04Efficiency and calculations

Ee04TA of the Electricity and Energy topic
• 01 Shifting energy between gravitational and kinetic storesEe04TAnugget01 Activity

Preparing the apparatus

What the activity is for

This demonstration allows you to calculate the energy shifted between kinetic and gravity stores. Several different starting points are easy to arrange, depending on whether the mass starts off up or down, and the trolley starts off moving or stationary. Adapt the possibilities to suit the class and the evolving discussion. You can and should calculate the efficiency of the system.

What to prepare

• 3 retort stands
• 6 bosses and clamps
• 2 glass rods
• 1 single pulley
• some Blu-tack
• 1 sturdy platform (approximately 5 cm by 15 cm)
• a 30 cm ruler
• a 1 m ruler
• 1 high-quality dynamics trolley (low friction – runs a long way from a moderate shove)
• some stiff card (about 13.5 cm by 10 cm) to attach to the top of the trolley
• 1.5 m of 15 lb breaking strain fishing line
• 1 light gate and timer
• 1 10 g mass holder
• 2 10 g and 1 5 g masses to fit holder

Safety note: Take care to anchor the retort stands carefully so that the glass rods are not inadvertently stressed.

What happens during this activity

The photograph shows one way to set up the equipment that works. If you have a low-friction pulley wheel then hook it over the top glass rod and fix it in place using a small amount of Blu-tack. If the pulley wheel is not so good, you may be better off just using the glass rod itself as a pulley. Arrange it so that the 10 g mass holder falls 30 cm. Pull the trolley 80 cm back from the bottom glass rod. Place the light gate 30 cm from the bottom glass rod so that when the trolley passes through it the 10 g mass has landed on the platform, allowing the fishing line to go slack. As you pull the trolley back, look down the length of the equipment to aim the line of sight of the trolley through the light gate – you don't want to miss.

Opening up the discussion

Teacher: Here we have a demonstration where we can calculate energy shifted. There's a small mass of 10 g, which will fall when I release it. This is attached to a dynamics trolley by some fishing line. The trolley has very free-wheeling wheels and the bench is very smooth. Why do you think that's important?

Bill: To minimise the energy wasted by frictional forces on the car wheels.

Teacher: Good, but can anyone suggest a clearer idea than just wasted? Neil?

Neil: Dissipated, Miss…

Teacher: That may be a more helpful description than wasted, but can you tell me a bit about the thinking that lies behind it? Yes, Judy…

Judy: The energy is spread out, Miss.

Teacher: Yes Judy, that's along the right lines. Can you remember where we look for energy?

Sharran: In stores, Miss. It's always stores.

Teacher: Now let's pull our suggestions together. Lower frictional forces result in less energy being shifted to many stores, and more energy being kept in fewer stores. Keep that in mind as we go back to the apparatus. Now, as I let the mass fall like so, you'll see that the trolley will begin to move. Picture the energy being shifted. The gravity store is emptied. Which store is filled?

Jess: The store to do with movement… what is it called?

Teacher: Yes – the kinetic store. Now this system, as you know, can't be 100 percent efficient: not all of the energy is shifted from the gravity store to the kinetic store. We can calculate the energy shifted from the gravity store and the energy shifted to the kinetic store. How can we do this?

Emil: one store of energy is mass (0.01 kilogram)  ×  g (9.8 m s -2)  × height (0.3 m), which is 0.029 J, and the other store of energy is 12  × m (0.25 kg)  ×  v2.

Discussing the experiment

Teacher: Good. Energy is shifted from the gravity store to the kinetic store. But does it all end up there? Yes, Katy?

Katy: No, Miss, some stuff gets warm.

