Chapter 7: Work, Energy, and Simple Machines

In earlier chapters, we study force, motion, Newton’s laws, and kinematic equations. But sometimes, forces may change with time or act in complicated ways. In such cases, the concepts of work, energy, and power help us understand motion more easily.

This chapter explains:

• how work is done by a force,
• how work changes the energy of an object,
• different forms of energy,
• kinetic energy and potential energy,
• conservation of mechanical energy,
• power,
• and simple machines like pulley, inclined plane and lever.

Energy is very important because almost every activity needs energy. Food gives us energy to walk, electricity gives energy to rotate a fan, and fuel gives energy to move a car.

In science, work has a special meaning. Work is said to be done only when a force causes displacement of an object in the direction of the force.

Definition of Work

Work done on an object by a constant force = Force applied × Displacement in the direction of the force

W = F × s

Where:

• W = work done
• F = force applied
• s = displacement in the direction of force

Example

If you lift a bag upward, you apply force upward and the bag also moves upward. So, work is done on the bag.

If you lift three bags instead of one, more force is needed, so more work is done. If you lift the same bag to a greater height, displacement increases, so work done also increases.

SI Unit of Work

The SI unit of work is joule, written as J.

1 J = 1 N × 1 m

So, 1 joule of work is done when a force of 1 newton displaces an object by 1 metre in the direction of the force.

Also,

1 J = 1 kg m²s⁻²

Work from Force-Displacement Graph

If force is plotted on the y-axis and displacement on the x-axis, then:

Work done = Area under force-displacement graph

For a constant force, the area is a rectangle:

Work = Force × Displacement

For example, if force = 10 N and displacement = 1 m,

W = 10 × 1 = 10 J

Work done is zero in the following cases:

1. When force is zero

If no force is applied, no work is done.

F = 0 ⇒ W = 0

2. When displacement is zero

If an object does not move, work done is zero even if force is applied.

Example: Pushing a rigid wall. You apply force, but the wall does not move. So, work done on the wall is zero.

3. When force is perpendicular to displacement

If force and displacement are at right angles, work done by that force is zero.

Example: A girl carrying a box while walking horizontally. She applies force upward to hold the box, but displacement is horizontal. Since force and displacement are perpendicular, work done by her upward force on the box is zero.

Important Point

You may feel tired while pushing a wall or carrying a box, but scientifically, work done on that object may be zero. This is because your muscles use internal energy even when the object does not move.

Work can be positive, negative, or zero depending on the direction of force and displacement.

Positive Work

When force and displacement are in the same direction, work done is positive.

Example

When a boy pushes a wheelchair forward, force and displacement are in the same direction. So, the boy does positive work on the wheelchair.

Negative Work

When force and displacement are in opposite directions, work done is negative.

Example

When a goalkeeper stops a moving ball, the force applied by the goalkeeper is opposite to the motion of the ball. So, the goalkeeper does negative work on the ball.

W = F × ( - s)

Example:

Force = 200 N Displacement = 0.15 m opposite to force

W = 200 × ( - 0.15) = - 30 J

So, work done = –30 J.

An object that has the capacity to do work is said to possess energy.

Examples

• A moving cricket ball can hit wickets and make them fall.
• A flowerpot kept at a height can damage something if it falls.
• A stretched rubber band can move an object when released.

In all these cases, the object has energy because it can do work.

Work-Energy Theorem

The relation between work done and change in energy is called the work-energy theorem.

Work done on an object = Change in its energy W = Δ E

If positive work is done on an object, its energy increases. If negative work is done, its energy decreases.

SI Unit of Energy

The SI unit of energy is also joule (J).

Energy Transfer

Energy can be transferred in many ways:

• by doing mechanical work,
• as heat,
• through radiation,
• through electric circuits,
• through sound waves,
• and in nuclear reactions.

Meet a Scientist: James Prescott Joule

The SI unit of work and energy, joule, is named after James Prescott Joule. He studied the relationship between mechanical energy and thermal energy. His work helped scientists understand that energy can be converted from one form to another.

Energy exists in many forms. It can change from one form to another.

