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D. Energy and Society · Work, Energy and Power

Work, Energy and Power: Unit Review

A1.1 A1.4 A1.5 A1.6 A1.8 A1.10 A1.12 A1.13 A2.1 A2.2 D1.1 D1.2 D2.1 D2.2 D2.3 D2.4 D2.5 D2.6 D2.7 D2.8 D3.1 D3.2 D3.3 D3.4 D3.5About 40 minutes
Learning goals
  • I can describe energy forms and transformations and apply the law of conservation of energy.
  • I can calculate work, kinetic energy, gravitational potential energy, thermal energy from friction, power and efficiency.
  • I can plan investigations of energy conservation and power, and analyse their errors.
  • I can compare methods of generating electrical energy and use E = mc².

Words to know

work
Energy transferred by a force acting along a displacement: W = FΔd.
kinetic energy
Energy of motion: Ek = ½mv².
gravitational potential energy
Energy due to height above a reference level: Eg = mgh.
power
Rate of energy transfer: P = ΔE ÷ Δt, in watts.
efficiency
Useful output ÷ total input × 100%.
mass–energy equivalence
E = mc²: mass is a form of energy.

Let's review!

In this unit you learned to track energy. You named its forms and followed its transformations. You defined work as energy transferred by a force along a displacement, and used it to derive kinetic energy and the work–energy theorem. You stored energy as gravitational potential energy and used conservation of energy, first without friction and then with thermal energy included, and tested it with your own investigation. You measured power, including your own, calculated efficiency, compared the ways we generate electrical energy, and finished with E = mc².

This review has questions from every lesson. Try each one, then press Show answer to check.

How to use this review

Do two or three sections at a time. For every problem, write the given values with units, the formula, the substitution and the answer with units and sensible significant digits. Draw a sketch or free-body diagram whenever forces or heights are involved, and mark your reference level. Use g = 9.8 N/kg. For each question you miss, write down why (wrong formula? units? sign? forgot friction?) and go back to that lesson's worked examples. Finish with the 10-question quiz.

WorkW = FΔdenergy transferKinetic energyEk = ½mv²W_net = ΔEkPotential energyEg = mghΔEg = mgΔhConservationEk₁ + Eg₁ + W= Ek₂ + Eg₂ + E_thPower and efficiencyP = ΔE ÷ Δteff = useful ÷ inputMass–energyE = mc²mass is energy too
How the unit fits together. Work transfers energy into kinetic and potential energy; conservation ties them together; power and efficiency describe how fast and how well energy is transferred; E = mc² shows that mass is energy too.
1 J = 1 N·m= 1 kg·m²/s²1 W = 1 J/spower unit1 kWh = 3.6 × 10⁶ Jenergy unit1 hp ≈ 746 Wpower unitg = 9.8 N/kgc = 3.00 × 10⁸ m/s
Units and constants to know by heart for this unit.

Forms of Energy and Energy Transformations

1

Write an energy flow chain for a gas-powered snowblower.

2

Is a solar panel charging a battery an energy transfer or transformation?

3

A motor takes in 900 J. It gives out 650 J of kinetic energy and 50 J of sound. How much thermal energy does it produce?

Work: When Is Work Done?

1

A 40 N horizontal pull moves a sled 25 m. Find the work done by the pull.

2

Does a person do work on a backpack while standing still with it? Explain.

3

Friction of 12 N acts on a box that slides 3.0 m. Find the work done by friction.

Solving Work Problems: Gravity, Friction, Net Work and Graphs

1

A 20 kg box is pulled 6.0 m across a floor by a 100 N horizontal force; μ_k = 0.25. Find the net work.

2

A force–displacement graph is a triangle rising from 0 N to 30 N over 4.0 m. Find the work.

3

How much work is done lifting a 15 kg bag 0.80 m at constant velocity?

Kinetic Energy and the Work–Energy Theorem

1

Find the Ek of a 0.43 kg soccer ball at 20 m/s.

2

A car's speed increases from 50 km/h to 100 km/h. By what factor does its Ek change?

3

A 1000 kg car slows from 15 m/s to 5.0 m/s. Find the net work done on it.

4

A 3.0 kg cart starts at rest; 54 J of net work is done on it. Final speed?

Gravitational Potential Energy

1

Find the Eg of a 0.60 kg ball 4.0 m above the ground.

2

A 70 kg hiker descends 120 m. Find ΔEg.

3

Why is ΔEg the same whether you take the stairs or a ramp?

Conservation of Mechanical Energy

1

A ball is dropped from 12 m. Ignoring air resistance, find its speed just before landing.

