1. What is Work?
In everyday language, work can mean any effort or activity. In physics, however, work is done when a force acting on an object produces displacement in the direction of the force.
Examples
If the box moves in the direction of the push, the applied force does work.
The upward force applied by you causes upward displacement, so work is done by that force.
You may exert force, but if the wall does not move, mechanical work on the wall is zero.
2. Work Done by a Constant Force
When a constant force acts along the direction of displacement:
where W is work, F is force and s is displacement.
One joule is the work done when a force of 1 newton displaces an object by 1 metre in the direction of the force.
When force is at an angle
For a constant force F making an angle θ with displacement s:
| Angle | Work | Meaning |
|---|---|---|
| θ = 0° | W = Fs | Force and displacement same direction; maximum positive work. |
| θ = 90° | W = 0 | Force is perpendicular to displacement. |
| θ = 180° | W = −Fs | Force opposes displacement; work is negative. |
Example
A force of 20 N moves an object 5 m in its direction:
3. What is Energy?
Energy is the capacity to do work. An object or system may possess energy because of its motion, position, shape or other physical/chemical conditions.
Energy due to motion.
Energy associated with position or configuration.
Thermal, chemical, electrical, light and nuclear energy are common forms.
The SI unit of energy is the joule (J). Work and energy have the same SI unit because doing work transfers energy.
4. Work-Energy Theorem
The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.
If the net work is positive, kinetic energy increases. If net work is negative, kinetic energy decreases.
5. Kinetic Energy
Kinetic energy is the energy possessed by an object because of its motion.
where m is mass in kg and v is speed in m/s.
Derivation
For an object of mass m, initially at rest, accelerated to speed v:
Using the equation v² = u² + 2as and u = 0:
Therefore:
Since work done becomes kinetic energy:
Important observation
Kinetic energy depends on the square of speed. If speed doubles, kinetic energy becomes four times, provided mass remains constant.
Example
A 4 kg object moves at 3 m/s:
6. Potential Energy
Potential energy is energy associated with the position or configuration of an object. In this chapter, the main example is gravitational potential energy of an object raised above a reference level.
where m is mass, g is acceleration due to gravity and h is height above the chosen reference level.
Derivation
To raise a mass m through height h at constant speed, the upward force needed against gravity is approximately mg. Work done is:
This work is stored as gravitational potential energy relative to the reference level.
Example
For a 2 kg object raised by 5 m, taking g = 10 m/s²:
7. Conversion Between Potential and Kinetic Energy
When an object falls freely, its gravitational potential energy decreases while its kinetic energy increases.
Ignoring air resistance, the total mechanical energy remains constant:
| Position | Potential Energy | Kinetic Energy |
|---|---|---|
| At highest point | Maximum relative to ground | Minimum; may be zero if released from rest |
| During fall | Decreases | Increases |
| Near lowest point | Minimum relative to chosen level | Maximum |
8. Law of Conservation of Energy
The law of conservation of energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of an isolated system remains constant.
Example: Falling object
Potential energy changes into kinetic energy. If air resistance and other losses are neglected, the total mechanical energy remains constant.
Example: Hydroelectric power
Real systems
In real machines, some useful mechanical energy may be transformed into thermal or sound energy because of friction and other effects. This does not violate conservation of energy; the total energy is still accounted for.
9. Power
Power is the rate at which work is done or energy is transferred.
where P is power, W is work and t is time.
One watt is one joule of work done or energy transferred per second.
Example
If a machine does 600 J of work in 20 s:
Average power
For a process that takes a measurable time, average power is total work divided by total time.
10. Simple Machines
A simple machine is a device that makes work easier by changing the magnitude or direction of an applied force, or by allowing a force to be applied more conveniently.
In this chapter, the main simple machines are the pulley, inclined plane and lever.
Can change the direction of effort; pulley systems can provide mechanical advantage.
Reduces the force needed to raise a load by increasing the distance over which the force acts.
A rigid bar that turns about a fixed point called the fulcrum.
11. Pulley
A pulley is a wheel with a groove over which a rope or belt passes. A fixed pulley can change the direction of effort. A movable pulley or pulley system can provide mechanical advantage.
Fixed pulley
In an ideal fixed pulley, the effort and load may have equal magnitudes, so the mechanical advantage is approximately 1, but the direction of effort changes. This can make lifting more convenient.