Main Forms of Energy

Examples of Energy Conversion

• Electrical energy → Light energy in a bulb.
• Electrical energy → Thermal energy in a heater.
• Chemical energy in food → Mechanical energy in muscles.
• Mechanical energy → Sound energy in a ringing bell.

Mechanical energy is the energy possessed by an object due to its motion or position.

There are two main types of mechanical energy:

• Kinetic energy
• Potential energy

Mechanical Energy = Kinetic Energy + Potential Energy

The energy possessed by an object due to its motion is called kinetic energy.

Examples

• A moving bicycle
• A rolling ball
• A moving car
• A flying arrow

A stationary object has zero kinetic energy.

Formula for Kinetic Energy

K = ½mv²

Where:

• K = kinetic energy
• m = mass of object
• v = velocity of object

Important Points

• Kinetic energy depends on mass and velocity.
• If mass increases, kinetic energy increases.
• If velocity doubles, kinetic energy becomes four times.

Why?

K = ½m(2v)² = 4 × ½mv²

So, kinetic energy becomes 4 times.

Unit of Kinetic Energy

The SI unit of kinetic energy is joule (J).

Relation with Work

If positive work is done on an object, its velocity increases and kinetic energy increases. If negative work is done, velocity decreases and kinetic energy decreases.

The energy stored in an object due to its position, shape, or configuration is called potential energy.

Examples of Potential Energy

1. Stretched rubber band

A stretched rubber band stores energy. When released, it can move an object.

2. Bent bow

A bent bow stores energy. When the string is released, the arrow moves forward.

3. Compressed spring

A compressed spring stores energy. When released, it returns to its original shape and can move an object.

4. Object raised to a height

A ball raised above the ground has gravitational potential energy.

Potential energy can be stored due to:

• deformation of an object,
• relative position of objects,
• gravitational force,
• magnetic force,
• electric force.

Gravitational Potential Energy

The potential energy possessed by an object due to its height above the Earth’s surface is called gravitational potential energy.

When an object is lifted to a height, work is done against gravity. This work gets stored as potential energy.

Formula

U = mgh

Where:

• U = gravitational potential energy
• m = mass of object
• g = acceleration due to gravity
• h = height above ground

Important Points

• Greater height means greater potential energy.
• Greater mass means greater potential energy.
• Potential energy near Earth’s surface is taken as mgh .

Example

Mass = 0.2 kg Height = 10 m

g = 10 m s⁻²

U = mgh = 0.2 × 10 × 10 = 20 J

So, potential energy = 20 J.

The sum of kinetic energy and potential energy is called mechanical energy.

Mechanical Energy = K + U

Conservation of Mechanical Energy

When only gravity acts on an object and there is no friction or air resistance, the total mechanical energy remains constant.

This is called conservation of mechanical energy.

K + U = constant

Example: Falling Object

Suppose an object is dropped from height h .

At the top

• Kinetic energy = 0
• Potential energy = mgh
• Total mechanical energy = mgh

During falling

• Potential energy decreases.
• Kinetic energy increases.
• Total mechanical energy remains mgh .

Just before reaching ground

• Potential energy = 0
• Kinetic energy = mgh
• Total mechanical energy = mgh

So, during free fall:

Loss in potential energy = Gain in kinetic energy

Example: Pendulum

In a pendulum:

• At extreme positions, potential energy is maximum and kinetic energy is zero.
• At the lowest point, kinetic energy is maximum and potential energy is minimum.
• In ideal conditions, total mechanical energy remains constant.

In real life, the pendulum slowly stops because some energy is lost due to air resistance and friction at the support.

The same amount of work can be done slowly or quickly. The rate at which work is done is called power.

Definition

Power is the rate of doing work.

P = W/t

Where:

• P = power
• W = work done
• t = time taken

SI Unit of Power

The SI unit of power is watt (W).

1 W = 1 J s⁻¹

So, 1 watt means 1 joule of work is done in 1 second.

Important Points

• More work in the same time means more power.
• Same work in less time means more power.
• If time taken is more, power is less.

Horsepower

Another unit of power is horsepower (hp).

