# Extension Is Proportional To Load Biology Essay

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The aim of my investigation is to find out if the amount of weight applied to an elastic band or steel spring is proportional to the amount the object's length increases by when the weight is applied.

I predict that the more load is applied to the spring and elastic band, the further down the spring and elastic band will stretch. This is because Hooke's Law states that extension is proportional to load. I also predict that as the load doubles the extension will double. So if the load triples the extension will also triple.

The spring and elastic band will go back to its original length when the force is removed so long as we don't exceed the elastic limit.

The elastic limit is where the graph departs from a straight line. Going past the elastic limit of a spring and elastic band, they won't go back to their original length. When the force is removed the spring and elastic band will have a permanent extension.

Below the elastic limit, the spring and the elastic band are showing "elastic behaviour": the extension is proportional to the force, and it'll go back to its original length when the force is removed.Beyond the elastic limit, the spring and elastic band shows "plastic behaviour" this means that when force is applied to the spring and the elastic band to extend it, it stays extended when the force is removed

http://www.racemath.info/graphics/graphs/hookes_law.gif

http://www.racemath.info/graphics/graphs/hookes_law.gif

How does a rubber band stretch?

How does a spring expand?

## Variables:

Spring - results will change if different springs are used

Elastic Band - results will change if a different elastic band is used because its elastic strength might be different. Use the same elastic band and draw a 5cm line on the elastic band to measure the extension accurately.

Number of coils on the spring

Tensile strength of the elastic material

Accuracy of equipment's

Extension of the spring and elastic band is a variable because the extension varies when a load is applied to it.

Different elastic materials have different elasticity

Rubber band will shrink if the temperature increases which means that you won't get the correct results if the temperature keeps increasing.

Spring will expand if the temperature increases which also means that the results you get will vary.

Weight of the mass attached- controlled by using only one mass. Use 100gweights.

Ruler - distance between lines can change if you use different ruler. Use a 1 meter ruler

Person calculating measurements - using different people can change the results recorded because the other person might not be using the same methods to calculate the measurements.

## Safety:

Keep your feet clear so that if the spring/rubber band breaks you aren't injured by the falling masses.apparatus diagram

Weight the clamp with books so that it doesn't tilt over.

Don't add too many masses on the spring as it could deform it.

Wear goggles to ensure that the spring from the clamp doesn't flick up and strike your eye after it has reached its elastic limit.

All stools have to be tucked in under the desk and coats and bags need to be hung up neatly at the side of the classroom away from any investigations.

http://www.batesville.k12.in.us/physics/phynet/mechanics/Newton3/Labs/SpringScale.html

## Equipment/Apparatus:

1 metre ruler

Stand

Medium sized elastic band Width- 0.4cm

Masses - 10 100g masses

Clamp

Medium sized Steel Coil Extension Spring - 2cm

Table

Books (to keep stand still)

## Method:

Assemble the apparatus as shown in the diagram at right. Weight the clamp with books so that it doesn't tilt over.

Measure length of spring and draw a 5cm (optional) line on the elastic band.

Create a data table to help you record the mass you hang from the spring and elastic band as well as the position the spring or elastic band stretches up to.

Record the mass the position of the spring/ rubber band before hanging the mass onto the spring/rubber band. At the end of each experiment record the new position of the spring.

## Experiment 1:

Put the spring or elastic band on the clamp.

Add 100g at the bottom of the spring or elastic band

Calculate how far the spring or elastic band has stretched with a 1 meter ruler without removing the mass (es).

Note: If you're using an elastic band don't remove the weights after 1000g. Keep the mass(es) on, calculating the extension length as you take the mass(es) off one by one.

## Experiment 2:

Repeat experiment 1 changing the following:

Add another 100g mass making 200g

## Experiment 3:

Repeat experiment 1 changing the following:

Add another 100g mass making 300g

## Experiment 4:

Repeat experiment 1 changing the following:

Add another 100g mass making 400g

## Experiments 5:

Repeat experiment 1 changing the following:

Add another 100g mass making 500g

## Experiment 6:

Repeat experiment 1 changing the following:

Add another 100g mass making 600g

## Experiment 7:

Repeat experiment 1 changing the following:

Add another 100g mass making 700g

## Experiment 8:

Repeat experiment 1 changing the following:

Add another 100g mass making 800g

## Experiment 9:

Repeat experiment 1 changing the following:

Add another 100g mass making 900g

## Experiment 10:

Repeat experiment 1 changing the following:

Add another 100g mass making 1000g

## REPEAT EXPERIMENT 3 TIMES.

Repeat experiment all over again with either a rubber band or spring depending on which you used for the first experiment.

