• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Hookes Law- to determine the spring constant of a metal spring

Extracts from this document...

Introduction

IB Physics

IB Physics Investigation – Mechanics

Title: Hooke’s Law- to determine the spring constant of a metal spring

  1. BACKGROUND/ INTRODUCTION

A branch of the mechanical energy, elastic potential energy is one of the fundamental base energy concepts that is very commonly used in the modern technology. Elastic potential energy deals with the elasticity of an object (e.g. to what extent a string can be stretched?), and it’s used in a wide range of everyday life situations; such as in the process of decelerating an airplane landing on an aircraft ship. And the type of strings used there, is regarded to the spring constant of that string, in which it may or may not be able to stop an airplane within a certain distance.

Under investigation of Hook’s Law, the aim of this experiment is to determine different spring constants of some springs, and that is done by measuring how far a spring stretches when a certain amount of mass added. In order to find the spring constant, we investigate it by rearranging energy formulas and basic knowledge:

  • The general formula for Energy is image00.pngimage00.png, where image12.pngimage12.png is force and image09.pngimage09.png is displacement.
  • The formula for Elastic Potential Energy is image35.pngimage35.png, where image01.pngimage01.png isimage29.png
  •  the spring constant and image08.pngimage08.png is

the extension of the spring.

  • The relation between the two formulas is that image09.pngimage09.png (displacement) is equal to image08.pngimage08.png (extension) since both have the same units (measured in meters). Therefore, we can state that image10.pngimage10.png
  • The area under the a Force-Extension (image11.pngimage11.png) graph gives the work done on the spring and therefore, the Elastic Potential Energy (image13.pngimage13.png). Since it’s the area of a triangle, then image14.pngimage14.png
  • From the graph, we know that image15.pngimage15.png, then image16.pngimage16.png. Therefore if we substitute this into the first formula (image14.pngimage14.png) we get image17.pngimage17.png and that is equal to image18.pngimage18.png

From this information we can extract that image01.pngimage01.png, the spring constant can be found as follows:

  1. Measure the force and extension of the spring
  2. Plot a image11.pngimage11.png graph
  3. Find the slop of the graph, which is image01.pngimage01.png, the spring constant
  1. QUESTION

What is the role of the spring constant in the relationship of force and extension and how can it be determined?        

  1. HYPOTHESIS

The independent variable of this experiment is Mass (the number of masses added) and the dependent variable is Extension (the extension of the spring). The control variables are the same ruler used (the same scale) with the same initial positions (each spring was measured by the ruler sat on 4 cm), as well as the same masses are used for each spring.

The expected findings of this experiment is that the spring with the largest spring constant will extended least with the same amount of force applied. Therefore, the variation of the spring constant causes variation of extensions of different springs at the same amount of added-force.

  1. EQUIPMENT & MATERIALS

The equipment used to conduct this experiment are:

  • Rulers
  • Masses
  • Springs
  • Retort Stand
...read more.

Middle

350

78.2

78.1

78.2

400

87.6

87.6

87.6

450

97.2

97.2

97.2

Spring B (Pink)

Mass, m (g)

Length, L1 (cm)

Length, L2 (cm)

Length, L3 (cm)

0

12.3

12.3

12.2

50

17.3

17.3

17.3

100

22.3

22.2

22.3

150

27.2

27.1

27.2

200

32.1

32.1

32.1

250

37.0

37.1

37.1

300

42.0

42.0

42.1

350

47.0

46.9

47.0

400

51.9

51.8

51.9

450

56.7

56.6

56.7

500

61.6

61.6

61.6

550

66.5

66.4

66.5

600

71.4

71.4

71.3

Spring C (Silver)

Mass, m (g)

Length, L1 (cm)

Length, L2 (cm)

Length, L3 (cm)

0

12.3

12.3

12.4

50

15.8

15.7

15.8

100

19.1

19.1

19.1

150

22.5

22.6

22.5

200

25.8

25.8

25.8

250

29.1

29.1

29.1

300

32.4

32.4

32.4

350

35.7

35.7

35.7

400

40.0

40.0

40.0

450

42.4

42.4

42.4

500

45.6

45.7

45.7

550

49.0

49.1

49.1

600

52.3

52.3

52.3

Spring D (Gold)

Mass, m (g)

Length, L1 (cm)

Length, L2 (cm)

Length, L3 (cm)

0

11.8

11.8

11.8

50

13.6

13.6

13.6

100

15.4

15.4

15.4

150

17.3

17.3

17.3

200

19.2

19.2

19.2

250

21.0

21.0

21.0

300

22.9

22.9

22.9

350

24.8

24.8

24.8

400

26.7

26.7

26.7

450

28.5

28.5

28.5

500

30.4

30.4

30.4

550

32.3

32.3

32.3

600

34.1

34.1

34.1

The uncertainty in the Masses Measurement was + 1 g

The uncertainty in the Ruler Measurement was + 0.05 cm

  1. Data Processing and Presentation:

image19.jpg


image20.jpg

  1. CONCLUSIONS

The results support my hypothesis that states that the spring with the least spring constant will extend most. And that’s shown in the graphs, the most extended spring, which is spring A has the smallest slope (i.e. the spring constant). Whereas spring D, which is the steepest linear graph extended least among all 4 springs.

