Work, Energy and Simple Machines Class 9 Notes and Questions

These Work, Energy, and Simple Machines Class 9 notes take you through the chapter in order: what work means in science, the work-energy theorem, kinetic and potential energy, conservation of energy, power, and how pulleys, ramps and levers make work easier. Each formula has a worked example with units, and the questions at the end are fully solved.

What "work" means in science

In science, work needs a force and a displacement of the object in the direction of the force.

W = F × s

If you push a rigid wall, you get tired, but no work is done on the wall, because it does not move.

• SI unit: joule (J). 1 J is the work done when a force of 1 N moves an object 1 m in the direction of the force.
• Since 1 N = 1 kg m s⁻², 1 J = 1 kg m² s⁻².
• Work is a scalar, but it can be positive, negative or zero.

Worked example: a girl lifts a 2 kg book 1.5 m (g = 10 m s⁻²).

• F = mg = 2 kg × 10 m s⁻² = 20 N
• W = F × s = 20 N × 1.5 m = 30 J

Energy and the work-energy theorem

Energy is the capacity to do work. When positive work is done on an object, it gains energy. A fielder throws a ball; the ball, now moving, can knock down the wicket.

Work-energy theorem: the work done on an object equals the change in its energy, W = ΔE. So if 50 J of work is done on a stationary object, its energy increases by 50 J.

Energy is measured in joules. It comes in many forms: mechanical, thermal, chemical, electrical, light, sound and nuclear, and these can change into one another. Chemical energy from food powers the work our muscles do.

Kinetic energy

Kinetic energy is the energy of motion. An object at rest has zero kinetic energy.

K = ½mv²

Where it comes from: from v² = u² + 2as, s = (v² − u²) ÷ 2a. Put this and F = ma into W = F × s to get W = ½m(v² − u²). If the object starts from rest (u = 0), the work done equals its final kinetic energy.

Since K depends on v², doubling the velocity makes kinetic energy four times. Kinetic energy is a scalar.

Worked example: A has mass m and B has mass 4m, with equal kinetic energy. Find vA : vB.

• ½m(vA)² = ½(4m)(vB)²
• (vA)² = 4(vB)², so vA = 2vB
• Ratio = 2 : 1

Potential energy

Potential energy is energy stored because of position or shape. Stretching a rubber band, pulling a bowstring or pressing a spring stores elastic potential energy, which turns into kinetic energy when released.

Gravitational potential energy: to lift mass m to height h, you apply a force equal to its weight, mg. Work = mg × h, stored as U = mgh. In this chapter g is taken as constant near Earth's surface.

Worked example: a 5 kg hammer is lifted 2 m.

• U = 5 kg × 10 m s⁻² × 2 m = 100 J

A ball moving horizontally at a constant height keeps the same potential energy, because h does not change.

Conservation of mechanical energy

Mechanical energy = K + U. If only gravity does work, this total stays constant.

An object of mass m is dropped from height h (point A): K = 0, U = mgh, total = mgh. At point B, height h′, its speed satisfies v² = 2g(h − h′). Then:

• K = ½mv² = mg(h − h′)
• U = mgh′
• K + U = mg(h − h′) + mgh′ = mgh

The total is unchanged. In real life, friction and air resistance turn some mechanical energy into heat or sound, which is why a pendulum finally stops. The total energy, heat included, still stays constant. In a pendulum, kinetic energy is greatest at the lowest point, where potential energy is least.

Power

Power is the rate of doing work: P = W ÷ t. Two people climbing the same stairs do the same work, but the one who runs up has more power.

• SI unit: watt (W); 1 W = 1 J s⁻¹.
• 1 horsepower (hp) = 746 W.

Worked example: an engine does 20,000 J of work in 10 s.

• P = 20,000 J ÷ 10 s = 2000 W = 2 kW

Simple machines: pulleys and inclined planes

A simple machine does not reduce the total work. It lets you use a smaller effort over a longer distance to move a bigger load.

Mechanical advantage: MA = Load ÷ Effort

A gentler slope (bigger L) makes pushing easier, but you push for longer. Example: a ramp 5 m long and 1 m high has MA = 5 ÷ 1 = 5, so, ignoring friction, the effort is one-fifth of the object's weight.

Levers

A lever is a rigid bar that turns about a fixed point, the fulcrum.

Principle of a lever: Effort × Effort arm = Load × Load arm. MA of a lever = effort arm ÷ load arm.

Class I and II levers usually give a force advantage (MA more than 1). Class III levers give speed or precision instead (MA less than 1).

Worked example: a 30 kg child sits 1 m from a seesaw's fulcrum. Where must a 15 kg child sit?

• 15 kg × L = 30 kg × 1 m
• L = 2 m from the fulcrum

Remember this

• W = F × s; unit J. No displacement means no work.
• K = ½mv²; U = mgh; W = ΔE.
• P = W ÷ t; unit W; 1 hp = 746 W.
• MA = Load ÷ Effort; inclined plane MA = L/h.
• Lever: Effort × Effort arm = Load × Load arm.

Important questions with answers

1. Why is no work done when you push a wall? The wall's displacement is zero, so W = F × 0 = 0.

2. Find the kinetic energy of a 2 kg ball moving at 3 m/s. K = ½ × 2 kg × (3 m/s)² = ½ × 2 × 9 = 9 J.

3. A 1 kg stone falls freely from 5 m. Find its kinetic energy just before it hits the ground (g = 10 m s⁻², no air resistance). U at the top = 1 × 10 × 5 = 50 J. All of it becomes kinetic energy, so K = 50 J.

4. A 50 kg student climbs 3 m of stairs in 5 s. Find the power (g = 10 m s⁻²). W = mgh = 50 × 10 × 3 = 1500 J. P = 1500 J ÷ 5 s = 300 W.

5. What happens to kinetic energy if velocity is doubled? It becomes four times, because K depends on v².

6. A lever has an effort arm of 2 m and a load arm of 0.5 m. What effort lifts a 400 N load? Effort × 2 = 400 × 0.5 = 200, so effort = 100 N. MA = 2 ÷ 0.5 = 4.

7. Does a simple machine reduce the work needed? No. It lets a smaller effort act over a longer distance; the total work is not reduced.

8. Why does a swinging pendulum finally stop? Friction and air resistance change some mechanical energy into heat and sound.

Common mistakes to avoid

• Using mass instead of weight (mg) as the force when lifting.
• Forgetting to square v in K = ½mv².
• Thinking a fixed pulley reduces effort. Its MA is 1; it only changes direction.
• Mixing up the lever classes. Ask: what is in the middle?

To practise more energy and lever numericals with hints, study this chapter with Joy.