This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

A PDF of the student activity is included.

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Students will:

- estimate the energy change of a system
- calculate the amount of energy converted by different activities
- use rates to determine inputs and/or outputs.

Students should discover that:

- energy transfer is proportional to work (the more force x distance, the more energy)
- different forms of energy are measured in different ways; we can use equivalent rates and units to convert from one form to another.

materials for each station (see teacher support material)

a classmate

station cards and mathematical questions (see copymasters)

FIO, Energy, Levels 3+-4+, Energy Stations, page 1

**Preparation and points to note**

The materials you will need for each station are:

Station 1: none

Station 2: plastic bowl, water, egg beater, thermometer

Station 3: round tin or can with lid, rubber band, toothpicks, tape, washers or lead sinker, instructions (see websites below)

Station 4: metal paper clips

Station 5: a weight or barbell

Station 6: a guitar or other simple stringed instrument, for example, a rubber band stretched around an open cardboard box.

Each station has an experiment and a related mathematics problem (provided on the copymasters). Think about how to set up the stations: for example, the paper clips need to be metal and you may need quite a few of them because some of them will break. Be specific about how you wish the students to record their observations and calculations and how they should present their answers. Decide whether you want more than one of each station and how you will signal the move from one station to the next.

Assemble the roll-back can ahead of time or ask some students to build it. Instructions can be found at the following sites:

www.acgilbert.org/Toys/media/Day08.pdf

www.raft.net/ideas/Rollback%20Can.pdf

www.youtube.com/watch?v=3BfQ-etVywU

Avoid over-explaining the activities – leave the students something to discover. Keep the big question to the fore: “Does **energy*** get used up, or does it just go somewhere else?”

Be clear about how the students should record their observations. It may be best to have them do the calculations when they have completed the entire series of experiments.

Leave time for a closing session. After the students have completed the activities and calculations, they are asked to discuss competing statements about energy and to find out what “**conservation of energy**” means. At the outset, it is likely that some will have the view that energy can be “used up”. By the end, all should be clear that energy cannot be created or destroyed, just changed from one form to another.

These activities require students to interact, share ideas, and work effectively with others, so the key

competency *relating to others* is a suitable focus.

**Points of entry: Mathematics**

See the answers section for comments on the mathematics for each station.

Most of the experiments are *qualitative*. In other words, they don’t lead to numerical data. Encourage the students to think about trends, relationships, and limits. For example, ask *What would happen to the water if you continued to turn the egg beater (at the same speed) for 5 minutes? *(The water would continue to warm up until the heat being added equalled the amount being lost to the environment.) Similarly, *Is there a limit to how far the roll-back can can go and still roll back?* (At some point, the rubber band will snap or the weight will wrap around the band.)

With any activity involving estimation, encourage the students to discuss the difference between guesswork and estimation. Challenge them to think about how they could gather data to answer the experimental questions quantitatively (with numbers).

Unlike the experiments, the mathematics questions associated with the various energy stations are *quantitative* and require numerical answers. The students have to convert from one unit to another (much like energy is converted from one form to another). They also need to apply rates in simple ways. A rate is a specified quantity of one **variable** for every unit of another (for example, $120 dollars per day, 11.3 kilometres per hour, or 33 **joules **per second).

[**Note for teachers**: For the rubbing hands experiment, skin has a coefficient of **friction** of about 0.8. As a rough guide, the distance that fingers move per rub is about 10 cm. You need to press your hands together with a force of 10 **newtons** and rub them about 10 cm (0.1 m) to perform 0.8 J of **work**.]

The problems use very approximate numbers (“1 J is about 1 kg x 10 cm”) and require assumptions to be made (“if the egg beater lifts the water about 8 cm each turn …”). This means that the students’ answers are in fact only estimates of the energy transfer involved. The students need to understand that estimating is a very important mathematical process and that there is a world of difference between estimation and guesswork. A guess can be entirely random, but an estimate is always arrived at via some kind of calculation and always based on some information or data.

At this level, avoid expressing rate problems as strings of fractions and operators. These will only confuse. All rates can be modelled using double number lines (see NDP *Book 7: Using Fractions, Decimals, and Percentages*).

**Points of entry: Science**

The aim of this activity is that students will discover or begin to understand the law of conservation of energy. Give them as few directions as possible, but try to ensure that they focus on the energy changes that are going on at each station.

Each activity and mathematics question involves a different set of energy changes:

- The roll-back can activity illustrates that the
**kinetic energy**of motion can be stored in a spring (the rubber band) and then converted (by the unwinding of the rubber band) back into motion. - The egg beater illustrates how kinetic energy (
**mechanical energy**) can be converted into heat. - The rubbing hands and paper clip activities show how mechanical energy can produce heat (through friction).
- The weightlifting is an example of how we can use the
**chemical energy**of food to do work. It introduces students to the term “**gravitational potential energy**”, which will be explored in more detail in the activities on pages**4–5**and**14–15**. - As the guitar is strummed, the vibrating strings transfer the kinetic energy of the motion of your hand into sound waves that travel through the air.

Different groups will get quantitively different results for the experiments. This is inevitable, given the

relatively uncontrolled conditions. What matters is that each group discovers the qualitative change that takes place as a result of the action.

