Science · Class 9 · Chapter 7

Work, Energy, and Simple Machines

• Work (W = F × s) — Force times displacement in the force's direction.
• Work-energy theorem — Work done on an object equals its change in energy.
• Kinetic energy (K = ½mv²) — The energy of motion.
• Potential energy (U = mgh) — Energy of position or deformation.
• Mechanical energy — Kinetic energy + potential energy.
• Power (P = W ÷ t) — The rate at which work is done.
• Simple machine — A device changing the size/direction of a force.
• Mechanical advantage — Load ÷ effort — how much a machine multiplies force.

Chapter 7 · Concept 1 of 11

Work Done by a Constant Force

• Work done = force applied × displacement in the direction of the force.
• W = F × s — The SI unit of work is the joule (J). 1 joule = 1 newton of force displacing an object by 1 metre in the force's direction. Lifting 3 bags, or lifting 1 bag 3× as high, both do 3× the work.

Chapter 7 · Concept 2 of 11

When Work Isn't Simply "Effort"

• Zero work — No force (F = 0), no displacement (s = 0), or a force perpendicular to displacement — like carrying a box while walking — all give zero work, however tiring it feels.
• Positive or negative — Force and displacement in the same direction: positive work (pushing a wheelchair forward). Opposite directions: negative work (a goalkeeper stopping a ball).

Chapter 7 · Concept 3 of 11

The Work-Energy Theorem

• An object with the capacity to do work is said to possess energy.
• Work done on an object = change in its energy — A thrown ball gains energy from the work done throwing it — then transfers that energy, knocking over the wicket it hits. The SI unit of energy is also the joule (J).

Chapter 7 · Concept 4 of 11

Forms of Energy

• Mechanical — Motion or position
• Thermal — Makes things warm or hot
• Sound — Vibrations of air or other matter
• Electrical — Motion or position of charges
• Nuclear — Stored in atomic nuclei
• Chemical — Stored in fuels and food

Chapter 7 · Concept 5 of 11

Kinetic Energy

• K = ½mv² — The energy an object has because it's moving. Doubling velocity quadruples kinetic energy — since v is squared.
• Worked example — A 0.2 kg cricket ball bowled at 43 m/s: K = ½ × 0.2 × 43² = ½ × 0.2 × 1849 ≈ 184.9 J

Chapter 7 · Concept 6 of 11

Potential Energy

• Stored by deformation or position — A stretched slingshot, a bent bow, a compressed spring, separated magnets, or a raised ball above the Earth — all store energy that can later become motion.
• U = mgh — Gravitational potential energy at height h. Example: a 200 g ball 10 m up has U = 0.2 × 10 × 10 = 20 J (taking g = 10 m/s²).

Chapter 7 · Concept 7 of 11

Conservation of Mechanical Energy

• Mechanical energy = kinetic energy + potential energy. As an object falls freely, one converts into the other — their sum stays constant.
• Pendulum position | Potential energy | Kinetic energy
• P — released from the side — Maximum (mgh) — Zero
• Q — swinging through the bottom — Zero — Maximum
• R — rising on the far side — Maximum again — Zero

Chapter 7 · Concept 8 of 11

Power

• P = W ÷ t — Power is the rate of doing work. Running up the stairs and walking up slowly do the same work — but running needs far more power. SI unit: watt (W) = 1 J/s.
• Worked example — A weightlifter lifts 75 kg by 2 m in 5 s: W = mgh = 75 × 10 × 2 = 1500 J P = 1500 J ÷ 5 s = 300 W

Chapter 7 · Concept 9 of 11

Simple Machines and Mechanical Advantage

• A machine can't reduce the total work needed — but it can change the size or direction of the force you apply.
• Mechanical advantage = Load ÷ Effort — The load is the force to be overcome; the effort is the force you apply. A pulley, an inclined plane, and a lever are three of the simplest machines.

Chapter 7 · Concept 10 of 11

The Pulley and the Inclined Plane

• Fixed pulley — Changes the direction of your effort (pulling down instead of lifting up), but doesn't reduce it — mechanical advantage = 1. A movable pulley system can do better.
• Inclined plane — Mechanical advantage = L ÷ h (ramp length ÷ height). A longer, gentler ramp needs less force — but you push it over a longer distance, so total work stays the same.

Chapter 7 · Concept 11 of 11

The Lever

• F₁ × d₁ = F₂ × d₂ — A longer effort arm lets a small force move a much larger load — the total work done stays the same either way.

Quick Recap

Check Your Understanding

1. 1When a ball thrown upwards reaches its highest point, which of these are correct? (i) The force acting on the ball is zero. (ii) The acceleration of the ball is zero. (iii) Its kinetic energy is zero. (iv) Its potential energy is maximum.
2. 2Identify the energy transformation in each situation.
3. 3A crane lifts a mass m to the 10th floor in a certain time t. It then raises the same mass to the 20th floor in double the time (2t). How much more energy and power are required?