Teacher: Yes. Some energy is shifted to different thermal stores. You can see that the potential energy lost by the mass is easy to find (0.029 joule). The final speed of the trolley once the mass has fallen 30 cm is more difficult to find. The way that we'll do it is by using a light gate. You can see that the trolley has a piece of card (0.135 m long) attached to it. When this card passes through the gate, the time taken to do so is recorded. We can then find the speed of the trolley as speed = distanceduration. So speed = length of the cardtime taken (in seconds). In fact, if we let the mass fall three times and then find the average time of the card through the light gate, this would be a more reliable method, so let's do that.

Now let the mass fall three times and write on the board the potential energy lost by the mass (0.029 J) and the average velocity and average energy in the kinetic store of the trolley.

The time displayed on the light gate will be in millisecond and you should be sure that the students know how to convert milliseconds into seconds (divide by 1000). For the relationship to work the time must be in seconds.

Teacher: Now we will use these to find the efficiency of this system. efficiency = average energy gained by the trolleyenergy lost by the falling mass × 100 %.

(The efficiency from trial data was around 60 percent.)

There is at least one other possibility worth exploring – the energy starts in the kinetic store, is shifted to the gravitational store and then returned to the kinetic store. You'll need to adjust the set-up to make the measurements, but it is worth exploring several possibilities as energy is shifted to and fro between the stores.

Getting a feel for efficiencies

What the activity is for

Here you can impart an idea of the relative values of different efficiencies. Having such an idea for different devices and processes allows the term efficiency to acquire meaning, and enables the values derived from calculations to be checked against an internal model of what is reasonable. The ladders are one-dimensional graphs, used often in the SPT14–16 topics to support quantification, putting any physical quantity into context.

What to prepare

• appropriate scale prints of the support sheets provided
• prepared values and items to place in order, if these are to be used.
• some Blu-tack

Support sheet

What happens during this activity

The support sheet provides two grids: one with electrical devices to provide some context and one blank. You can use them in a number of ways.

You could provide a blank ladder, of a large scale, on the laboratory wall, and add values to it over the duration of the topic as you encounter these values. It may be helpful to have a number of ladders, one for each class of device: maybe for those switching from the electrical pathway or those switching to the mechanical working pathway, for example. An alternative is to maintain a column for each class of device, as done in the Physics Narrative.

You could provide a completed ladder, adding your own values to it as these come up in the conversations in the class. These could be stimulated by distributing a range of research questions to groups within the class to populate the values.

You could provide a blank ladder to a group, together with a selection of objects and processes, and ask them to agree on how to place these items. Groups might then usefully compare their placements before being given the matching values, and so reordering their values. Or you might provide the unmatched values and objects/processes, only then placing them on the ladder afterwards.

Placing about five items on such a ladder produces a manageable demand.

• 03 Calculate the efficiency of a motor in two waysEe04TAnugget03 Activity

Practical measurements and calculations as exemplars to learn from

What the activity is for

In this activity a motor is used to lift a load. The efficiency of the motor is calculated in two ways:

• Considering the energy shifted from the chemical store to the gravity store once the load has been lifted.
• Considering the power in the electrical and mechanical pathways as the load is lifted.

What to prepare

• a 12 V power pack
• a small motor with pulley/axle attachment
• 2 G clamps
• a 1 m rule
• some Blu-tack
• a 100 g mass holder
• 3 100 g masses
• an SEP energy meter
• 1 m of light, strong, thin string

Safety note: Both the falling masses and the strained string line present possible hazards.

What happens during this activity

This account includes sample values to give an indication of the kind of values expected. Your own values may differ and should be used.

Calculating using stores and energy

Set up the equipment to lift a mass of 400 g through a distance of 80.0 cm. Blu-tack a 1 metre ruler close to the load to show distance moved clearly. Have the SEP energy meter set to read energy and the power pack set at 5 volt DC.

Teacher: So, we're using a motor to lift a load from the floor. We have an energy meter, which is connected directly to the power supply to let us know how much energy is being shifted from the store. The kind of store depends on our local power station. Here we burn gas, so it'll be a chemical store.