2

A coaster car moves at 5.0 m/s at the top of a 30 m hill. Ignoring friction, find its speed at ground level.

3

A pendulum bob moves at 1.4 m/s at the bottom. How high will it swing?

Conservation of Energy with Friction: Work, Heat and Thermal Energy

1

A 50 kg skier starts from rest at the top of a 10 m slope and reaches the bottom at 12 m/s. How much thermal energy was produced?

2

If that slope is 40 m long, what was the average friction force?

3

Distinguish heat from thermal energy.

Just for fun

Review riddle: what has energy, does work, has power, but is never 100% efficient?

A student studying for a physics test. (Some energy always goes into snacks.)

Investigation: Testing Conservation of Energy on a Ramp and a Pendulum

1

A 0.050 kg cart is released from 0.30 m and measured at 2.2 m/s at the bottom. What percentage of ΔEg became Ek?

2

Is the shortfall a random or systematic error? Name a likely cause.

3

Name the independent and dependent variables in that investigation.

Power: How Fast Energy Is Transferred

1

A motor lifts 200 kg up 15 m in 30 s. Find its useful power.

2

A 1.5 kW heater runs for 4.0 h. Find the energy in kWh and in J.

3

A boat's engine provides 3000 N at a steady 5.0 m/s. Find its power.

Investigation: How Powerful Are You?

1

A 55 kg student climbs 18 risers of 0.17 m in 4.5 s. Find her power.

2

Give two reasons the measured power underestimates her body's actual energy use.

3

How could you reduce timing error?

Efficiency and Thermal Energy

1

A winch uses 2500 J to lift a 60 kg load 3.0 m. Find its efficiency.

2

Find the overall efficiency of stages that are 40%, 95% and 85% efficient.

3

Explain the relationship between efficiency and thermal energy transfer.

Generating Electrical Energy: Comparing Input, Output and Efficiency

1

Each second, 5.0 × 10⁴ kg of water falls 60 m through an 88% efficient station. Find the electrical output.

2

A gas station takes in 1000 MW of fuel energy and delivers 550 MW. What type of station is it most likely, and why?

3

Give one environmental advantage of raising the efficiency of a natural gas station.

Mass–Energy Equivalence: E = mc²

1

Find the energy equivalent of 3.0 g.

2

A reaction releases 1.8 × 10⁻¹² J. What mass was converted?

3

Why does conservation of mass work so well in chemistry?

Check your understanding

Quiz

1.

A 30 N force moves a box 5.0 m along the line of the force. The work done is:

2.

If an object's speed triples, its kinetic energy becomes:

3.

A 2.0 kg book is lifted 1.5 m. Its increase in Eg is about:

4.

A ball is dropped from 20 m (no air resistance). Just before landing its speed is about:

5.

A sled loses 600 J of mechanical energy sliding 20 m on a flat field. The average friction force is:

6.

In a ramp investigation, Ek at the bottom is always 10% less than ΔEg. This is best described as:

7.

A 70 kg student climbs 3.0 m in 3.5 s. Her power is about:

8.

A device is 80% efficient and takes in 500 J. Its useful output is:

9.

Which method of generating electrical energy is typically the most efficient?

10.

The energy equivalent of 1.0 kg of mass is:

For parents and teachers

How to use the results:

  • Mixing up transfer and transformation, or saying energy is "used up" → revisit Forms of Energy and Energy Transformations.
  • Work answers with wrong signs or that use mass instead of weight → revisit Work: When Is Work Done? and Solving Work Problems.
  • Forgetting to square v, or errors with W_net = ΔEk → revisit Kinetic Energy and the Work–Energy Theorem.
  • Reference-level mistakes or using ramp length for height → revisit Gravitational Potential Energy.
  • Wrong speeds or heights in coaster, pendulum or falling problems → revisit Conservation of Mechanical Energy.
  • Ignoring friction, or putting E_th on the wrong side → revisit Conservation of Energy with Friction.
  • Trouble with variables, percent difference or types of error → revisit the two Investigation lessons.
  • Confusing kW and kWh, or time-unit errors → revisit Power.
  • Efficiency above 100%, or adding efficiencies in a chain → revisit Efficiency and Thermal Energy.
  • Not knowing input forms or typical efficiencies of stations → revisit Generating Electrical Energy.
  • Scientific notation or gram/kilogram errors with E = mc² → revisit Mass–Energy Equivalence.

Thermal energy calculations (Q = mcΔT, latent heat), fission, fusion and radioactivity are in the Thermal and Nuclear Energy unit.