To work out the extension use this calculation:

## New length - Original length = Extension

From these results I now know the method I am going to use in my investigation. I am not going to make any changes or alter the method I used for my trial runs because I think it's the best method to use to find out if the extension of the rubber band and spring is proportional to its load. I know my method is suitable because the results I got for my trial run follows my prediction. The range I tested was very good as there was a difference of only 100g between all 10 100g masses.

Trial Run

## Spring

Original Length

(cm)

Mass

(g)

New length - Original length (cm)

Extension

(cm)

2.10

100

5.20 - 2.10

3.10

200

9.40 - 2.10

7.30

300

13.00 - 2.10

10.90

400

17.20 - 2.10

15.10

500

20.80 - 2.10

18.70

600

25.00 - 2.10

22.90

700

28.70 - 2.10

26.60

800

33.10 - 2.10

31.00

900

34.10 - 2.10

32.00

1000

40.00 - 2.10

37.90

When 500g of weight was added to the spring it extended by 18.70 cm. If you double 18.70 cm you will get 37.40 this is very close to the extension for when 1000 g of weight was added to the spring, the extension was 37.90 cm.

When 300 g of weight was added to the spring, the spring extended by 10.90 cm. If you treble this result you will get 32.70 cm this is very close to the extension 32.00 cm for when 900g of weight is added to the spring.

Original Length (cm)

Try

Mass

(g)

New Length (cm)

New length - Original length = Extension (cm)

Total Extension (cm)

Average Extension (cm)

5.00

1

100

5.30

5.30 - 5.00 = 0.30

0.60

/2 = 0.30

2

5.30

5.30 - 5.00 = 0.30

1

200

5.40

5.40 - 5.00 = 0.40

0.80

/2 = 0.40

2

5.40

5.40 - 5.00 = 0.40

1

300

5.50

5.50 - 5.00 = 0.50

1.00

/2 = 0.50

2

5.50

5.50 - 5.00 = 0.50

1

400

5.90

5.90 - 5.00 = 0.90

1.90

/2 = 0.95

2

6.00

6.00 - 5.00 = 1.00

1

500

6.40

6.40 - 5.00 = 1.40

3.10

/2 = 1.55

2

6.70

6.70 - 5.00 = 1.70

1

600

7.00

7.00 - 5.00 = 2.00

4.40

/2 = 2.20

2

7.40

7.40 - 5.00 = 2.40

1

700

7.60

7.60 - 5.00 = 2.60

5.60

/2 = 2.80

2

8.00

8.00 - 5.00 = 3.00

1

800

8.50

8.50 - 5.00 = 3.50

7.30

/2 = 3.65

2

8.80

8.80 - 5.00 = 3.80

1

900

9.00

9.00 - 5.00 = 4.00

8.50

/2 = 4.25

2

9.50

9.50 - 5.00 = 4.50

1

1000

10.40

10.40 - 5.00 = 5.40

10.80

/2 = 5.40

2

10.40

10.40 - 5.00 = 5.40

When 100 g of weight was added to the elastic band the average extension was 0.30 cm. If you double this result you'll get 0.60 cm. When the result is trebled you'll get 0.90 cm. 200 g of weight has an average result of 0.40 cm. 300 g of weight has an average extension of 0.50 cm. Compared to the results for the spring the Hooke's law works with springs more than elastic bands.

Comps

Elastic Band

## Table of Results - Spring (original length = 2.10cm)

Experiment

Try

Original Length

(cm)

Mass

(g)

New length - Original length

(cm)

Extension

(cm)

Total Extension

(cm)

Average Extension

(cm)

1

2

3

4

5

6

7

8

9

10

## =36.20

Experiment

Mass (g)

TRY 1: New length-original length = Extension (cm)

TRY 2: New length-original length = Extension (cm)

TRY 3: New length-original length = Extension (cm)

Total Extension (cm)

Average Extension (cm)