Switch on the power supply and the energy meter simultaneously. Allow the load to move through a distance of 80 cm and then switch the supply and energy meter off simultaneously. (Use a student to help because three hands are needed and the mass will start to fall back down immediately.)

Teacher: How much energy is shifted to the motor?

Lola: 21.7 joule.

It's probably worth writing this on the board:

Energy shifted from the chemical store is 21.7 joule

Teacher: Excellent, and you used the correct unit too. The gravity store is filling as the load is lifted. How could we calculate how much energy is shifted to the store?

Bill: Gravity force × vertical distance moved.

Teacher: Good. Now we can calculate the energy shifted as the load is lifted further from the earth.

We'd suggest writing this on the board (don't forget the units to make it more intelligible):

energy shifted = 0.4 kilogram  × 9.8 N kg -1 × 0.8 m

energy is 3.14 J

Teacher: We know that energy is neither created nor destroyed, so why is this change not the same as that shifted from the store?

Julie: Energy must have been shifted to other stores: stores that are not useful.

Explain that there is also energy being shifted to thermal stores. Now calculate the efficiency of the motor on the board using the equation.

A clear written-out calculation can serve as a good model, perhaps written on a board.

efficiency = useful energy shiftedtotal energy input to the system × 100 %. Put the numbers in to get 3.14 joule21.7 joule  × 100 percent, which can be worked out to be an efficiency of 14.5 percent.

Calculating using power in pathways

Change the SEP energy meter to read average power. The average power in the electrical pathway can be read directly from the meter. The motor switches this power more or less effectively to mechanical working. The power in the mechanical pathway can be found from force  × velocity.

If all of the power in the electrical working pathway is switched to mechanical working, then the efficiency is 100 percent. So efficiency can also be calculated using power values. After this preamble we suggest you get a new set of measurements to get these data.

Teacher: What do we need to know if we want to find the average power in the mechanical working pathway as the load is lifted?

David: The force required to lift the load and the speed of the load.

Lift the load as before, recording the average power shifted to the motor as read from the SEP meter and the time taken to lift the load.

Here are some sample values, showing the line of argument you might follow.

The average input power to the motor is 4.34 watt

The power needed to lift the load(the output power) is 0.4 kilogram  × 9.8 N kg -1  × 0.8 metre5second which is 3.92 N  × 0.16 m s -1, and therefore the output power is 0.63 W.

Now for some efficiencies:

efficiency = power in mechanical pathwaypower in electrical pathway × 100 %

Putting the values in, you get: 0.63 watt4.34 watt  × 100, which evaluates to give an efficiency of 14.5 percent

This activity has been written containing only one lifting of the load for the energy and power calculations for ease of explanation. It could be run several times and average values used to calculate the efficiencies.

Some possibilities to extend the experiment:

• Change the load size to see if this affects the efficiency of the motor.
• Change the distances moved by the load to see if this affects the efficiency of the motor.
• 04 Internal resistance of fruit and vegetable cellsEe04TAnugget04 Activity

Real cells with real resistance

What the activity is for

This activity introduces the internal resistance of a cell. You can easily point out the distance that the charged particles have to move through the cell, and even vary this distance, thereby altering the internal resistance in a natural way. You can also show that this internal resistance reduces the power provided by the cell because the potential difference falls as soon as there is current in the cell.

What to prepare

• chosen fruit or vegetable (e.g. cucumber, citrus fruits, kiwi fruit, pineapple, potato) – cut a thin strip off the fruit to form a stable base, or use Bluâ€“tack to stabilise it.)
• 5 copper sheet electrodes (3 cm by 3 cm)
• 5 zinc sheet electrodes (3 cm by 3 cm) (A good cell requires electrodes of large surface area, and of close separation. Alter the size of the electrodes to suit your fruit.)
• 10 crocodile clips
• a multimeter (2000 milliVolt full scale deflection is likely to be best.)
• 4 long 4 mm leads
• several short 4 mm leads
• 1 LED (alternatives 1 of variable resistor, 1 of LED clock designed to run off fruit batteries)

Safety note: Wear eye protection when piercing citrus fruit as fruit acid can irritate the eye. Do not eat any of the fruit at the end of the activity.

