C. Energy and Momentum · Work, Energy and Simple Harmonic MotionEnergy Technologies: Analyse, Improve and Assess
C1 C1.2 C2.2 A2.1About 70 minutes
Learning goals- I can analyse the energy transformations in a technology such as regenerative braking, an elevator or pumped storage.
- I can propose a physics-based improvement to an energy technology and describe its trade-offs.
- I can assess the social and environmental impacts of energy technologies.
- I can describe careers that apply energy principles.
Words to know
regenerative braking
Using an electric motor as a generator while slowing down, so that kinetic energy is stored (in a battery) instead of becoming thermal energy in friction brakes.
counterweight
A mass that balances part of an elevator car's weight so the motor does less work.
pumped storage
A hydroelectric system that pumps water uphill when demand is low and lets it flow back through turbines when demand is high.
round-trip efficiency
The fraction of energy put into a storage system that comes back out.
energy return
The fraction of stored elastic energy that a material or device gives back, rather than turning into thermal energy.
Physics with a purpose
Every idea in this unit shows up in machines people rely on: elevators, cars, transit, roller coasters, sports gear, power systems. The curriculum asks you to analyse technologies that use energy principles, propose ways to improve them, and assess their social and environmental impact. In this lesson you will practise a step-by-step method on several real technologies. (Technologies that depend on momentum, such as airbags and helmets, are analysed in the sibling unit Momentum and Collisions.)
A framework for analysing a technology
- Purpose: what problem does it solve?
- Energy transformations: trace the energy from input to useful output. Which forces do work? Where is energy stored (Eg, Ee, Ek)?
- Efficiency: where is energy transformed into thermal energy or sound? Estimate with numbers when you can.
- Improvement: propose a change based on physics (less friction, storing energy that is now wasted, better damping), and say what it would cost or what trade-offs it brings.
- Impact: who benefits and who bears the costs? Consider safety, cost, access, jobs, land, materials, emissions and waste.
Regenerative braking
Ordinary brakes use friction to turn a vehicle's kinetic energy into thermal energy, which is lost to the air. Electric and hybrid cars, and many electric trains and subway cars, can instead run their electric motors as generators when slowing down. The car's kinetic energy is turned into electrical energy and stored in the battery (or, for trains, fed back to the line) to be used again. This is called regenerative braking.
- It is most useful in stop-and-go driving, where a lot of kinetic energy would otherwise be thrown away at every stop.
- It cannot recover all the kinetic energy: the generator, the electronics and the battery all have losses, and friction brakes are still needed for hard stops and very low speeds.
- A side benefit: brake pads wear more slowly, so there is less brake dust.
Worked exampleExample 1: How much energy can regenerative braking save?
A 1500 kg car stops from 50 km/h. Suppose 60% of its kinetic energy is recovered (an assumption for this example; real values depend on the vehicle and the driving). How much energy is recovered per stop? Over 40 such stops a day?
- v = 50 ÷ 3.6 = 13.89 m/s. Ek = ½(1500)(13.89)² = 1.447 × 10⁵ J.
- Recovered per stop: 0.60 × 1.447 × 10⁵ = 8.7 × 10⁴ J (0.024 kWh).
- 40 stops: 40 × 8.68 × 10⁴ = 3.5 × 10⁶ J (about 0.96 kWh).
About 87 kJ per stop and about 1 kWh per day. That would otherwise all become thermal energy in the brakes.
Elevators and counterweights
A traction elevator hangs its car from cables that pass over a pulley to a heavy counterweight. As the car rises, the counterweight descends, so gravity does positive work on the counterweight while it does negative work on the car. The motor only has to supply the difference. Counterweights are commonly sized to balance the empty car plus part of the rated load, so the motor rarely has to lift the full weight. Some modern elevators also use regenerative drives that feed energy back to the building when a heavy car goes down or a light car goes up.
Worked exampleExample 2: The value of a counterweight
An elevator car with passengers has a total mass of 1400 kg. Its counterweight is 1200 kg. How much work must the motor do to raise the car 30 m at constant speed, with and without the counterweight (ignore friction)?
- Without: W = mgΔh = (1400)(9.8)(30) = 4.1 × 10⁵ J.
- With: the counterweight's Eg drops by (1200)(9.8)(30) = 352 800 J while the car's rises by 411 600 J. The motor supplies the difference: 5.9 × 10⁴ J.
With the counterweight, the motor does only about one seventh of the work: 59 kJ instead of 412 kJ. Smaller motors, less electricity and less heat.
