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Liquid Friction.

Extracts from this document...

Introduction

Nick Earnshaw

Bedford School

Candidate 3440

AS Coursework – Making Sense of Data

“Liquid Friction”

Apparatus

Not in diagram:

  • Stopwatch
  • Top pan balance (accurate to nearest 0.1g)
  • Micrometer screw gauge
  • Several different size ball bearings.
  • Small magnet
  • Long ruler

Method

The apparatus was setup as on the previous page, a ruler was used to mark the depths of 0.2m and 0.7m. The glycerol was left to settle.

The mass of each steel ball bearing was measured using a top pan balance and the diameter was measured using a micrometer screw gauge. The results from this were recorded and each measuring device was reset to zero each time.

Each steel ball bearing was coated in glycerol and then released from just below the surface of the glycerol, using tweezers.

The time taken for each steel ball bearing to drop from a depth of 0.2m and 0.7m was timed using a stopwatch and then recorded. This step was repeated a further two times for each steel ball bearing.

The steel ball bearings were retrieved after each attempt, using a small magnet.

Results

I have formatted a table with the data attained from the experiment described above, each row of data relates to a different steel ball bearing.

The density of glycerol used was 1262 kg/m3.

mass

diameter

time to fall

 0.5m 

(g)

(mm)

(s)

1

2

3

Average

low*

1.58

70.4

70.8

70.5

70.6

0.13

3.18

18.2

18.1

18.3

18.2

0.25

3.91

12.2

12.5

12.4

12.4

0.44

4.75

8.7

8.7

8.7

8.7

0.88

6.00

6.0

6.0

6.0

6.0

1.04

6.35

5.3

5.4

5.4

5.4

1.40

7.00

4.4

4.6

4.6

4.5

2.04

7.91

3.6

3.8

3.7

3.7

3.44

9.45

2.8

2.8

2.9

2.8

* This mass could not be accurately recorded using the top balance.

Strategy and Approach

The above text is descriptive, it does not analyse the physics involved. My role within the investigation is to analyse results given to me. To effectively approach this target, I need to do some planning.

When the experiment was shown to me I took some notes, these are on a separate A4 lined sheet.

...read more.

Middle

image06.pngx image11.png

image06.png= image07.png

We can therefore equate this. This gives us the force in Newton’s.

Force (gravity) = image12.png

This allows us to make a statement, which then can be simplified.

Force (downwards) = image12.png - image08.png

Force (downwards) =image13.png

The force acting downwards can also be expressed using stokes law.

image14.png - radius of ball bearing        

image16.png- velocity of ball (at terminal velocity)

image17.png - coefficient of viscosity

Force (downwards) = image18.png

This is an expression for stokes law, and requires that the ball is travelling at its terminal velocity. We can use stokes law, and the equation for Force (downwards) found earlier to allow us to find the coefficient of viscosity of the liquid that the ball is moving through.

image13.png = image18.png

image17.png        = image19.png

I used this approach to find the coefficient of friction of the liquid as shown in the table below.

Velocity was calculated by the equation below.

Speed = image20.png

mass

radius

velocity

b volume

b density

f viscosity

(kg)

(m)

(ms-1)

(m3)

(kg/m3)

η image21.png

4dp

1.61E-05

7.90E-04

7.09E-03

2.07E-09

7.82E+03

1.2586

1.30E-04

1.59E-03

2.75E-02

1.68E-08

7.72E+03

1.2955

2.50E-04

1.96E-03

4.04E-02

3.13E-08

7.99E+03

1.3858

4.40E-04

2.38E-03

5.75E-02

5.61E-08

7.84E+03

1.4074

8.80E-04

3.00E-03

8.33E-02

1.13E-07

7.78E+03

1.5346

1.04E-03

3.18E-03

9.32E-02

1.34E-07

7.76E+03

1.5318

1.40E-03

3.50E-03

1.10E-01

1.80E-07

7.79E+03

1.5816

2.04E-03

3.96E-03

1.35E-01

2.59E-07

7.87E+03

1.6678

3.44E-03

4.73E-03

1.76E-01

4.42E-07

7.78E+03

1.7988

Averages:

7.82E+03 *

1.4815

The coefficient of friction that the experiment data has produced seems reasonable, and follows a trend. As the radius of a sphere increase so does the coefficient of friction. This is a positive relationship. However, the coefficient of friction should be the same for all the different ball bearings used.

The actual frictional drag will increase with radius, but viscosity is a ratio between shearing stress and the velocity gradient, hence it should remain constant as long as other factors such as temperature are not changed.

There is a positive relationship between radius2 and velocity.

...read more.

Conclusion

Human error

This is likely to contribute the biggest problem to reliability and accuracy to the investigation; calculations are based on data collected from a human.

Humans can only judge things to an accuracy of ±0.1s. The human reaction time coupled with the accuracy of the basic stop watched used could see a variation of almost ±0.2s.

This means that the velocity calculated based on the time it takes the ball to travel the 0.7m distance can be inaccurate because of the human error involved when using a stopwatch.

The problems of the stopwatch and the use of are probably the biggest factor sin causing uncertainties and inaccurate results.  But this did not prevent me from making suitable analysis.

Temperature

Temperature can have a large effect on the viscosity of a fluid, since it gives the molecules more energy and the bonds will become weaker, meaning that the viscosity will be decreased. But the experiment was all done on the same day, in the same room so any change in temperature will be negligible.

Improvements

To solve the problem of human error, a photodiode arrangement could be setup to electronically calculate the speed of the ball bearing. Also, a more instantaneous result could be attained if the distance was shorter, and closer to the bottom of the cylinder.

There are problems with the photodiode setup, and would require the ball bearing to be accurately dropped from a specific position.

An extension to the investigation could be the measurement of velocities at more than one intervals, perhaps every 0.1m, this would allow me to work out if the ball had reached terminal velocity or not.

Also, more care should be taken when releasing the ball bearing. The position from which the ball is dropped should be measured, and kept the same each repeat.

End of Investigation

pages         type

17                 total

12                 normal

02                 graphs

03                data

...read more.

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

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