Note: an LED is a polarised component so must be connected the right way around in a circuit. The leg next to the flat section of the plastic body of the LED must be connected to the negative side of a cell. This leg is sometimes shorter than the other. Applying too much force where the legs meet the plastic casing will cause the legs to break off. Avoid this by bending the legs outwards, away from one another at the centre of each leg.

Energy dissipated in the cell

What happens during this activity

Take the chosen fruit or vegetable and embed one zinc and one copper electrode into it so that they're approximately 0.5 cm apart and pushed in approximately 2 cm deep. They shouldn't be touching inside the fruit. Repeat this process along the length of the fruit so that you have up to five cells, each separated by a few centimetres (the metals should alternate along the fruit).

Attach each cell in series to the next using crocodile clips and leads. (The two electrodes comprising each cell should not be connected by a lead.) The crocodile clips should not be touching one another.

Now get the multimeter and set it to read millivolt (on the 2000 milliVolt scale). Attach the positive lead to the outermost copper and the negative lead to the outermost zinc. You should say that this is a simple battery of cells. It has electrodes of different metals in acid (here we have fruit acids). Show the class that there is a potential difference (voltage reading) between the two outermost electrodes. Write this battery potential on the board (e.g. 1000 milliVolt).

Remove the multimeter and connect the two outermost leads to the LED. Make sure that the positive terminal of the LED is connected to the copper.

Does it light? (Yes.)

Now, with the LED in place, measure the potential difference across the LED. Write it on the board (e.g. 800 milliVolt).

You should emphasise that the readings are different and ask, Why is the potential difference measured across the battery different from that measured across the LED? That's not what the simple circuit theory we've studied so far predicts. Something new is going on.

Now say that to answer this question we must think carefully about potential difference and electric current. Ask, How can we picture an electric current? (A flow of charged particles.. Very good!) Explain that, if the potential difference measured across the cell was 1000 mV (or 1 V) then each coulomb of charge would be able to shift 1 J of energy.

Explain that if the potential difference measured across the LED is only 800 milliVolt (or 0.8 V) then this means that each coulomb of charge is shifting 0.8 J of energy when flowing through the LED. Where is the other 0.2 J of energy being shifted to if not to the LED?

The answer is that energy is also being dissipated by the cell itself. Between the two electrode plates there is some fruit matter. This also contains charged particles, which are flowing between the two electrodes (hydrogen ions (H+) from the fruit acid flow towards the negative electrode). The missing 0.2 joule of energy per coulomb is being shifted by charged particles as they flow through the matter of the cell. The cell has its own resistance to the flow of charged particles. We call this an internal resistance.

The cell will rise in temperature due to this energy shifting. Remind students that they may have noticed batteries that they use at home also get hot. Here the current is not very large, so if we stick a thermometer into the fruit we'll be disappointed.

For the next part we suggest a long fruit (e.g. cucumber), and just a cell, with two terminals only. The LED will not glow, but what's happening is otherwise much clearer.

Now look at the effect of increasing the amount of matter between the electrodes. Ask, What do you think will happen to the internal resistance of each cell? (It will increase as there is more matter for the charged particles to flow through.) Ask, Do you think the charge flowing in the battery will shift more or less energy as it flows through more matter? (More.) Ask: So will there be more or less energy shifted to the LED? (Less.) Ask, So will the LED be brighter or dimmer? (Dimmer.)

Move the electrodes so that each pair is about 1 cm apart. Measure the potential difference. Repeat with the electrodes about 5 cm apart to get the same potential difference. That's not surprising because there is no current, so no energy is shifted inside the cell. Now add the LED. Measure the potential differences again. Note that both drop, but the reading corresponding to the largest separation of plates drops most because the internal resistance is highest.

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