1

100

5.10-5.00=0.10

5.10-5.00=0.10

5.15-5.00=0.15

0.10+0.10+0.15 = 0.35

/3 = 0.12

2

200

5.25-5.00=0.25

5.25-5.00=0.25

5.35-5.00=0.35

0.25+0.25+0.35 = 0.85

/3 = 0.28

3

300

5.55-5.00=0.55

5.40-5.00=0.40

5.60-5.00=0.60

0.55+0.60 = 1.15

/2 = 0.58

4

400

5.75-5.00=0.75

5.70-5.00=0.70

5.90-5.00=0.90

0.75+0.70= 1.45

/2 = 0.73

5

500

6.00-5.00=1.00

6.10-5.00=1.10

6.20-5.00=1.20

1.00+1.10+1.20 = 3.30

/3 = 1.10

6

600

6.30-5.00=1.30

6.55-5.00=1.55

6.40-5.00=1.40

1.30+1.40 = 2.70

/2 = 1.35

7

700

6.60-5.00=1.60

6.90-5.00=1.90

7.00-5.00=2.00

1.90+2.00 = 3.90

/2 = 1.95

8

800

7.05-5.00=2.05

7.40-5.00=2.40

7.40-5.00=2.40

2.40+2.40 = 4.80

/2 = 2.40

9

900

7.45-5.00=2.45

7.60-5.00=2.60

7.55-5.00=2.55

2.45+2.60+2.55 = 7.60

/3 = 2.53

10

1000

8.00-5.00=3.00

8.10-5.00=3.10

8.20-5.00=3.20

3.00+3.10+3.20 = 9.30

/3 = 3.10

## Table of Results - Elastic Band (original length = 5.00cm)

Experiment

Mass (g)

TRY 1: New length-original length = Extension (cm)

TRY 2: New length-original length = Extension (cm)

TRY 3: New length-original length = Extension (cm)

Total Extension (cm)

Average Extension (cm)

1

100

5.25-5.00=0.25

5.20-5.00=0.20

5.05-5.00=0.05

0.25+0.20 = 0.45

/2 = 0.15

2

200

5.45-5.00=0.45

5.40-5.00=0.40

5.30-5.00=0.30

0.45+0.40+0.30 = 1.15

/3 = 0.38

3

300

5.65-5.00=0.65

5.50-5.00=0.50

5.60-5.00=0.60

0.65+0.50+0.60 = 1.75

/3 = 0.58

4

400

5.95-5.00=0.95

5.80-5.00=0.80

5.90-5.00=0.90

0.95+0.80+0.90 = 2.65

/3 = 0.88

5

500

6.25-5.00=1.25

6.25-5.00=1.25

6.25-5.00=1.25

1.25+1.25+1.25 = 3.75

/3 = 1.25

6

600

6.55-5.00=1.55

6.60-5.00=1.60

6.70-5.00=1.70

1.55+1.60+1.70 = 4.85

/3 = 1.62

7

700

6.95-5.00=1.95

7.00-5.00=2.00

6.90-5.00=1.90

1.95+2.00+1.90 = 5.85

/3 = 1.95

8

800

7.75-5.00=2.75

7.40-5.00=2.40

7.50-5.00=2.50

2.40+2.50 = 4.90

/2 = 2.45

9

900

7.85-5.00=2.85

7.70-5.00=2.70

7.85-5.00=2.85

2.85+2.85 = 5.70

/2 = 2.85

10

1000

8.05-5.00=3.05

8.10-5.00=3.10

8.20-5.00=3.20

3.05+3.10+3.20 = 9.35

/3 = 3.12

The adding load table for the elastic band shows that as the load increases the average extension also increases. The total extension would have shown that as the load increases the extension also increases but because there's an outlier in try 3 when 800g is added to the elastic band, the total extension for experiment 8 decreased giving 4.90cm as the total extension. The table reveals that as the load doubles the average extension also doubles, this is evident in the table because when 100g is added to the elastic band the average extension is 0.12cm. When doubled the sum is 0.24cm by looking at the table you will notice that when 200g is added to the elastic band the average extension is 0.28cm. The result for when 0.12cm is doubled and 0.28cm are not far from each other.

The removing load table for the elastic band also shows that as the load increases the total and average extension also increases. The table also shows that as the load doubles the average extension doubles. This is because when 100g was removed from the average extension was 0.15cm when this result is doubled it gives a sum of 0.30. On the table it shows that when 200g of load is removed from the spring the average extension is 0.38cm this is not far from the result I got from doubling 0.15cm.

