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

Explore and review the basic physics of how different things relate to one another.

Extracts from this document...

Introduction

Lab Report 1                               Physical Relationships

By   Ben Sefcik        ID#2245154                Physics 200                Athabasca University

Introduction

This lab is intended to explore and review the basic physics of how different things relate to one another.  The lab is broken up into four different parts: rubber band force constant, pendulum, combination of errors, and quadratic functions.

The first to be looked at was elasticity compared to weight and gravitational force: rubber band force constant.  The relationship should produce a linear relationship and a linear regression was performed to verify that it was linear and to see more closely the relationship of the two components.  

The next section looked at the relationship between the amount of time required for a pendulum to complete 10 oscillations and the length of string used.  It was expected that the length of string used would have an exponential effect to the time used.  In other words, as the string gets longer the time required to do 10 full oscillations would become exponentially larger.

The third part of the lab looked at taking errors into consideration.  There are two different types of errors: random and systematic.  These errors can have different impacts on the analysis of the results depending on the regression curve that best fits the data collected.

...read more.

Middle

12

8

6.97

0.5470

71

15

9

6.97

0.6154

74

18

10

6.97

0.6838

78

22

11

6.97

0.7521

83

27

12

6.97

0.8205

88

32

13

6.97

0.8889

93

37

In Table 1, the mass is the mass added not including the container and rubber band.  The total mass is the total mass of the loonies in the container.  The results regarding length was the raw reading from the ruler and the extension is just the subtraction of the ruler reading from the starting length.  The total weight was the total mass multiplied by 9.81 m/s2.  The results were graphed using Graphical Analysis and a linear regression was performed to see the relationship between the extension and the force applied.  Figure 1 is the graph that was produced with the linear regression line.  The line was the best fit for this particular model.image00.png

The total weight is the applied force so the graph is a representation of Hooke’s Law. F=-kx.  With this being the case then k (proportionality constant) is 31.95 N/m, which is the slope of the regression line.


Analysis Part A

The Graphical Analysis fit could have been better.  Since Hooke’s law is a linear law a linear regression was performed.  Not all of the dots aligned as good as was hoped.  The errors were probably due to random errors in measurement.

...read more.

Conclusion

when y = 0.  To figure this out the quadratic function can be rewritten as: x = -b/2a ± √b2 – 4ac   / 2a.  The graph is helpful to quickly see where the roots are.  The Graphical Analysis software allowed me to zoom into the roots closer than what figure 3 allows to be seen.  Visually the roots looked to be –0.32 and 6.44 but with a calculator the equation was a little more accurate for the first root at –0.317.  Using the proper number of significant figures then the answers would be the same whether calculated or visually enhanced.  

Looking at the equation more closely shows an interesting equation within the bigger one.  Before the “±” symbol is –b / 2a, which is the same for both roots.  This is important because the quadratic equation is symmetrical and the –b / 2a equation points to the apex of the curve, like a mid-point.  Another note on this point is that the point is also where the slope = 0, which is when the ball would begin falling back to the earth.

Conclusion

This lab looked at some of the different physical relationships that are current theories or laws.  The experiments verified these relationships.

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics 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 AS and A Level Core & Pure Mathematics essays

  1. Marked by a teacher

    Estimate a consumption function for the UK economy explaining the economic theory and statistical ...

    3 star(s)

    There is another method can be used to estimate whether the equation fits the data properly is look at how well the equation predicts consumption. This is done in Figure1. The Figure 1 (a) has two lines, the red line is the actual value, the blue line is the fitted value (predicted value).

  2. Determine an appropriate parabolic model that fits the data I collected of whirlybird wing ...

    Time (s) 14 1.29 12 1.7 10 2.27 8 2.33 6 2.1 4 1.65 2 0.99 A graphic calculator was used to find out the turning point, and it was concluded that the wing length that would produce longest flight time was 8.5000008712cm, which could produce a maximum flight time of 2.33 seconds.

  1. Math Portfolio Type II - Applications of Sinusoidal Functions

    Therefore, the answer becomes , which is 0.017. 7. The graph of function f, which represents the time of sunrise in Toronto, can be transformed to the graph of function g, which represents the time of sunrise in Miami. One of the transformations that occurs is a vertical stretch.

  2. Estimate a consumption function for the UK economy explaining the economic theory and statistical ...

    Inflation erodes the value of debt meaning that those in debt (usually the corporate and government sectors) gain while those creditors (usually the private sector) lose out. However real disposable income doesn't take this into account and so an inflation variable must be added to the consumption function.

  1. The open box problem

    x x 12 15-2x x 15-2x 12 Again I use the same equation as before but this time I replace 12 with 15. So the equation will be V= x(15-2x)^2 . I will now construct tables and two graphs to again show the maximum volume and x.

  2. Estimate a consumption function for the UK economy explaining the statistical techniques you have ...

    Using linear regression I obtain the equation below: C = 13064.8 + 0.925Y The marginal propensity to consume is 0.925. This supported the Keynesian's view that the m.p.c is less than 1. The autonomous consumption is 13064.8. This is positive and very large. Real interest rate can influence autonomous consumption.

  1. Examining, analysing and comparing three different ways in which to find the roots to ...

    see towards which value the root lies closest to: 4.197 4.1971 4.1972 4.1973 4.1974 4.1975 4.1976 4.1977 4.1978 4.1979 4.198 -0.0256 -0.0219 -0.0181 -0.0143 -0.0105 -0.0067 -0.0029 0.0009 0.0046 0.0084 0.012 As this shows, the root lies between the interval [4.1976, 4.1977] and this means that the root is closer

  2. Fractals. In order to create a fractal, you will need to be acquainted ...

    = -i z6 = -1 + i and the orbit behaves in a cyclic manner, thus its inclusion in the Mandelbrot set. The Mandelbrot set (M) consists of all the complex numbers that stay bounded, or do not escape to infinity namely, those seeds that generate periodic sequences (cyclic, confined sequences)

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