Work, Energy, and Simple Machines · Lesson 3 of 13
The Work-Energy Theorem
“Energy changes hands whenever work steps into the conversation.”
• Explain energy as the capacity to do work. • Connect positive and negative work with changes in energy. • State and apply the work-energy theorem. • Trace energy transfer during collisions. • Recognise ways energy can be transferred besides mechanical work.
A stationary cricket ball cannot knock down a wicket, but a rapidly moving ball can. A flowerpot resting on the ground may be harmless, while the same pot raised above the ground can damage something if it falls. Motion and position have given these objects a capacity to produce change. That capacity is described by energy.
Energy is the capacity of an object or system to do work.
The moving ball gained energy because the fielder did positive work on it while throwing it. The raised flowerpot gained energy because an external force did work while lifting it against gravity. When either object later applies a force and moves another object, energy is transferred onward. Work and energy are therefore not separate stories: work is one way energy moves into or out of an object or system.
The Central Relationship
The work done on an object or system is equal to the change in its energy.
A positive value of work means the final energy is greater than the initial energy. A negative value means the final energy is smaller. If the net work is zero, the energy represented in the chosen form does not change. The theorem can be applied to a single object or a system of interacting objects, and it remains useful even when the applied force changes.
| Work on the Object | Energy Change | Interpretation |
|---|---|---|
| Positive | Energy increases | Energy is transferred to the object |
| Negative | Energy decreases | Energy is transferred away from the object |
| Zero | No change in the relevant energy | No net transfer by work |
Energy Transfer in a Carrom Shot
Consider a moving striker that hits a white coin, which then hits a black coin. The striker applies a force in the direction of the white coin’s displacement and does positive work on it. The white coin gains energy. The white coin simultaneously applies an opposite force on the striker and does negative work on it, so the striker loses energy. The same pattern repeats when the white coin hits the black coin. The energy does not appear from nowhere; it travels through the collision sequence.
Problem
A force does 180 J of net work on a cart that initially has 70 J of kinetic energy. Find its final kinetic energy.
- 1.Write the theorem: W = Kfinal - Kinitial.
- 2.Substitute the known values: 180 J = Kfinal - 70 J.
- 3.Add 70 J to both sides.
- 4.Kfinal = 250 J.
- 5.The positive work increased the cart’s kinetic energy by 180 J.
Problem
The brakes of a moving bicycle do -420 J of work. If the bicycle and rider initially have 650 J of kinetic energy, find the remaining kinetic energy.
- 1.Use W = Kfinal - Kinitial.
- 2.Substitute: -420 J = Kfinal - 650 J.
- 3.Add 650 J to both sides.
- 4.Kfinal = 230 J.
- 5.The brakes have transferred 420 J away from the bicycle’s mechanical motion.
Other Ways Energy Is Transferred
Mechanical work is not the only means of transferring energy. When objects at different temperatures touch, energy can flow from the hotter object to the colder one as heat. Energy from the Sun reaches Earth through radiation without direct contact. Energy is also transferred through electric circuits and sound waves. Nuclear reactions inside the Sun release energy that later reaches Earth as radiation.
Why Net Work Matters
Several forces can do work on the same object. The change in its kinetic energy is connected to the sum of their works, called net work. A forward engine force may do positive work on a vehicle while air resistance and rolling friction do negative work. If positive and negative contributions are equal, net work is zero and kinetic energy remains unchanged even though individual forces continue transferring energy.
This distinction explains constant-speed motion on a level road. The engine continues to transfer energy to the vehicle, while resistive forces transfer energy from mechanical motion into thermal energy and the surroundings. The vehicle’s kinetic energy remains constant because the net work associated with its speed change is zero, not because no force is doing work.
Problem
A pulling force does 500 J of positive work on a sled while friction does -180 J. Find the net work and the change in kinetic energy.
- 1.Add the work done by all forces: Wnet = 500 J + (-180 J).
- 2.Wnet = 320 J.
- 3.By the work-energy theorem, net work equals the change in kinetic energy.
- 4.The sled’s kinetic energy therefore increases by 320 J.
The same event can be described differently depending on whether the system is one object or several interacting objects. State what belongs to the system before tracking energy entering, leaving or changing form.
Quiz
Which description best matches Energy?
Which description best matches Work-Energy Theorem?
Which term matches this description: Energy is the capacity of an object or system to do work.
Which term matches this description: The work done on an object or system is equal to the change in its energy.
Which statement is a key takeaway from this lesson?
Practice Problems
- A net force does 90 J of work on an object whose initial energy is 35 J. Find its final energy.
- An object loses 120 J of kinetic energy. What is the net work done on it?
- Trace the work and energy changes when one moving coin hits a stationary coin.
- Give one example each of energy transfer by work, heating, radiation and an electric circuit.
Key Takeaways
• Energy is the capacity to do work. • Work is one method of transferring energy. • Net work equals final energy minus initial energy. • Positive work increases energy and negative work decreases it. • Energy can also be transferred through heating, radiation, electricity and waves.