Elastic Band Results (all results)

Experiment

Mass (g)

TRY 1: New length-original length = Extension (cm)

TRY 2: New length-original length = Extension (cm)

TRY 3: New length-original length = Extension (cm)

Total Extension (cm)

Average Extension (cm)

1

100

5.10-5.00=0.10

5.10-5.00=0.10

5.15-5.00=0.15

0.10+0.10+0.15+0.25+0.20+0.05=0.85

/6=0.14

5.25-5.00=0.25

5.20-5.00=0.20

5.05-5.00=0.05

2

200

5.25-5.00=0.25

5.25-5.00=0.25

5.35-5.00=0.35

0.25+0.25+0.35+0.45+0.40+0.30=2.00

/6=0.33

5.45-5.00=0.45

5.40-5.00=0.40

5.30-5.00=0.30

3

300

5.55-5.00=0.55

5.40-5.00=0.40

5.60-5.00=0.60

0.55+0.40+0.60+0.65+0.50+0.60=3.30

/6=0.55

5.65-5.00=0.65

5.50-5.00=0.50

5.60-5.00=0.60

4

400

5.75-5.00=0.75

5.70-5.00=0.70

5.90-5.00=0.90

0.75+0.70+0.90+0.95+0.90+0.90=5.00

/6=0.83

5.95-5.00=0.95

5.80-5.00=0.80

5.90-5.00=0.90

5

500

6.00-5.00=1.00

6.10-5.00=1.10

6.20-5.00=1.20

1.00+1.10+1.20+1.25+1.25+1.25=7.05

/6= 1.18

6.25-5.00=1.25

6.25-5.00=1.25

6.25-5.00=1.25

6

600

6.30-5.00=1.30

6.55-5.00=1.55

6.40-5.00=1.40

1.30+1.55+1.40+1.55+1.60+1.70=9.10

/6=1.52

6.55-5.00=1.55

6.60-5.00=1.60

6.70-5.00=1.70

7

700

6.60-5.00=1.60

6.90-5.00=1.90

7.00-5.00=2.00

1.60+1.90+2.00+1.90+2.00+1.90=11.35

/6=1.89

6.95-5.00=1.95

7.00-5.00=2.00

6.90-5.00=1.90

8

800

7.05-5.00=2.05

7.40-5.00=2.40

7.40-5.00=2.40

2.40+2.40+2.75+2.40+2.50=12.45

/5=2.49

7.75-5.00=2.75

7.40-5.00=2.40

7.50-5.00=2.50

9

900

7.45-5.00=2.45

7.60-5.00=2.60

7.90-5.00=2.90

2.45+2.60+2.90+2.85+2.70+2.85=16.35

/6=2.73

7.85-5.00=2.85

7.70-5.00=2.70

7.85-5.00=2.85

10

1000

8.00-5.00=3.00

8.10-5.00=3.10

8.20-5.00=3.20

3.00+3.10+3.20+3.05+3.10+3.20=18.65

/6=3.11

8.05-5.00=3.05

8.10-5.00=3.10

8.20-5.00=3.20

## SPRING

Original Length

(cm)

Weight

(g)

New length - Original length (cm)

Extension

(cm)

100g

5.2 cm - 2.1 cm

3.1 cm

200g

9.4 cm - 2.1 cm

7.3 cm

300g

13 cm - 2.1 cm

10.9 cm

400g

17.2 cm - 2.1 cm

15.1 cm

500g

20.8 cm - 2.1 cm

18.7 cm

600g

25 cm - 2.1 cm

22.9 cm

700g

28.7 cm - 2.1 cm

26.6 cm

800g

33.1 cm - 2.1 cm

31 cm

900g

34.1 cm - 2.1 cm

32 cm

1000g

40 cm - 2.1 cm

37.9 cm

## SPRINGConclusion

I predicted that the more load is applied to the spring and elastic band, the further down the spring and elastic band will stretch, I also predicted that as the load doubles the extension will also double. So if the load triples the extension will also triple. My results almost proved this, by looking at my table of results you will notice that as the load increases the extension of the spring and elastic band also increases. If the elastic band and spring has a steady force acting upon it the extension will increase with the force. I expected the spring to double as the force was doubled. This nearly happened. When the mass on the spring doubled from 200g to 400g, the spring went from 6.00cm to 12.88cm also when the mass on the elastic band doubled from 300g to 600g, the elastic band went from 0.58cm to 1.52cm.

My spring table of results shows that my extensions are very close to each other. For example when 100g is added to the spring and repeated 3 times the extensions are 2.70cm, 2.50cm and 2.70cm. This supports my prediction because when the 2.70cm is doubled the result is 5.40cm. On my table of results it shows the extension for when the load of 100g is doubled should be 6.00cm. When the total extension 5.40cm is tripled the sum is 16.20cm on my table of results it shows that the results is 18.85cm. This proves that Hooke's law is almost completely proven by the spring because the extension is roughly proportional to the load. When some of the results are doubled and/or tripled, it nearly follows Hooke's Law. Which states that extension is proportional to load so doubling/tripling the load doubles/triples the extension.

