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Dropping ball-bearing of various diameters into a viscous liquid, glycerol, timing the fall between two markers that are a known distance apart.

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Introduction

Asheeth Govindia

02/05/2007

Physics : Data Analysis

Aim

In this experiment I dropped ball-bearing of various diameters into a viscous liquid, glycerol, timing the fall between two markers that are a known distance apart.

I will then be looking for a relationship between the velocity of descent and the diameter.

Diagram

Method

  1. I measured the diameter of the ball bearing.
  2. I dropped a steel ball bearing down the pipe filled with glycerol.
  3. As the ball bearing passed the first marker I started the stop clock.
  4. As the ball bearing passed the second marker I stopped the stop clock.
...read more.

Middle

2.18

9.55

3.19

3.22

3.2

9.61

10

3

3

3

3

4

14.1

14.02

14.09

14.07


Data Analysis

Stokes Law states that spheres falling through a fluid exhibit the following relationship.

image00.png

Viscosity – any object moving through a viscous fluid is acted on by friction due to the fluid.  A higher viscosity will increase this friction that opposes its motion.

Calculating Viscosity

The force needed to separate molecules of the fluid according to Stokes is

Eq. (1) -> F = 6(pi)Rnvc,

Where R is the radius of the sphere, n is the viscosity of the fluid, and vc is the velocity of the sphere through the infinite fluid. This force can be set equal to the gravitational force modified to account for the buoyant effect as follows

Eq. (2) -> 6 (pi) R n vc = 4/3 (pi) R3 (pS-pL) g,

...read more.

Conclusion

Eq. (7) -> n = [2 g R2 (pS-pL) t] / [9L (1 + 2.4x) (1 + 1.65y)].

Viscosity of glycerol

2 x 9.8 x 0.0022 x (8.02 – 1.26) x 14.07 = 2.628 poise

9 x 0.515

Resultant Force = W – Fr – u

W = mg

W = 4/3πr3 x density of steel x g

u = 4/3πr3σg

At terminal velocity:

W – Fr – u = 0

Because there is therefore no acceleration

Conclusion

From my results I concluded that as the diameter of the ball increases the speed of the ball increases, but so does the drag. This means that the force pulling the ball the ball is greater than the frictional force pushing the ball upwards. So as the ball’s diameter increases the drag increased but still the speed at which it falls through the liquid increases.


Bibliography

Page

Topic

Source

3

Stokes Law

http://hyperphysics.phy-astr.gsu.edu

3

Calculating Viscosity

http://www.cord.edu

...read more.

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