Pumped storage: a giant gravitational battery
Electricity must be produced at the moment it is used. Pumped-storage hydroelectric stations store energy as gravitational potential energy: when demand is low (often at night), they pump water uphill into a reservoir; when demand is high, the water flows back down through turbines. Ontario has one at Niagara: the Sir Adam Beck Pump Generating Station pumps water into a reservoir and releases it through its generators when it is needed. Pumped storage loses energy on the way up and on the way down; overall round-trip efficiencies of roughly 70 to 80% are typical. It does not create energy; it shifts it in time.
Impacts to weigh: it can store large amounts of energy, a station can operate for many decades, and it helps balance wind and solar power, but reservoirs flood land, change rivers and fish habitat, and need the consent and involvement of the communities and First Nations whose lands and waters are affected.
Worked exampleExample 3: Energy in a pumped-storage reservoir
Suppose a pump lifts 2.0 × 10⁹ kg of water (2.0 million cubic metres) up 25 m, and the station recovers 75% of the stored energy. How much electrical energy comes back out?
- Eg = mgΔh = (2.0 × 10⁹)(9.8)(25) = 4.9 × 10¹¹ J.
- In kWh: 4.9 × 10¹¹ ÷ 3.6 × 10⁶ = 1.36 × 10⁵ kWh (136 MWh).
- Recovered: 0.75 × 136 MWh = 1.0 × 10² MWh (102 MWh).
About 100 MWh: a few hours of output from a medium-sized station. Large volumes of water are needed because g and Δh are modest.
Energy in sports equipment
Many pieces of sports equipment work by storing and returning elastic potential energy: the bending of a pole vaulter's fibreglass pole, the flex of a composite hockey stick during a slapshot, the compression of a running shoe's midsole, the stretch of a trampoline bed. Designers try to store as much energy as possible and to return as much as possible (less turned into thermal energy). Rules sometimes limit equipment for fairness and safety, which is itself a social decision about technology.
Just for funRegenerative braking is the only time in life when slowing down actually pays you back.
Hands-on activityAnalyse and improve a technology
Choose one technology you can observe: a bicycle, an elevator in a building you visit, a car or bus with regenerative braking, a playground swing or slide, a pair of running shoes, or a garage-door opener (which uses springs to balance the door: never adjust or loosen its springs, which hold dangerous amounts of energy).
- Write the purpose in one sentence.
- Draw an energy-flow (Sankey) sketch from input to useful output, and label where energy becomes thermal energy or sound.
- Estimate one energy or power with numbers (for example, the Ek of your bike at cruising speed, or the Eg of the elevator car per floor).
- Propose one physics-based improvement, and one trade-off it brings (cost, weight, safety, comfort).
- List one social and one environmental impact of the technology.
- Name a career that works on it (see the list below) and write one question you would ask that person.
What to look for: a strong analysis follows the energy step by step, uses numbers where possible, and gives improvements that clearly come from the physics (for example: "store the energy now lost in the brakes" rather than "make it better").
Careers that use these ideas
- Mechanical and automotive engineers design suspensions, brakes, drivetrains and regenerative braking systems.
- Elevator and escalator technicians (a skilled trade with apprenticeship training in Ontario) install and maintain lifts, counterweights and safety brakes.
- Structural engineers design buildings and bridges, including dampers for wind and earthquakes.
- Energy systems engineers plan storage such as pumped hydro and batteries.
- Kinesiologists and biomechanists study energy in human movement and help design sports equipment.
- Amusement ride engineers use energy conservation to design safe roller coasters and launch and braking systems.
Your turn
1An 1800 kg car stops from 20 m/s, and regenerative braking recovers 50% of its kinetic energy. How much energy is recovered?
Ek = ½(1800)(20)² = 3.6 × 10⁵ J. Recovered: 1.8 × 10⁵ J.
2Explain, using energy, why an elevator counterweight reduces the work the motor must do.
As the car rises, the counterweight falls, so its gravitational energy decrease supplies most of the car's gravitational energy increase. The motor supplies only the difference (plus friction).
3Give one environmental benefit and one environmental cost of pumped-storage hydroelectricity.
Benefit: it stores energy so wind and solar power can be used when needed, reducing the need for fossil-fuel peaking plants. Cost: reservoirs flood land and change river and fish habitats.
4Name two careers that apply the energy concepts of this unit.
For example, mechanical (automotive) engineer and elevator technician (others: structural engineer, kinesiologist, ride engineer, energy systems engineer).
