• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12

Mathematics Mechanics 2.

Extracts from this document...

Introduction

Mathematics Mechanics 2 Coursework

Brief

Balance a standard laboratory metre rule on your index fingers horizontally as far apart as possible. Now slide your fingers towards one another maintaining the rule horizontal, and observe what happens. Does the same thing happen each time you try it? Do your fingers ever come together other that in the centre?

image00.png

Preliminary Experiment

This was an initial experiment carried out to observe the motion of the fingers as they slide towards one another. The first observation noticed was that each finger moves consecutively, never at the same time. Another observation noticed was that after the first finger (A) moved, the first move by the second finger (B) was considerably greater. Each consecutive move would decrease in distance until the fingers would meet. Also, the fingers always came together in the centre of the rule. The measurements of the preliminary experiment were recorded from the centre of the rule:

Move Number with Distances From the Centre of the Rule (m)

1

2

3

4

5

6

A

0.36

0.19

0.07

0.02

0.01

0

B

0.27

0.13

0.04

0.02

0.01

0

Modelling Assumptions

  1. Rule is constant (Consistent density throughout)
...read more.

Middle

5

0.06

0.03

0.01

6

0.04

0.01

0.00

7

0.02

0.01

0.00

8

0.02

0.00

0.00

9

0.01

0.00

0.00

Finger B

Move

Max (m)

Min (m)

Av (m)

1

0.31

0.21

0.26

2

0.20

0.09

0.13

3

0.12

0.04

0.07

4

0.08

0.02

0.04

5

0.05

0.01

0.02

6

0.03

0.00

0.01

7

0.02

0.00

0.01

8

0.01

0.00

0.00

9

0.01

0.00

0.00

Below are the theoretical results conveyed on graphs:

image15.png

image21.png

Conducting the Experiment

To test the model an experiment must now be conducted and involves the following:

Apparatus

  • A standard laboratory metre rule
  • The index fingers on a pair of hands

Diagram

image00.png

Method

  1. Place both fingers at 0.5 m from the centre either side.
  2. As slow as possible, slide apply force into the centre of the rule horizontally.
  3. Record distances from centre at switching points
  4. Repeat 10 times

Steps taken to reduce experimental error

  • There was an observer to measure the switching points
  • The observer also made sure that the rule was always horizontal

Results

...read more.

Conclusion

0.34

0.19

0.09

0.07

0.04

0.03

0.01

0.00

B

0.38

0.20

0.12

0.07

0.03

0.03

0.01

0.00

A

0.38

0.21

0.09

0.06

0.04

0.02

0.02

0.00

B

0.36

0.21

0.10

0.08

0.05

0.02

0.02

0.00

Max A

0.38

0.22

0.13

0.08

0.04

0.04

0.02

0.00

Max B

0.29

0.18

0.11

0.06

0.04

0.03

0.02

0.00

Min A

0.34

0.18

0.09

0.05

0.03

0.02

0.01

0.00

Min B

0.24

0.13

0.07

0.04

0.02

0.01

0.00

0.00

Av A

0.36

0.20

0.10

0.06

0.04

0.03

0.01

0.00

Av B

0.26

0.15

0.08

0.05

0.03

0.02

0.01

0.00

The results of the experiment shown on graphs:

image22.png

image23.png

Comparisons

Theoretical        Experimental

image15.pngimage16.png

image17.pngimage18.png

As you can see, the experimental values are all within the bounds of the theoretical values calculated. This shows that the model worked accurately and accounted for all the values. But, as you can see, the range in the values in the model is considerably wider then that of the actual experiment. For this reason the model needs to be refined.

Revision of the process

To improve the model, the value for the angle measured to calculate the static friction could have been more accurate. The effect of this would be that the bounds of each distance would be smaller and closer to the real experimental results. If the angle was measured to an accuracy of 0.5º, then the model and graphs would be as follows:

max μS

0.43

av μS

0.42

min μS

0.41

max μD

0.31

av μD

0.31

min μD

0.30

Max x        =        0.31y

                        0.41

Min x        =        0.30y

                        0.43

Av x        =        0.31y

                        0.42

Therefore, the graphs would now look like:

image19.png

image20.png

These graphs are now much closer to the experimental values than previously calculated.

...read more.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion 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 GCSE Forces and Motion essays

  1. Approximate Stopping Distances

    Using a mobile phone increases the time it takes the driver to react. Tiredness makes the human body do things slower than usual, such as thinking; this will make the brain work slower as the body will be trying to rest.

  2. Mechanics 2 Coursework - 'woosh' down the slide

    This has benefits because although we are ignoring the effect of air resistance in the calculations, we should minimise the affect that it has. A lighter object, or one that has a larger surface area (i.e. is less dense), would show more affect from air resistance.

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