Possible sources of errors that may have limited the certainty of the results could be:

  • Human errors (in recording measurements)
  • Accuracy of the masses (do the masses exactly weigh as they’re labeled?)
  • Each spring sat on an initial position on the ruler (at 4 cm), which may has slightly moved by the time.
  • The springs possibly touched the ruler very rarely, which may caused less extension due to friction.
...read more.

Conclusion

The gradient of spring C’s graph:          image46.pngimage46.png

image47.png

image48.png

image49.pngimage49.png)

image50.pngimage50.png
                                                                     
image51.pngimage51.png

The percentage uncertainty of spring C is image52.pngimage52.png

Spring D:

The gradient of spring D’s graph:          image53.pngimage53.png

image02.png

image03.png

image04.pngimage04.png)

image05.pngimage05.png
                                                                     
image06.pngimage06.png

The percentage uncertainty of spring D is 1.08image07.pngimage07.png

  1. EVALUATION

The followed procedure achieved a good level of accuracy which was demonstrated in the results that were quite reasonable in comparison to reality. The equipment used in the procedure are not very sensitive however, hence the results weren’t very accurate because the range of uncertainty is not negligible. But the range could be narrowed by developing the design of the procedure, using some more sensitive equipments/better method.

Possible solutions to reduce sources of errors:

  • Hanging the ruler and the spring into two separate Retort Stands, so we can more clearly see and measure both.
  • Using light for example to determine the level between the spring and the ruler, or any better pointer for the spring. Because the current spring pointer keeps rotating which makes it hard for the observer to record accurately.
  • Using bars for the Retort Stand instead of the current handles that hold the ruler; so the ruler will be attached/hanged to it. Because the handle is made to hold beakers often (it has a rounded shape which makes the ruler not very stable).

        

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Physics essays

  1. Physics Extended essay

    The experiment setup with labeled measurements 12 Figure 4. The experiment setup with labeled measurements 27 Figure 5. The experiment setup showing sign convention used 28 Images Image 1. The Severn Suspension Bridge 5 Image 2. Shows the wooden board with the string hanging 10 Image 3.

  2. Hooke's Law Experiment. Aim: To determine the spring constant.

    The results were observed and copied in a notebook, were a table was made showing the masses, and the (cm) results of the extensions for each trial. Method Diagram: Results Table: Mass(g) Weight (N) Trial 1(cm) Trial 2(cm) Trial 3(cm)

  1. Hook's law. Aim of the experiment: To understand the Hookes Law by calculating the ...

    F= kx Graph 1: Graph of Force vs. Elongation in the spring. The slope of the F-x graph gives the spring constant. Therefore the spring constant is found to be 36.42 N/m. Percent Error= |kslope - kmean|/kslope x100 |36.42- 18.37|/36.42 x 100 49.56% Conclusion and Evaluation: By conducting this experiment, Hook's Law of springs is tested and it

  2. Hooke's Law

    is proportional to the applied force. The value of k is constant for a particular spring. The relationship should be directly linear. Furthermore, the spring used in the experiment should also be varied as to prove Hooke's law which states that each spring has its own spring constant.

  1. Determine the spring constant of a vertical spiral spring in simple harmonic motion using ...

    at 60.00cm, Vertical Oscillation of 0.00cm Mass of 100g: Mass of 200g: Mass of 300g: Mass of 400g: Mass of 500g: Mass of 600g: - Data Table #3: The Spring Constant Mass Added �0.2g Oscillation of Spring �0.05 cm Fg (Fg=mg)

  2. Physics Wave revision question

    Calculate the angle between a refracted wavefront and the normal to the boundary. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (ii) On the diagram above, construct three wavefronts to show the refraction of the wave at the boundary. (3) (Total 11 marks)

  1. In this extended essay, I will be investigating projectile motion via studying the movement ...

    When both the monkey and the bullet come into contact, their vertical mid-air displacement are the same. Therefore, the dart will inevitably hit the monkey. Hence, we can conclude that the vertical acceleration of gravity does not affect the

  2. Suspension Bridges. this extended essay is an investigation to study the variation in tension ...

    The experiment setup with labeled measurements 12 Figure 4. The experiment setup with labeled measurements 27 Figure 5. The experiment setup showing sign convention used 28 Images Image 1. The Severn Suspension Bridge 5 Image 2. Shows the wooden board with the string hanging 10 Image 3.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work