5Why can regenerative braking not recover 100% of a car's kinetic energy?
The generator, the electronics and the battery all convert some energy to thermal energy, and friction brakes are still needed for hard or very slow stops.
6A running shoe's midsole stores 7.5 J each step and returns 4.5 J. What is its energy-return efficiency, and where does the rest go?
4.5 ÷ 7.5 = 60%. The other 40% becomes thermal energy in the foam (and a little sound).
More practice: warm-up
1What is regenerative braking?
Using a vehicle's electric motor as a generator to turn kinetic energy into stored electrical energy while slowing down.
2What form of energy does pumped storage use to store energy?
Gravitational potential energy of water.
3In which kind of driving does regenerative braking help most?
Stop-and-go (city) driving.
4What does a counterweight do in an elevator?
It balances much of the car's weight, so the motor does less work.
5Name a piece of sports equipment that stores elastic potential energy.
For example, a pole vaulting pole, a hockey stick, or a trampoline.
More practice: on your own
1A reservoir holds 1.0 × 10⁹ kg of water 30 m above a station's turbines. How much energy is stored, in J and in MWh? How much is recovered at 75% efficiency?
Eg = (1.0 × 10⁹)(9.8)(30) = 2.9 × 10¹¹ J = 2.94 × 10¹¹ ÷ 3.6 × 10⁹ = 82 MWh. Recovered: 61 MWh.
2A hockey stick behaves like a spring with k = 4000 N/m and bends 5.0 cm during a shot. How much energy does it store?
3A running-shoe midsole compresses 1.0 cm under a peak force of 1500 N (assume it acts like an ideal spring). How much energy does it store?
Ee = ½Fx = ½(1500)(0.010) = 7.5 J.
4Propose one physics-based improvement to a city bus system and give one trade-off.
For example: add regenerative braking to buses, recovering kinetic energy at every stop. Trade-off: higher purchase cost and battery weight, and batteries need materials that must be mined and recycled.
5Assess one social impact of elevators with counterweights and regenerative drives.
For example: elevators make buildings accessible to people who use wheelchairs, older adults and parents with strollers; energy-saving drives lower operating costs for building owners and tenants.
Challenge
1A 15 000 kg city bus stops from 15 m/s about 200 times a day. If regenerative braking recovers 50% of its kinetic energy at each stop, how much energy is recovered per day, in MJ and kWh?
Per stop: ½(15 000)(15)² = 1.6875 × 10⁶ J; half is 8.44 × 10⁵ J. Per day: 200 × 8.44 × 10⁵ = 1.7 × 10⁸ J (169 MJ) = 47 kWh.
2Elevator counterweights are often chosen to equal the mass of the empty car plus about half the rated load. Explain why that is a good choice.
Passenger loads vary from empty to full. With this choice the imbalance is never more than about half the rated load in either direction, whether the car is empty or full, so the motor can be smaller and uses less energy on average than if the counterweight matched only the empty car.
3A roller coaster advertisement claims its new magnetic brakes "recover energy so the ride powers itself." Evaluate the claim.
Brakes can recover part of the train's kinetic energy, but every step loses some to thermal energy, and the train's energy came from the lift or launch in the first place. Recovered energy can reduce the electricity needed, but by conservation of energy the ride cannot power itself; it still needs an external energy input every cycle.
Quiz
1. Regenerative braking saves energy by:
2. An elevator car (1000 kg) and its counterweight (900 kg) move 20 m, the car up. Ignoring friction, how much work does the motor do?
3. Pumped-storage hydroelectricity:
4. Which is a physics-based improvement to reduce energy waste in a delivery van that makes many stops?
5. A composite hockey stick helps a shot mainly because it:
6. Which career most directly designs suspensions and regenerative braking systems?
Big idea (C1, C1.2): the energy ideas in this unit explain and improve real technologies: regenerative braking, elevator counterweights, pumped storage and sports equipment. Students analyse the energy flow, propose physics-based improvements and weigh social and environmental impacts.
How to help: pick a technology you use (a bike, the family car, an elevator at work) and ask your teen to explain where the energy comes from and where it goes. Encourage specific, number-based answers. Talk about careers: who in your family or community works with machines or energy?
Common difficulties:
- Vague improvements ("make it better") instead of physics-based ones ("recover the energy now lost in the brakes").
- Forgetting that every conversion step loses some energy.
- Listing impacts without saying who is affected.
- Assuming energy-storage systems create energy rather than shift it in time.