While a load moves horizontally, what work does a purely upward supporting force do?

Zero work. Perpendicular support does zero work, even though holding the load takes effort.

A push does 100 J; friction does −40 J. All other forces do zero work. What kinetic energy is gained?

60 J. Counting both forces gives 60 J instead of the push’s 100 J.

A force–position graph lies entirely below the axis, and position increases. What sign does the work have?

Negative. Below-axis force opposes displacement, so its area contributes negative work, not positive work.

With relaxed spring energy set to zero, what sign does its energy have when compressed?

Positive. Compression stores energy that the spring can release while returning to its relaxed shape.

At the top, what happens to the string if the mass reaches zero speed?

It goes slack. The string cannot push outward to balance gravity and hold the mass there.

A pump delivers 600 W usefully at 60% efficiency. What input power does it need?

1000 W. Dividing gives 1000 W, while multiplying gives 360 W, less than useful output.

An isolated moving cart sticks to an identical stationary cart. What fraction of their initial kinetic energy remains?

Half. Their combined mass doubles and speed halves, leaving half their initial kinetic energy.

Sand leaves at a moving trolley’s horizontal speed, with no horizontal thrust or external horizontal force. What happens to the momentum magnitude of the trolley plus its remaining sand?

It decreases. The departing sand carries momentum away while the remaining trolley keeps its speed.

Teach Work, Energy and Power in eight steps.

For each idea: show it, ask before you tell, then say one line.

Gather a book, paper, a pencil and a soft ball, with a clear table and walking space.

Common misconceptions & worked visual for this chapter · 15 practice questions with answers

Why it matters

A skidding cycle slows as road friction removes kinetic energy.
Pumps need extra input power because some energy becomes unavailable for lifting water.
Braking trains can recover electricity that helps other trains accelerate.

What to teach

How to teach it

Work and motion

One hand holding a book just above a wooden table.

1. Work

A force transfers energy through displacement along its direction.

Show: Hold a book just above the table, ready to lift it.
Ask: If you keep it still, how much work does your upward force do?
Say: Your upward force does no work while the book stays still.
Used in: Lifting a load transfers energy to it, raising it against gravity.

If your child says…“Holding something heavy must do work.”

Ask: What distance has the book moved while you hold it still?
What’s true: Supporting a stationary load takes effort but does no mechanical work on that load.

$K_i=\tfrac12(2)(2^2)=4\,\mathrm{J}$

$K_f=\tfrac12(2)(4^2)=16\,\mathrm{J}$

2. Kinetic energy and the work–energy theorem

Motion energy changes by the total work of all forces.

Show: Write these lines for 2 kg speeding from 2 m/s to 4 m/s. Say: kinetic energy is half mass times speed squared.
Ask: How much net work supplies this increase?
Say: Net work is 12 J: final energy minus initial energy. Doubling speed quadruples kinetic energy.
Used in: Including air resistance improves falling-speed predictions.

If your child says…“Only my push changes its kinetic energy.”

Ask: Does the energy change depend on your push alone, or every force together?
What’s true: Work by every force counts.

Force–position diagram with a wide positive rectangle and a narrower negative rectangle.

3. Work by a variable force

Signed graph area gives work.

Show: Look at the force–position diagram. Find the +30 J area above the axis, then the −10 J area below.
Ask: What total work results as position increases?
Say: Subtract the lower area: 20 J.
Used in: These graphs calculate work when pulling forces vary.

If your child says…“All areas add positively.”

Ask: Does opposing force add energy?
What’s true: Below-axis forces oppose increasing position.

Stored energy and circular motion

Spring and energy graph showing the kinetic-energy gap and two turning points.

4. Potential energy, spring energy and turning points

Stored energy limits reachable positions.

Show: Find the frictionless spring in the diagram, then the graph's zero and both crossings.
Ask: Where must the block reverse?
Say: Compression and extension store positive energy above relaxed energy. The block reverses at each crossing, where kinetic energy vanishes; beyond, motion would require negative kinetic energy.
Used in: Spring clips release stored energy to grip papers.

If your child says…“Compression stores negative energy.”

Ask: Where is the potential-energy curve compared with zero on the compression side?
What’s true: We choose zero potential energy when the spring is relaxed.

Vertical circle with inward top forces, tangential speeds and the bottom-to-top height.

5. Mechanical energy and vertical circular motion

Completing circles requires speed at the top.

Show: Look at the diagram's top forces, then its bottom-to-top height. R is the radius, and g is gravitational acceleration. Neglect air resistance and string stretching.
Ask: Would reaching the top with zero speed be enough to complete this circle?
Say: No. Minimum top speed is the square root of the product of g and R. Conserved mechanical energy then gives minimum bottom speed $\sqrt{5gR}$ .
Used in: Allowing for drag improves pendulum-speed predictions.

