the hammer is back at the reference level, so $PE = 0$, which means all of the mechanical energy has become kinetic energy.

KE just before impact = 9800 J.

Competitive stretch

On impact, this 9800 J of kinetic energy does work driving the pile into the ground, with a portion lost as heat and sound at the collision — a reminder that "conserved" mechanical energy only holds while friction and resistive losses are negligible, which stops being true the instant the hammer meets the pile.

• Treating PE as an absolute number with one "correct" value — it is always relative to a chosen reference level; only changes in PE usually matter physically.
• Using the length of a slanted ramp or path instead of the true vertical height $h$ in $PE = mgh$.
• Assuming a motionless body has no energy — a book resting on a shelf has zero KE but nonzero PE relative to the floor; PE depends on position, not motion.
• Forgetting that mechanical energy conservation ($KE + PE = \text{constant}$) only applies when friction and air resistance are negligible; real falls and collisions lose some energy as heat and sound.

Ask the tutor: Want to try a problem where a pendulum swings between two heights and you have to track PE and KE trading back and forth at several points along the swing?