My elastic band table of results also shows my results are close together because when 100g is added to my elastic band the extensions are 0.10cm, 0.10cm and 0.15cm. My table of results shows that as the load increases the average extension increases. This also supports the first part of my prediction but not the second part because when the total extension of 0.85 is doubled the sum is 1.70cm. My table of results shows the extension should be 2.00cm. This reveals that Hooke's law is not completely proven by the elastic band because the extension is almost proportional to the load when the some of the results are doubled but when it's tripled the elastic band doesn't follow Hooke's law.

The pattern occurred in the spring extension and average extension graphs because the results are either very close or on my line of best fit. This tells me that my extension results were almost proportional to the load. Hooke's Law states that the extension is proportional to the load, so if the load doubles/triples the extension should also double/triple. Since my results are close to my line of best fit I think that Hooke's Law was almost completely proven by my graph. There's a pattern on my elastic band graphs and the pattern is that my results formed curved lines. This tells me that an elastic band doesn't follow Hooke's law.

There is a variable which might have affected my results more than others and that is the temperature which may have changed slightly, giving an incorrect result. This is because when the temperature is increased the spring expands but with an elastic band, the molecules move around more because of the heat. This makes them become less aligned as a result and the rubber band shrinks instead of expanding when temperature increases.

My spring trial run supports my prediction because the load increases the extension also increases. My extension for adding 500g to my spring is 18.70cm when the result is doubled it is 37. 40cm. On my trial run table it shows that when 500g is doubled to 1000g the result is 37.90cm. This is very close to the sum I got when I doubled the extension for 500g. The trial run for the elastic band supports the first part of my prediction because the load increased as the extension increased but my trial run doesn't support the second part of my prediction because when 200g is added to the elastic band the extension is 0.40cm if this is doubled the result is 0.80cm. On my trial run table when 200g is doubled to 400g the extension is 0.95. When 0.40cm is tripled the result is 1.20cm, the table shows that when the load 200g is tripled to 600g the extension is 2.20cm. For my experiment I used the same methods because I believed it was the best method to use for my investigation.

## Evaluation

I am quite confident with my conclusion and results because I believe they are reliable since they are very close together and the outliers in my results are 2.50cm, 6.15cm, 9.65cm, 28.55cm, 31.85cm, 41.10cm and 64.00cm, these are found on the spring table of results. Outlier 2.05cm is found on the elastic band table of results and for the elastic band removing and adding table of results the outliers found are 0.40cm, 0.90cm, 1.55cm, 1.60cm, 2.05cm, 2.70cm, 0.05cm, 4.90cm and 2.75cm. The ranges I used for my investigation were very good as I repeated my experiments 3 times during my experiment to make my results more reliable.

My spring extensions graph (Extension vs. Load) shows that my experiment and the equipment I used for that investigation were very accurate and reliable the only outlier I got for that experiment was try 3 600g which was 28.55cm. The reason for this outlier could be due to the fact that I might have read the measurement wrongly. My elastic band removing load graph is very reliable and accurate graph as it shows that the extension increases as the load increases. It also shows there are no outliers for that table and /or graph.

I think my investigation went well and I have almost proved my prediction which states that the more load is applied to the spring, the further down the spring will stretch and that as the load doubles the extension will also double. So if the load triples the extension will also triple. My measurements were reasonably accurate; this enabled me to obtain an almost proportional set of results. But the experiment may have been faulty by several factors: The spring may have been bent beyond visual detection and the elastic band could have been stretched or bent as well so the results wouldn't have been proportional and human error would lead to inaccurate results. If the spring and elastic band was wavering, stretched, expanded or vibrating this would lead to the measurements continuously changing. Some of my results for both the spring and elastic band were outliers this could be because the spring or elastic band reached its elastic limit or I read the measurements wrongly. Moreover if the ruler was damaged, bent, or not regulated correctly this would lead to inaccurate changing. Also, parallax errors caused by viewing the spring from different angles each time could affect the results; the results would have been wrong by 1 cm or 2 cm.

I could make the investigation more reliable by making sure the spring was not moving or vibrating in any way when I was measuring the extension. I would make sure that I was measuring the extension from the same angle so that all parallax errors will be ruled out. I could have made sure my ruler was perfectly aligned for my measurements. Instead of using the apparatus for Hooke's Law I could have used more precise equipment like the Searle's apparatus to make my experiment much more accurate. This apparatus will give me more precise and accurate measurements for my investigation. Instead of doing my experiments 2 hours once a week for 3/4 weeks I could have done it all on the same day to prevent change in temperature which could have affected my results.