# Hooke’s Law Lab

September 24, 2017 September 1st, 2019 Free Essays Online for College Students

In 1676 the English physicist Robert Hooke discovered that elastic objects, such as metal springs, stretch in proportion to the force that acts on them. Despite all the advances that have been made in physics since 1676, this simple law still holds true.

This means that if a weight is added to a spring, it will stretch in proportion to that force and when the force is removed, the spring will return to its original shape. The extension or the strain will keep increasing as you increase the weight added as long as the spring doesn’t remain stretched permanently. A point is reached where the spring can’t stretch any more when more tension force is applied to it and snaps. This is defined as the ‘elastic limit’ of the spring.

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The force constant ‘k’ of a spring is the force needed to cause unit extension, i.e. 5cm. If a force ‘F’ produces extension ‘e’ then,

k = F

e

HYPOTHESIS:

Hooke’s Law states that the extension produced by the spring is directly proportional to the tension force applied to it. Therefore, in this experiment I hypothesize that the extension produced by the spring will increase as more weights are added. The graph for this extension will be as follows:

The Y-Axis shows the stretching force ‘F’ and the X-Axis represents the extension produced by the spring.

VARIABLES:

Constant:

– surroundings

– equipment used

Independent:

Dependent:

– extension produced by the spring

APPARATUS:

– Clamp stand with a stable base.

– Uniform metre- rule.

– Metal spring with a pointer at the end.

– Uniform metal weights of 100g each.

FAIR TEST:

– The same equipment must be used for all the trials so that the uncertainties remain constant for every reading taken.

– The surroundings must not be too breezy so that the spring which is suspended from the clamp stand doesn’t oscillate.

– The pointer of the spring must be completely horizontal so that correct measurements of the extension can be taken from the metre-rule.

– The metre rule used must be calibrated uniformly and it should be kept parallel to the suspended spring while taking the readings.

– All readings must be taken at eye-level.

– The clamp stand used must be very stable so that the suspended spring doesn’t oscillate during the experiment is being performed and thus to prevent anomalous results.

– There should be no contact of the spring with the hand which would apply an extra tension force to the spring and thus give inaccurate results.

SAFETY PRECAUTIONS:

– All the weights must be handled with care and should not fall on any part of the body causing injuries.

– The clamp stand should have a stable base so that when weights are added to the attached spring, the balance doesn’t shift and so the stand doesn’t topple over.

– Any rusted metal should be kept away from cuts in the body to prevent any contact with the bacteria present on the rust.

– The sharp edges of the metal spring must not poke any part of the body causing any injuries.

MODIFICATIONS TO THE EXPERIMENT:

– Instead of using one spring, the experiment was carried out using two springs with different elasticity.

– The metre rule was held in a straight position by attaching it to the clamp stand. Thus the data could be recorded more efficiently.

– Since the base of the clamp stand was not very stable, loads were put on the base to make it more stable.

DIAGRAM OF THE SET-UP APPARATUS:

RESULTS:

RAW DATA:

Table 1.1

Length after adding weights on spring 1:

Sr.No.

Original length(cm)

ï¿½ 0.05cm

ï¿½0.01g

Trial 1: new length(cm)

ï¿½ 0.05cm

Trial 2: new length(cm)

ï¿½ 0.05cm

1.

13

100

13.5

13.4

2.

13

200

15.7

15.8

3.

13

300

19.4

19.4

4.

13

400

24.5

24.6

5.

13.2

500

28.3

28.0

Table 1.2

Length after adding weights on spring 2:

Sr.No.

Original length(cm)

ï¿½ 0.05cm

ï¿½0.01g

Trial 1: new length(cm)

ï¿½ 0.05cm

Trial 2: new length(cm)

ï¿½ 0.05cm

1.

14.8

100

24.3

24.3

2.

14.8

200

34.4

34.3

3.

14.8

300

43.2

43.2

4.

14.8

400

53.3

53.2

5.

15.1

500

62.9

63.1

PROCESSED DATA:

100g = 0.1kg

Gravity= 10m/s2

Weight= 0.1 X 10

= 1N

Table 2.1

Extension caused by adding weights on spring 1:

Sr.No.

Original length(cm)

ï¿½ 0.05cm

Force applied (N)

Average new length

(Trial 1+ trial 2)

ï¿½ 0.05cm

Change in length

(Extension)(cm)

ï¿½ 0.05cm

1.

13

1

13.45

0.45

2.

13

2

15.75

2.75

3.

13

3

19.40

6.40

4.

13

4

24.55

11.55

5.

13.2

5

28.15

14.95

Table 2.2

Extension caused by adding weights on spring 2:

Sr.No.

Original length(cm)

ï¿½ 0.05cm

Force applied (N)

Average new length

(Trial 1+ trial 2)

ï¿½ 0.05cm

Change in length

(Extension)(cm)

ï¿½ 0.05cm

1.

14.8

1

24.30

9.5

2.

14.8

2

34.35

19.55

3.

14.8

3

43.20

28.40

4.

14.8

4

53.25

38.45

5.

15.1

5

63.00

47.90

Table 3.1

Table to calculate the spring constant for spring 1:

Sr.No.

Force applied (F) (N)

Extension produced (e) (in cm)

ï¿½ 0.05cm

Spring constant

(k) where k= F/e

1.

1

0.45

2.22

2.

2

2.75

0.72

3.

