# An Investigation into the terminal velocity of steel ball bearings in Glycerol.

Nicholas Metzgen

## Physics A2 Coursework –

An Investigation into the terminal velocity of steel ball bearings in Glycerol

Hypothesis

In this experiment, I plan to investigate the relationship between velocity and viscosity, as this is something that has always interested me. I am going to carry out an experiment to find the terminal velocity of steel ball bearings in glycerol.

According to Stoke’s Law, spheres falling through a fluid exhibit the following relationship:

4/3 Π r² (ρ-σ) g  =  6 Π η r vt

Therefore:

vt  =  2 r² (ρ-σ) g

9 η

Where η is viscosity, σ is fluid density, ρ is sphere density, r is radius of the sphere and vt is the terminal velocity.

From this we can conclude that terminal velocity is proportional to radius².

Investigation

In this investigation there are several variables that will affect the final results. All the following variables have been considered and so, various precautions have been taken to minimise their influences.

Temperature – If the temperature increases, the viscosity of the liquid will decrease. As the volume of glycerol being used is sufficient enough that fluctuations in temperature will be minimal. However, as the experiment is being carried out over two weeks, I shall monitor the temperature closely.

Viscosity – The internal friction in the liquid (viscosity) will have to be constant throughout the experiment. If the viscosity increases then there will be an increase in friction opposing the motion of the balls. To keep the viscosity constant, I shall use the same concentration glycerol (1 mol/dm³) throughout the investigation.

Sphere radius – Only one sized ball bearing will be used at one time.

Distance – In order to make accurate measurements and timings, the time taken for the ball to fall will be determined over equal distances.

Friction due to ball bearing surface – To eliminate/minimise friction caused by the ball surface, the ball bearing chosen for the experiment will all be smooth and have a shiny surface. If they are not shiny, they are more likely to have a damaged surface or dirt that would change the friction.

Prediction/Understanding

If we think about a ball bearing in air, when the ball is released from rest, there is no frictional force F=0. So, let us say that the resultant force is R.

The velocity will increase as long as F<R. The resultant force is R-F.

Terminal velocity is reached when F=R. There is no acceleration. R-F = 0

Friction forces will oppose the motion of the falling ball. Friction will increase as the ball falls. When the ball is released from rest, the initial speed is zero, there is no friction force and ...