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Forces and Motion 3.4 Determining the terminal velocity of a small sphere falling down through a liquid

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INDEX for physics notes on acceleration of falling objects, experiments, friction, drag effects, gravity, terminal velocity


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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Physics notes index on acceleration of falling objects, experiments, friction, drag effects, gravity, terminal velocity

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