Derive K = tfrac12mv2 for a body starting from rest.

A constant force F = ma acts through S. From v2 = 2aS, S = v2/2a. Work W = FS = ma × v2/2a = tfrac12mv2, which is stored as kinetic energy.

Work Energy and Power

Q: Name the SI and cgs units of work and state the relation between them.

Joule (SI) and erg (cgs); 1 J = 107 erg.

Q: Express 1 kW h in joules and 1 eV in joules.

1 kW h = 3.6 × 106 J; 1 eV = 1.6 × 10-19 J.

ICSE Class 10 · Physics · Chapter 2

What this chapter covers

Work
Energy
Power
Work, energy, power and their relation with force
Mechanical energy and potential energy
Kinetic energy
Different forms of energy and their conversion
Principle of conservation of energy
Numerical problems on work, power and energy

Key definitions

Work is said to be done by a force when the body on which it acts is displaced, and the amount of work is measured as the product of the force and the component of the displacement in the direction of the force.

Power is the rate of doing work, that is, the work done per unit time.

Mechanical energy is the energy possessed by a body due to its position, configuration or motion, and it is of two kinds: potential energy and kinetic energy.

Potential energy is the energy possessed by a body because of its position or its changed configuration (shape or state).

Gravitational potential energy is the energy possessed by a body because of its height above the surface of the earth, measured by the work done against gravity in raising it to that height.

Kinetic energy is the energy possessed by a body by virtue of its motion, measured by the work the body can do before it comes to rest.

Translational kinetic energy is the kinetic energy of a body moving from one place to another along a straight or curved path.

Rotational kinetic energy is the kinetic energy of a body spinning about an axis.

Vibrational kinetic energy is the kinetic energy of a body moving to and fro about a fixed position.

Chemical energy is the energy stored in the bonds between atoms in a substance, released when the substance takes part in a chemical reaction.

Heat energy is the energy a body has due to the random motion of its molecules, and it flows from a hotter body to a colder one.

Electrical energy is the energy carried by moving electric charges in a conductor.

Key points

Work is done only when a force displaces its point of application; W = FScosθ.
At θ = 0°, W = FS (maximum); at θ = 90°, W = 0; at θ = 180°, the work is negative.
Work against gravity in raising a mass m through height h is W = mgh.
Work and energy are scalars measured in joules; 1 J = 10⁷ erg.
Energy is the capacity to do work; a body's energy is measured by the work it can do.
1 cal ≈ 4.2 J; 1 kW h = 3.6 × 10⁶ J; 1 eV = 1.6 × 10^-19 J.
Power is the rate of doing work, P = W/t; SI unit watt, cgs unit erg s^-1; 1 W = 10⁷ erg s^-1.
1 kW = 10³ W, 1 MW = 10⁶ W, 1 GW = 10⁹ W, 1 hp = 746 W.
For a steady force at steady velocity, P = Fv.
Work-energy theorem: work done by the net force equals the change in kinetic energy.
Potential energy is energy due to position or configuration; gravitational U = mgh.
Kinetic energy is energy due to motion; K = tfrac12mv²; it may be translational, rotational or vibrational.
Other forms of energy are chemical, heat, electrical, nuclear, light and sound; devices convert one form into another.
Energy can neither be created nor destroyed; for a freely falling body U + K = mgh at every point.
In a simple pendulum, energy is all potential at the extremes and all kinetic at the mean position; air resistance slowly turns it into heat.

Questions answered

Define work. State the condition under which a force does no work even though the body moves.

Work is done by a force when the body on which it acts is displaced, and it equals the product of the force and the component of displacement in the direction of the force, W = FScosθ. No work is done when the force is at right angles to the displacement (θ = 90°).

A coolie holds a 20 kg box on his head while standing still for 10 minutes. How much work does he do on the box? Give a reason.

Zero. The box has no displacement, so W = FScosθ = 0, although his muscles tire.

Name the SI and cgs units of work and state the relation between them.

Joule (SI) and erg (cgs); 1 J = 10⁷ erg.

Express 1 kW h in joules and 1 eV in joules.

1 kW h = 3.6 × 10⁶ J; 1 eV = 1.6 × 10^-19 J.

Distinguish between power and energy, giving the SI unit of each.

Energy is the capacity to do work, measured in joules; power is the rate of doing work, measured in watts. The power of a source tells how quickly it delivers energy, so it depends on the time taken; the energy delivered does not.

How many watts is 3 hp?

3 × 746 = 2238 W.

Derive the expression for the gravitational potential energy of a body of mass m at height h.

Raising it slowly needs a force mg upward through displacement h; work done W = mg × h. This work is stored as potential energy, so U = mgh.

