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

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Introduction

Physics 20IB: Restoring Force

Aim:Determine the spring constant of a vertical spiral spring in simple harmonic motion using Hooke’s law. Produce a graph that will enable you to find the spring constant using an appropriate averaging technique.

Experimental Design: 100g masses will be hooked to a suspended spring on a retort stand and create an oscillation on the spring. The masses are going to be adjusted at a constant with an addition of a newly hooked 100g mass in each trial, the oscillation of the spring in centimetres will be recorded vs. the mass hooked to the spring, this will help us determine the spring constant, K derived from Hooke’s Law image00.pngimage00.png.

Materials:

  • Test Spring (Manufacture Unknown, Weight Resistance Unknown)
  • Standard Lab Retort Stand
  • Meter Stick (used for measuring the oscillation of spring) 100.00 ±0.05 cm
  • A set of 100.0 ±0.2g Standard test masses (Used to manipulate spring oscillation.)

Variables:

  • Manipulated Variable: Mass Added

The mass added will be kept at a constant increase of 100g per trial; each 100g mass will be hooked on to the mass bottom of the previous mass.

  • Responding Variable: Spring Oscillation

The increase in the oscillation of the spring will be measured by a stationary meter stick placed vertically beside the spring placed in between the retort stand holder; each measurement taken will be measured to the nearest 0.05 cm and recorded on a data table.

  • Controlled Variable(s): Environmental Conditions; Type of Mass Added;

The environmental conditions such as room temperature will be kept constant at around 20-24°C in order to keep the oscillation of the spring at a minimum, this would make a more accurate result of the spring constant. The mass added will be controlled by using the same mass of 100g (manufactured by one manufacturer with same color texture..etc.) for every trial, this would keep the uncertainty of the masses at a minimum and produce a better result for the spring constant.

image07.png

Data Collection and Processing

  • Data Table #1: Final Lab Results

Mass Added to Spring ±0.2g

Vertical Oscillation of Spring Shown on Meter Stick±0.05 cm

0

60.00

100.0

57.30

200.0

54.40

300.0

51.10

400.0

48.00

500.0

44.80

600.0

41.70

*Initial Position Of Spring On Meter Stick: 60.00 cm

** The height of the spring increases after each mass is added, but a decrease in value will be shown on the ruler because the ruler is placed up side down for ease of reading.

  • Data Table #2: Processed Data From Recorded Data
...read more.

Middle

image31.png

Mass of 400g: image01.pngimage01.png

Mass of 500g: image02.pngimage02.png

Mass of 600g: image03.pngimage03.png

  • Data Table #3: The Spring Constant

Mass Added ±0.2g

Oscillation of Spring ±0.05 cm

Fg (Fg=mg)

±0.2N

...read more.

Conclusion

ght:30px;margin-left:0px;margin-top:0px;" alt="image15.png" />

600.00g

18.30

image16.pngimage16.png

image17.pngimage17.png

*Notable Measurement Conversion of Units: 1m=100cm; 1kg=1000g

Propagation of Uncertainties:

Since image18.pngimage18.png = image19.pngimage19.png two uncertainties are involved in this experiment.

Uncertainty of Mass Scale ±0.2g = ±0.0002kg

Uncertainty of Meter Stick: ±0.05cm = ±0.0005m

Average Mass Added:

image20.png

Average Oscillation of Spring:

image21.png

Average Fg: Uncertainty is Related to Mass.

Percent Uncertainty for Mass Added: image22.pngimage22.png

Percent Uncertainty for Oscillation of Spring: image23.pngimage23.png

Final (Average) Percent Uncertainty for Spring Constant (k):

image24.pngimage24.png = 0.5365%

Average Value of “The Spring Constant” (image26.pngimage26.png):

image27.pngimage27.png33.595

Final Average Value and Uncertainty for K:

33.595 ±0.5365% or ±0.1781image28.pngimage28.png

Graph: Oscillation of Spring Vs. Fg (See Graph Paper)

Slope of Graph: image29.pngimage29.png

The General Equation for the image30.pngimage30.png Ratio for the Spring Tested is: x=0.0311Fg

...read more.

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