If your child says…“Reaching the top suffices.”

Ask: At zero top speed, what could stop gravity pulling the mass inside the circle?
What’s true: The string can pull inward but cannot push outward to cancel gravity.

Power and momentum

$W_{\mathrm{useful}}=5\times10\times2=100\,\mathrm{J}$

Useful power is 50 watts.

Input power is 100 watts.

6. Power and efficiency

Power measures transfer rate; efficiency measures the useful fraction.

Show: Write these lines: a motor uses 200 J in 2 s, lifting 5 kg through 2 m. Start and finish at rest; take gravitational acceleration as 10 metres per second squared.
Ask: What percentage becomes useful work?
Say: Efficiency is 50%.
Used in: Efficiency helps size pump motors.

If your child says…“Multiply output by efficiency for input.”

Ask: Can useful output exceed input?
What’s true: Input equals useful output divided by efficiency, expressed as a fraction.

$(1)(2)+(1)(0)=(1+1)v$

$v=1\,\mathrm{m/s}$

$K_i=\tfrac12(1)(2^2)=2\,\mathrm{J}$

7. Collisions

An isolated pair conserves momentum; sticking changes its kinetic energy.

Show: Write these lines for two 1 kg carts sticking together. Neglect external horizontal impulse. Say: v is their shared velocity.
Ask: How much kinetic energy remains after they stick?
Say: Their final kinetic energy is 1 J. The other 1 J becomes internal energy; total momentum stays unchanged.
Used in: Collision calculations predict whether an incoming cart rebounds or continues forward.

If your child says…“Sticking carts keep all their kinetic energy.”

Ask: If the joined mass doubles but its speed halves, can its kinetic energy stay unchanged?
What’s true: An isolated moving cart sticking to an identical stationary cart leaves half the initial kinetic energy.

A soft ball on a clear wooden floor, seen from the side.

8. Mass leaving a moving system

Departing mass carries momentum away.

Show: Walk steadily, holding the ball at waist height. Release without throwing; keep walking. Your child watches sideways.
Ask: Will the falling ball move forward?
Say: The ball carries forward momentum away.
Used in: Conveyor outlets allow falling material’s forward motion to reach bins.

If your child says…“Leaking trolleys speed up.”

Ask: Does departing sand lose its forward momentum?
What’s true: Without horizontal thrust or external horizontal force, a trolley keeps its speed as sand leaves.

A real problem

Recovered braking energy helps other trains accelerate.

Conventional electric train braking dissipates the train’s kinetic energy as waste.

Regenerative braking generates electricity and returns it to the power supply.

In Delhi, other accelerating trains on the same line use this recovered electricity.

Press Information Bureau Climate Technology Centre & Network The Times of India

A metro train approaching a station beneath overhead electrical wires.

Concept Lab · Common misconception

The tempting mistake in Work, Energy and Power

Open standalone misconception page →

Does effort always mean positive work on an object?

Wrong

The brake force does positive work because it acts on the moving car.

Why it feels right. I associate any applied force with a positive contribution.

Right

Work depends on the component of force along displacement.

Worked example

The 10 N force is opposite the 2 m motion. Their dot product gives negative work.

A 10 N force opposite a 2 m displacement does −20 J of work.
It removes kinetic energy when other work is negligible.

Ask your child eight quick questions.

One per step. The answer and the reason are given.

While a load moves horizontally, what work does a purely upward supporting force do?

Zero work. Perpendicular support does zero work, even though holding the load takes effort.
A push does 100 J; friction does −40 J. All other forces do zero work. What kinetic energy is gained?

60 J. Counting both forces gives 60 J instead of the push’s 100 J.
A force–position graph lies entirely below the axis, and position increases. What sign does the work have?

Negative. Below-axis force opposes displacement, so its area contributes negative work, not positive work.
With relaxed spring energy set to zero, what sign does its energy have when compressed?

Positive. Compression stores energy that the spring can release while returning to its relaxed shape.
At the top, what happens to the string if the mass reaches zero speed?

It goes slack. The string cannot push outward to balance gravity and hold the mass there.
A pump delivers 600 W usefully at 60% efficiency. What input power does it need?

1000 W. Dividing gives 1000 W, while multiplying gives 360 W, less than useful output.
An isolated moving cart sticks to an identical stationary cart. What fraction of their initial kinetic energy remains?

Half. Their combined mass doubles and speed halves, leaving half their initial kinetic energy.
Sand leaves at a moving trolley’s horizontal speed, with no horizontal thrust or external horizontal force. What happens to the momentum magnitude of the trolley plus its remaining sand?

It decreases. The departing sand carries momentum away while the remaining trolley keeps its speed.

15 more questions with answers, 3 with pictures

Teach Work, Energy and Power in eight steps.

Why it matters