3. Acceleration, friction, drag effects and terminal velocity
Doc Brown's Physics Revision Notes
Suitable for GCSE/IGCSE Physics/Science courses or their equivalent
This page will help answer questions such as ...
What causes the drag effect in fluids?
What is air resistance? What has it got to do with friction?
What do we mean by 'terminal velocity?
Describe an experiment to illustrate terminal velocity?
How and why does a parachute work?
Friction and motion (solid surface contact and objects moving through a fluid)
You first appreciate friction when two solid surfaces rub together. When you pull a heavy object across the floor you experience the resistive force between the two surfaces. This resistive force is called friction and is caused by the atoms of the two surfaces bumping in to each other from opposite directions. The moment you stop applying a force, the dragged object ceases moving immediately.
The force of friction always acts in the opposite direction to an object's movement and it can involve ANY type of surface contact effect.
If an object is moving at a steady speed the thrust or driving force (engine or gravity etc.) is being balanced by the opposing force of friction.
If a moving object has no thrust force acting on it, then it will always slow down and come to a halt e.g. on a level road, if you take your foot of the accelerator, the car will eventually come to a halt as the resistive forces act against the car's forward motion. The total friction effects will bring the car to a halt.
How does speed affect the drag effect and how can we reduce it?
In these next examples you are reducing the loss from a kinetic energy store to the surrounding air/water thermal energy store - the destination of most wasted or dissipated energy.
The faster an object moves through a fluid the greater the rate of particle collisions between the object's surface and the fluid (e.g. air or water.
To reduce the drag effect its not always easy to reduce the surface area, hence reduce friction, but you can design the shape of an object to allow the fluid to flow more easily across the surface.
There are times when we wish to increase the drag effect - see parachuting further down the page.
Terminal velocity (balancing forces - rolling down hill and objects falling downwards under gravity in fluids)
(a) Trolley and running board
If you set up a running board and let an object like a trolley roll down it, the 'diluted' effect of gravity gets the object to roll down the incline. At first it speeds up as the force of gravity exceeds the friction of the trolley movement. The force of gravity is constant, but as the speed of the trolley increases, so does the effect of friction e.g. the wheels and axle, wheel contact with running board.
You can actually demonstrate this with a ticker tape timer experiment (results illustrated above). You attach a long piece of ticker tape to the trolley and the tape passes through a little 'ticker tape' machine that stamps a dot onto the tape every fraction of a second. The distance between the dots gives you the relative speed. At the start the dots are close together at the lowest speeds, but as the trolley speeds up the distance between the dots increases. Eventually the dots are evenly spaced at their maximum distance apart showing the terminal velocity of the trolley was reached (first at time T).
I presume you can do a similar experiment with a series of light gates to show the same effect, not as much fun though!
The above example illustrate the idea of terminal velocity, but next we consider objects falling down in a fluid due to the force of gravity (air or a liquid).
(b) Small spheres falling down through a liquid
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.
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 should find the 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.
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 that at first 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.
The complex behaviour of a parachutist
This is an interesting case because it involves an acceleration, a deceleration and two terminal velocities!
speed/velocity-time graph for a parachute descent
weight due to gravity W↓ and the drag effect due to air resistance D↑ (I'm ignoring the minor effect of upthrust U↑)
force vectors operating in the jump
(1) The parachutist jumps out of the aircraft and immediately accelerates due to gravity (weight force W↓), but the parachute is not opened yet, so the parachutist is in free fall!
Between (1) to (3) acceleration is taking place, but although W↓ is constant, the drag force D↑ due to air friction (air resistance) is increasing, so the acceleration is decreasing (gradient decreasing).
At (3) the terminal velocity is first reached when the drag force D↑ = weight W of the parachutist.
Between (3) to (5) the descent continues at the (1st) constant terminal velocity because the resultant force is zero.
At (5) the parachutist opens the parachute to increase air resistance. The wide area brushing through the air produces a massive air resistance (friction) drag effect so D↑ massively increases, and is far greater than W, so rapid deceleration immediately takes place.
Between (5) to (7) the deceleration continues and as the parachutist decreases in speed, so the drag forces decreases too.
At (7) the drag force once again equals the weight force and the parachutist attains a 2nd, somewhat slower, terminal velocity.
Between (7) and (8) the parachutist descends far more slowly with constant speed to land safely at ~15 mph, again the resultant force is zero.
Terminal velocity experiments
You do simple experiments with toy parachutes attached to a weight to determine their terminal velocities.
Other terminal velocity or otherwise situations!
Some 'actual' and 'thought' experiments.
You need to consider the W (weigh, depends on local gravitational field strength), U (upthrust) and F (friction, drag) forces described in the ball bearing - liquid filled tube experiment and the four objects illustrated above.
(a) When the first astronauts landed on the moon they carried a beautifully simple experiment.
(b) If you drop the feather and hammer simultaneously on Earth the feather takes much longer to fall to the ground because it has a relative greater surface area/mass ratio greatly increasing drag effect.
(c) If you simultaneously dropped the dense pool ball and light hollow plastic ball with the same radius (giving same surface area) the pool ball will hit the ground before the lighter hollow plastic ball. This is because the greater weight of the pool ball will overcome the drag effect of air resistance more than the less 'weighty' plastic ball and will accelerate at a greater rate.
(d) If you drop any object (safely!) from a tall building on Earth, it will always achieve a terminal velocity due to the friction effect of air resistance.
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