1 hp = 746 W

Horsepower is often used for engines and pumps.

Meet a Scientist: James Watt

The unit of power, watt, is named in honour of James Watt. He developed an efficient steam engine that could generate rotational motion and move wheels.

Simple machines are devices that make work easier by changing the magnitude or direction of force.

Important Point

Simple machines do not reduce the total work done. They only make the work easier by:

• reducing the effort,
• changing the direction of effort,
• or allowing force to be applied conveniently.

Effort and Load

• Effort: Force applied by us to a machine.
• Load: Force that needs to be overcome.

Mechanical Advantage

Mechanical advantage tells us how much a machine multiplies force.

Mechanical Advantage = Load/Effort

If mechanical advantage is greater than 1, the machine reduces the effort needed.

A pulley is a wheel with a groove through which a rope passes.

Fixed Pulley

A fixed pulley is attached to a fixed support.

Function

It changes the direction of effort.

Example: When a flag is raised, we pull the rope downward, but the flag moves upward.

Mechanical Advantage of Fixed Pulley

For an ideal fixed pulley:

Mechanical Advantage = 1

This means it does not reduce the force, but it makes the work more convenient by changing the direction of force.

Movable Pulley

A movable pulley moves along with the load.

A movable pulley or a system of pulleys can have mechanical advantage greater than 1. It can help lift heavier loads with smaller effort.

Uses of Pulley

• cranes,
• elevators,
• flag hoisting,
• lifting heavy objects.

An inclined plane is a sloping surface used to move a heavy object to a higher or lower level.

Example

A ramp used to push a heavy box into a truck is an inclined plane.

How Inclined Plane Helps

Lifting a box vertically requires a large force equal to its weight. But pushing the same box along a ramp requires smaller force. However, the force has to be applied over a longer distance.

So:

• force decreases,
• distance increases,
• total work remains nearly the same.

Mechanical Advantage of Inclined Plane

Mechanical Advantage = L/h

Where:

• L = length of inclined plane
• h = height of inclined plane

Since L is greater than h , mechanical advantage is greater than 1.

Important Point

A longer and less steep inclined plane requires less effort.

Examples

• ramps,
• hill roads,
• inclined ladders,
• loading planks.

Hill roads are made winding and gentle instead of straight up because a gentle slope reduces the force required to move upward.

A lever is a rigid bar that can rotate about a fixed point.

Main Parts of a Lever

• Fulcrum: Fixed point about which the lever rotates.
• Load: Force to be overcome.
• Effort: Force applied.
• Load arm: Distance of load from fulcrum.
• Effort arm: Distance of effort from fulcrum.

Principle of Lever

Effort × Effort arm = Load × Load arm

If the effort arm is increased, less effort is required to lift the load.

Mechanical Advantage of Lever

Mechanical Advantage = Load/Effort

or

Mechanical Advantage = Effort arm/Load arm

Important Point

A lever reduces the force required, but it does not reduce the total work done. The smaller effort moves through a larger distance.

Classes of Levers

Work is done when a force moves an object in the direction of the force. The formula for work is W = F × s , and its SI unit is joule. Work can be positive, negative, or zero depending on the direction of force and displacement. If there is no displacement, or if force is perpendicular to displacement, work done is zero.

Energy is the capacity to do work. According to the work-energy theorem, work done on an object is equal to the change in its energy. Energy exists in many forms such as mechanical, thermal, light, sound, electrical, chemical and nuclear energy.

Mechanical energy is the energy due to motion or position. Kinetic energy is energy due to motion and is given by K = ½mv² . Potential energy is stored energy due to position or shape. Near Earth’s surface, gravitational potential energy is U = mgh .

When an object falls freely, its potential energy changes into kinetic energy. If friction and air resistance are ignored, the total mechanical energy remains constant. This is called conservation of mechanical energy.

Power is the rate of doing work. Its formula is P = W/t , and its SI unit is watt. Simple machines make work easier by changing the magnitude or direction of force. Pulley, inclined plane and lever are common simple machines. They do not reduce total work, but they help us apply force more conveniently.