Movable pulley
In an ideal single movable pulley, the load is supported by two rope segments, giving an ideal mechanical advantage of about 2.
12. Inclined Plane
An inclined plane is a sloping surface used to raise or lower a load. It allows the load to be moved through a longer distance with a smaller effort than lifting it vertically, under ideal conditions.
Everyday examples
- Ramps for wheelchairs and trolleys.
- Loading ramps used for vehicles and goods.
- Sloping roads in hilly areas.
- Slides and some lifting arrangements.
For an ideal inclined plane, ignoring friction:
A longer, gentler ramp can reduce the required effort, although the load must travel a greater distance.
13. Lever
A lever is a rigid bar that can rotate about a fixed point called the fulcrum. The main terms are effort, load and fulcrum.
Three classes of levers
| Class | Arrangement | Examples |
|---|---|---|
| First class | Fulcrum between effort and load | Seesaw, scissors, crowbar |
| Second class | Load between fulcrum and effort | Wheelbarrow, nutcracker, bottle opener |
| Third class | Effort between fulcrum and load | Human forearm, tweezers, fishing rod |
Mechanical advantage of a lever
For an ideal lever, the law of moments gives:
14. Mechanical Advantage
Mechanical advantage (MA) tells us how much a machine multiplies the applied effort.
If MA = 4, an ideal interpretation is that a 1 N effort can support a 4 N load under the stated arrangement.
Ideal and real machines
| Machine | Ideal idea | Real situation |
|---|---|---|
| Pulley | Mechanical advantage depends on supporting rope segments. | Friction and pulley mass reduce performance. |
| Inclined plane | MA = length/height. | Friction makes actual MA smaller. |
| Lever | MA depends on relative arm lengths. | Friction at fulcrum and deformation may cause losses. |
Mechanical advantage is not energy creation
If a machine reduces the effort force, the effort generally acts through a greater distance. In an ideal machine, input work equals output work:
Real machines require more input work than useful output work because of losses such as friction.
15. Applications in Everyday Life
Inclined planes make it easier to move loads through a height.
A second-class lever helps lift and move a load.
Two first-class levers operate around pivots.
A larger distance from the pivot makes turning easier.
Useful for lifting loads and changing the direction of effort.
Bones, joints and muscles form lever-like systems.
16. Formula Sheet
| Quantity | SI unit |
|---|---|
| Work / Energy | joule (J) |
| Force | newton (N) |
| Power | watt (W) |
| Mass | kilogram (kg) |
| Speed / velocity | m/s |
| Height / displacement | metre (m) |
17. Quick Revision
18. Practice Questions
- Define work in physics.
- State the SI unit of work and define one joule.
- Write the formula for work when force and displacement are in the same direction.
- When is work done by a force zero?
- Write the general formula for work done by a constant force making angle θ with displacement.
- A force of 25 N moves an object by 4 m in its direction. Calculate work done.
- Define energy and state its SI unit.
- State the work-energy theorem.
- Define kinetic energy and derive K = ½mv².
- Calculate the kinetic energy of a 5 kg object moving at 4 m/s.
- What happens to kinetic energy if speed is doubled?
- Define gravitational potential energy.
- Derive U = mgh for an object raised through height h.
- Calculate potential energy of a 3 kg object at a height of 10 m, taking g = 10 m/s².
- Explain the conversion of potential energy into kinetic energy during free fall.
- State the law of conservation of energy.
- Explain why friction does not violate conservation of energy.
- Define power and state its SI unit.
- A machine does 900 J of work in 30 s. Find its power.
- What is a simple machine?
- Name three simple machines included in this chapter.
- Explain the function of a fixed pulley.
- What is the ideal mechanical advantage of a single movable pulley?
- Explain how an inclined plane makes lifting a load easier.
- State the formula for the ideal mechanical advantage of an inclined plane.
- Define fulcrum, effort and load in a lever.
- Differentiate the three classes of levers with examples.
- A machine lifts a 400 N load with an effort of 100 N. Find its mechanical advantage.
- Explain why a real machine cannot create energy.
- Explain how a ramp, wheelbarrow and pulley demonstrate the use of simple machines in everyday life.
19. Interactive 30-Question Quiz
Choose one option for every question, then click Check Score.