3.4
The terminal velocity of a
small sphere falling down through a
liquid
(balancing forces - objects falling downwards under gravity in fluids)
Apparatus
You can demonstrate the effect of resistive
forces in a fluid using the experiment illustrated in the diagram above.
Theory: When an object falls through a
fluid there are three forces to take into consideration.
W↓ is the weight of the ball bearing
due to gravity (Weight = mass x gravity, W = mg)
U↑ is the upthrust experienced by any object in a fluid.
See section
6.
Pressure in liquid fluids
F↑ is the resistive force of friction
between the ball and the fluid.
W and U are constant and so W-U is a
constant and the resultant force in the downward direction.
Initially F is zero at the point where
the ball enters the fluid, but, as it descends and speeds up F increases and
when F equals W-U the ball bearing descends with uniform velocity - its
maximum velocity = terminal velocity.
Method:
A large glass tube, sealed at
one end with a rubber bung. is filled with a viscous liquid e.g. oil or
glycerine (the latter I think is the best and easier to clean out). You need at
least a 50 cm depth of liquid.
The glass tube is marked with suitable depth
intervals e.g. every 10 cm.
Small steel ball bearings are carefully
dropped down a thinner glass tube to make the entry into the fluid as smooth as
possible.
The time it takes for the tiny ball to fall
between the distance markers is timed.
You need an accurate stopwatch and
convert the cm or mm of h into m.
(vertical)
velocity (m/s) = d (m) ÷ t
(s)
You should find the steel ball falls relatively slowly
at first and then attains a maximum velocity - the terminal velocity when the
force of the weight of the object is balanced by the resistive forces of
friction as the surface of the ball interacts with the liquid.
The 'theoretical results' are shown in the
velocity-time graph below.
The more viscous the liquid, the
smaller the terminal velocity as the friction forces are increasing.
At first when the object starts to fall
the accelerating force due to gravity, W↓, is greater than the
frictional force slowing it down.
You can tell this from the steep positive
gradient at the start where you get the biggest acceleration.
As the speed increases, friction (force
F↑, drag effect) increases and this reduces the acceleration.
But, as time goes on, the acceleration
decreases (gradient decreasing) because the value of F↑ is increasing.
When all the forces balanced (W-U) = F,
the resultant force is zero and the graph becomes horizontal (at time T)
and the horizontal value is the maximum speed or terminal velocity.
Physics notes index on
acceleration of falling objects, experiments, friction, drag effects,
gravity, terminal velocity
Keywords, phrases and learning objectives for
friction between solid an liquid surfaces
Be able to describe and explain an experiment to
investigate and
determine the terminal velocity of small sphere
falling down through liquid - know the method, observations,
results analysis and calculations and graph.
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