• 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?

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)

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:

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

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

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:

Comparisons

Theoretical        Experimental

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 0.3

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:

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

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

# Related GCSE Forces and Motion essays

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

Determining the work done against friction: mgcos ? f =???R mgsin ? O mg ? From the diagram above I known when the block just slides, the components of weight parallel to the slope should be equalled, which means: mgsin ?

2. ## Approximate Stopping Distances

the driver gets older they tend to decrease speed which they drive at. Illnesses can affect safe driving, there are various illnesses that can be dangerous for drivers these include the following: * Blackouts * Vision Problems * Epilepsy * Heart disease * Sleep Disorders * Diabetes * Psychiatric Disorders

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