Each of the stations is designed to prompt extension questions, for example, *What are the variables in this investigation? What data needs to be measured and recorded? Is this a fair and repeatable experiment?* Encourage students who finish early to consider other variables, for example, *Will doubling the size of the egg beater double the rate at which the temperature increases? *(Probably, depending on the outside air temperature and the rate at which heat is being lost from the water)

A broad extension question is *If energy is conserved (not lost), why is there so much talk about an energy crisis?* The issue is that much of our stored energy is converted into wasted heat. For example, some of the energy released by burning petrol in a car’s engine goes into producing mechanical energy, but a lot of it goes out into the atmosphere as hot exhaust fumes. That energy might eventually create wind gusts and be converted into useful energy through a wind turbine, but the work done in digging for oil, refining the petroleum, or transporting the petrol to a pumping station will have been wasted. An understanding of energy changes will give students a better understanding of how energy is wasted (converted into unusable forms) and how they

can go about conserving it.

In the next activity, students will explore the difference between kinetic and potential energy and classify examples of each form.

**Answers**

**1. i.–ii.** Answers for each station are listed below.

**Station 1: Rubbing Hands****Experiment:** When you rub your hands together vigorously, you should notice that your hands warm up. The more you rub, the warmer your hands get and the more tired you get! The motion of your muscles and the friction on your skin produces heat energy. In other words, you’re converting your energy into heat. You eat food to get energy, so by rubbing your hands you’re converting the energy of the food you have eaten into motion, and friction converts motion into heat energy.

**Question:** 1 250 rubs. 1 rub is 0.8 joules (J), so divide 1 000 by 0.8. Another way to think about

it is that 1 rub = 0.8 J, 10 rubs = 8 J, 100 rubs = 80 J, and 1 000 rubs = 800 J, so 1 250 rubs = 1 000 J (the extra 200 J added to 800 J to make 1 000 J is 1/4 [0.25] of 800; 1/4 of 1 000 rubs is 250, so 1 250 rubs = 1 000 J).

**Station 2: Beating WaterExperiment: **Make sure that you leave the thermometer fully immersed in the water long enough to get an accurate reading. You should fi nd that the water in the bowl becomes hotter as the egg beater moves, as long as the egg beater is moving fast enough for long enough. You will probably be unable to sustain the speed of the egg beater for an indefinite amount of time because your muscles will need time to recover; the heat in the water soon transfers to the outside air after the beating has stopped. Energy is required to move the egg beater, and this energy is converted into heat.

**Question:** About 25 000 turns. To fi nd the answer, make a list of equivalent quantities (how much of one thing is equal to another). Heating 1 litre (L) of water by 1°C is equal to the work of 1 kg x 400 m. 5°C is therefore equal to lifting 1 kg x 2 000 m. 1 L of water weighs 1 kg, so you need to lift the water in the bowl about 2 000 m or 200 000 cm (1 m = 100 cm). The egg beater lifts water at a rate of 8 cm per turn. 200 000 ÷ 8 = 25 000 (so 25 000 turns x 8 cm per turn = 200 000 cm).

**Station 3: Rolling a CanExperiment: **The weight causes the rubber band to twist as the can rolls forward. Friction and the resistance of the rubber band eventually cause the can to stop rolling, at which point the rubber band starts to unwind. The stored energy in the rubber band is transferred back into the can, which rolls back towards you.

**Question: **About 90 cm. 2/3 of a full turn makes the can roll 10 cm, so 1/3 of a turn will roll it 5 cm and 1 full turn (3/3) will roll it 3 x 5 = 15 cm. This means 6 full turns will roll it 6 x 15 = 90 cm.

**Station 4: Bending a Paper ClipExperiment:** Metal is a good conductor of heat, so it should feel cool to the touch when you first pick it up (try it against your cheek). (By contrast, wool is not a good conductor and usually feels warm when you put it on.) As you work it back and forth, you should find that the portion of the paper clip that you are bending gets warmer (if it doesn’t, bend it quickly back and forth a bit more). Your muscles add energy into the paper clip. The paper clip releases this energy back into the atmosphere as heat.

**Question:** Answers will vary. The number of joules (J) should be equal to the number of times you bent the clip. If 1 bend requires you to lift 10 kg up 1 cm, you use 1 J every bend because 10 kg x 1 cm is the same as 1 kg x 10 cm.

**Station 5: Lifting a WeightExperiment**: It might not seem that anything happens to the weight of the barbell when you lift it, but you’re actually increasing the gravitational potential energy. When you increase the height of the energy, you work against gravity. Your work is stored in the weight as gravitational potential energy. You can tell this is true because the higher you lift it, the more energetically (harder) it will hit the ground when you drop it. Your arms tire when continually lifting and lowering the weight because it takes energy to move it. The energy stored in your body is converted into kinetic energy as you move your muscles, and this kinetic energy is converted into potential energy in the lifted weight.

**Question:** Answers will vary depending on the weight. For example, if you lift 10 kg by 100 cm,

you do 100 J of work because you’re lifting 10 x 1 kg a distance of 10 x 10 cm or 100 x 1 J.

**Station 6: Playing a GuitarExperiment: **The harder you strum a guitar, the louder the sound it makes. The pitch and tune of the note shouldn’t change, just the volume.

**Question: **The table has a linear pattern, going up by 0.4 J per setting. At the lowest setting, it probably uses 3.0 J.

Volume setting | Low | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Max |

Energy used per hour (J) | 3.0 | 3.4 | 3.8 | 4.2 | 4.6 | 5.0 | 5.4 | 5.8 | 6.2 | 6.6 |

**2. a.** Discussion may vary. However, energy doesn’t get “used” up; rather, it changes from one form to another.

**b. i.** The law of conservation of energy states that energy is neither created nor destroyed, just transferred from one form to another.

**ii. **Answers will vary. You may be surprised that energy is never destroyed because it seems as if energy gets used up in many situations. However, you can usually find out where the energy goes.

For example, when you use the brakes on a bicycle, friction changes the energy of your motion into heat and the brake pads get warm.