3

6.40

0.46

4.

4

11.55

0.34

5.

5

14.95

0.33

= shows an anomalous result

Average value for the spring constant= (2.22+0.72+0.46+0.34+0.33)/5

= 0.81

Table 3.2

Table to calculate spring constant for spring 2:

Sr.No.

Force applied (F) (N)

Extension produced (e) (in cm)

ï¿½ 0.05cm

Spring constant

(k) where k= F/e

1.

1

9.5

0.10

2.

2

19.55

0.10

3.

3

28.40

0.10

4.

4

38.45

0.10

5.

5

47.90

0.10

GRAPHS OF RESULTS ATTACHED AS PAGES 7 AND 8.

Gradient of the l.o.b.f= spring constant.

Graph 1)

Gradient of the line= y2- y1

x2- x1

= 3-2

9-6

= 1/3

= 0.33

Graph 2)

Gradient of the line= y2- y1

x2- x1

= 4-3

38.45-28.4

= 1/10.0

= 0.1

ANALYSIS:

Tables 1.1 and 2.1 show the raw and processed data for the first spring. As observed, this spring was quite rigid and its coils were extremely close to each other. The total length of this spring was 13 cm and with the weights added, the spring did not show a large extension. Although a positive relationship is shown between the force applied an extension produced, it is not uniform since no trend can be seen between the two. When a force of 1N (100g) is applied, the extension produced is only 0.45 cm and when a force of 5N (500g) is applied, the extension produced is 14.95cm. This shows that the extension produced by the spring is over a very short range. The results of the first trial are anomalous because the value of the spring constant is way different from the values obtained with the other trials. After the experiment is performed with weights of 400g, the spring doesn’t return back to its original length of 13cm and it stops at 13.2cm. This shows that the spring has now been permanently stretched and the Hooke’s law can’t be applied to the spring anymore as the extension produced will not be proportional to the force applied.

However, the graph drawn for the results obtained is not a uniform straight line as it is supposed to be theoretically. This may have happened due to the inaccuracy in the experiment or because of changes in the surroundings which were supposed to be constant. The errors are identified in this report. The spring constant is calculated for the results obtained by using the formula k=F/e. This value is not a constant as it should have been due to the errors in the experiment. The average value is calculated as 0.814. The gradient of the graph of results also gives the spring constant. This value is found to be 0.33 and when this value is compared to the value obtained as the gradient of the graph, it can be seen that the two values differ. The reason for this is that there were errors in performing this experiment and the results of the first trial were anomalous.

Tables 1.2 and 2.2 contain the raw and processed data for the second spring. This spring is very flexible and its coils are not extremely close to each other. This spring was longer than the first spring with a length of 14.8cm and this was because of its coils not being so close to each other. This spring being flexible, produced a large extension with every 100g weight added. There is a constant trend seen in the results. For every 100g added, the extension produced by the spring is approximately 10cm. this shows that the extension is proportional to the force applied. The extension shown by the spring ranges from 9.5 to 47.90cm which shows how flexible the spring is.

However, the Hooke’s law can’t be applied for the fifth reading. This is because after the fourth reading, the spring becomes permanently stretched because of which the extension produced in the fifth trial is not directly proportional to the 5N weight added.

The graph obtained for these results is a uniform straight line graph which shows the proportionality between the force and extension. The last point plotted on the graph for the extension produced when 5N force is applied doesn’t fall on the straight line since Hooke’s law is not applicable to the spring after the fourth trial. The gradient of the line gives a value of 0.1 which was same as the value obtained when the spring constant was calculated using the results. These results seem to be very accurate since there is an explanation related to the Hooke’s law for every trial performed.

When the two springs are compared, it can be said that the second spring produces more extension as force is applied to it. This happens because it is more flexible than the first spring and because its coils are further apart when compared to the first spring. Also, the second spring gives more accurate results than the first spring since the graph plotted for the second set of results is a uniform straight line graph with almost all of the points falling in the line of best fit.

SOURCES OF ERRORS:

– The springs used kept oscillating when the weights were added on them. This caused a lot of inconvenience while taking measurements and thus could have led to inaccuracy.

– The pointers of the springs were not exactly horizontal thus causing the measurements to be slightly incorrect.

– It was not possible to take all the readings at eye-level thus causing parallax errors.

– Since the pendulum was oscillating too much, I had to use my hand to hold the spring steady.

– The ruler attached to the clamp stand to make the experiment more efficient. However, it was not in a straight line thus causing some inaccuracy in measurements.

– This would have caused extra force to be applied and the exact measurements could not be taken.

– All the weights were assumed to be 100g and their exact weight was not taken. Thus it is possible that extra or inadequate force may have been applied.

SUGGESTED IMPROVEMENTS:

– More readings can have been taken to improve the accuracy of the experiment.

– All the weights used should be measured on a digital balance before using them so that the exact force applied can be calculated.

– The pointer of the spring should be totally horizontal to get accurate measurements of the extension.

CONCLUSION:

From the experiment performed above, it can be concluded that the Hooke’s law holds true for a metal spring. This is because the extension produced by the spring is directly proportional to the force applied on it. For the first spring, the results obtained are not very accurate due to the sources of errors identified above. However, the second spring gave very accurate results as I had hypothesized according to the theory. Therefore, this experiment is a reliable way of verifying Hooke’s law using a metal spring.

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