Derive K = tfrac12mv² for a body starting from rest.

A constant force F = ma acts through S. From v² = 2aS, S = v²/2a. Work W = FS = ma × v²/2a = tfrac12mv², which is stored as kinetic energy.

Past board exam questions

ICSE 2027 sample paper · 1 mark

Two balls, A and B have the same gravitational potential energy. Ball A is six times the mass of ball B. How do their heights above the ground compare?

Height of A is the same as height of B.
Height of A is twice the height of B.
Height of A is one-sixth the height of B.
Height of A is six times the height of B.

Show answer

Height of A is one-sixth the height of B.

ICSE 2027 sample paper · 4 marks

An empty supermarket trolley of mass 10 kg is moving with a speed of 8 m s⁻¹. An identical trolley is loaded with 10 kg of goods and moves with a speed of 4 m s⁻¹. Both trolleys are brought to rest over the same stopping distance. (a) Calculate the kinetic energy of the empty trolley. (b) Calculate the kinetic energy of the loaded trolley. (c) Compare the braking force required to stop the empty trolley and the loaded trolley. (d) Name the principle applied in solving part (c).

Show answer

(a) KE = ½mv² = ½ × 10 × 8² = 320 J (b) Loaded trolley: m = 10 + 10 = 20 kg, KE = ½ × 20 × 4² = 160 J (c) Work done by the braking force = loss of KE: F₁s = 320 J and F₂s = 160 J with the same s, so F₁ : F₂ = 320 : 160 = 2 : 1 – the empty trolley needs twice the braking force. (d) Work–energy theorem.

ICSE 2026 sample paper · 1 mark

The kinetic energy of a given body depends on the:

position
centre of gravity
momentum
displacement

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momentum

ICSE 2026 board paper · 1 mark

The energy transformation taking place during photosynthesis in plants is:

heat to chemical
chemical to light
light to chemical
chemical to heat

Show answer

light to chemical

ICSE 2026 sample paper · 1 mark

During power production in a coal-based thermoelectric power plant, the correct sequence of energy conversions taking place is:

heat → mechanical → chemical
heat → mechanical → electrical
chemical → heat → light
heat → chemical → electrical

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heat → mechanical → electrical

ICSE 2026 board paper · 1 mark

A fast-moving cyclist stops pedalling on reaching a hilly track. If he continues to move with the acquired energy, then assuming no loss of energy:

his kinetic energy remains constant at all times.
his potential energy remains constant at all times.
his total mechanical energy continuously increases.
his total mechanical energy remains constant.

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his total mechanical energy remains constant.

ICSE 2026 sample paper · 4 marks

A, B, C and D are four points on a hemispherical cup placed inverted on the ground. Diameter BC = 360 cm and AE = R/3 (R is the radius of the cup). A is the top of the cup; B and C are the ends of the diameter on the ground; E is on the vertical line from A down to the centre of the base; D is on the surface of the cup at the same level as E. A small spherical mass 500 g at rest at the point A, slides down along the smooth surface of the cup. Assuming that there is no loss of energy, calculate its: (a) Potential Energy at A relative to B. (b) Speed at the point B (lowest point). (c) Kinetic Energy at D (g = 10 ms⁻²).

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R = 360/2 = 180 cm = 1.8 m; m = 500 g = 0.5 kg. Height of A above B = R = 1.8 m. (a) PE at A = mgh = 0.5 × 10 × 1.8 = 9 J (b) PE at A = KE at B: mgh = ½mv² v = √(2gh) = √(2 × 10 × 1.8) = √36 = 6 m s⁻¹ (c) Height of D above B = R − R/3 = 2R/3 = 1.2 m PE at D = 0.5 × 10 × 1.2 = 6 J KE at D = total energy − PE at D = 9 − 6 = 3 J

ICSE 2026 board paper · 4 marks

A ball of mass 20 g falls from a height of 45 m. It rebounds from the ground to a height of 40 m. Calculate: (a) the initial potential energy of the ball. (b) the speed of the ball at which it hits the ground. (c) the loss in kinetic energy on striking the ground. [g = 10 m/s²]

Show answer

m = 20 g = 0.02 kg. (a) Initial PE = mgh = 0.02 × 10 × 45 = 9 J. (b) PE lost = KE gained: (1)/(2)mv² = 9 ⇒ v² = (2 × 9)/(0.02) = 900 ⇒ v = 30 m/s. (c) KE just before striking = 9 J. KE just after rebound = PE at 40 m = 0.02 × 10 × 40 = 8 J. Loss in KE = 9 − 8 = 1 J.