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  • Express mathematically the drag force.
  • Discuss the applications of drag force.
  • Define terminal velocity.
  • Determine the terminal velocity given mass.

Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid). You feel the drag force when you move your hand through water. You might also feel it if you move your hand during a strong wind. The faster you move your hand, the harder it is to move. You feel a smaller drag force when you tilt your hand so only the side goes through the air—you have decreased the area of your hand that faces the direction of motion. Like friction, the drag force    always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects such as bicyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force F D size 12{F rSub { size 8{D} } } {} is found to be proportional to the square of the speed of the object. We can write this relationship mathematically as F D v 2 size 12{F rSub { size 8{D} } α`v rSup { size 8{2} } } {} . When taking into account other factors, this relationship becomes

F D = 1 2 Av 2 , size 12{F rSub { size 8{D} } =0 "." 5Cρ ital "Av" rSup { size 8{2} } } {}

where C size 12{C} {} is the drag coefficient, A size 12{A} {} is the area of the object facing the fluid, and ρ size 12{ρ} {} is the density of the fluid. (Recall that density is mass per unit volume.) This equation can also be written in a more generalized fashion as F D = bv 2 , where b is a constant equivalent to 0 .5 CρA . We have set the exponent for these equations as 2 because, when an object is moving at high velocity through air, the magnitude of the drag force is proportional to the square of the speed. As we shall see in a few pages on fluid dynamics, for small particles moving at low speeds in a fluid, the exponent is equal to 1.

Drag force

Drag force F D size 12{F rSub { size 8{D} } } {} is found to be proportional to the square of the speed of the object. Mathematically

F D v 2 size 12{F rSub { size 8{D} } α`v rSup { size 8{2} } } {}
F D = 1 2 Av 2 , size 12{F rSub { size 8{D} } =0 "." 5Cρ ital "Av" rSup { size 8{2} } } {}

where C size 12{C} {} is the drag coefficient, A size 12{A} {} is the area of the object facing the fluid, and ρ size 12{ρ} {} is the density of the fluid.

Athletes as well as car designers seek to reduce the drag force to lower their race times. (See [link] ). “Aerodynamic” shaping of an automobile can reduce the drag force and so increase a car’s gas mileage.

A two-person team in a bobsled race. The bobsled has an aerodynamic design and smooth runners so it can go as fast as possible.
From racing cars to bobsled racers, aerodynamic shaping is crucial to achieving top speeds. Bobsleds are designed for speed. They are shaped like a bullet with tapered fins. (credit: U.S. Army, via Wikimedia Commons)

The value of the drag coefficient, C size 12{C} {} , is determined empirically, usually with the use of a wind tunnel. (See [link] ).

A model plane is can be seen being tested in a wind tunnel.
NASA researchers test a model plane in a wind tunnel. (credit: NASA/Ames)

The drag coefficient can depend upon velocity, but we will assume that it is a constant here. [link] lists some typical drag coefficients for a variety of objects. Notice that the drag coefficient is a dimensionless quantity. At highway speeds, over 50% of the power of a car is used to overcome air drag. The most fuel-efficient cruising speed is about 70–80 km/h (about 45–50 mi/h). For this reason, during the 1970s oil crisis in the United States, maximum speeds on highways were set at about 90 km/h (55 mi/h).

Questions & Answers

what is Andromeda
smart Reply
what is velocity
Fati Reply
displacement per unit time
Murlidhar
the ratec of displacement over time
Jamie
the rate of displacement over time
Jamie
the rate of displacement over time
Jamie
did you need it right now
Pathani
up to tomorrow
Santosh
i need a description and derivation of kinetic theory of gas
Santosh
pls the sum of change in kinetic and potential energy is always what ?
Faith
i need a description and derivation of kinetic theory of gas
Santosh
did you need it right now
Pathani
A few grains of table salt were put in a cup of cold water kept at constant temperature and left undisturbed. eventually all the water tasted salty. this is due to?
Faith Reply
Aunt Faith,please i am thinking the dissolution here from the word "solution" exposed the grains of salt to be dissolved in the water.Thankyou
Junior
dissolution please
Junior
Aunt Faith,please i am thinking the dissolution here from the word "solution" exposed the grains of salt to be dissolved in the water.Thankyou
Junior
it is either diffusion or osmosis. just confused
Faith
due to solvation....
Pathani
what is solvation pls
Faith
water molecule surround the salt molecules . solute solute attraction break in the same manner solvent solvent interaction also break. as a result solute and solvent attraction took place.
Pathani
okay thanks
Faith
my pleasure
Pathani
what is solvation pls
Faith
water act as a solvent and salt act as solute
Pathani
okay thanks
Faith
its ok
Pathani
due to solvation....
Pathani
water molecule surround the salt molecules . solute solute attraction break in the same manner solvent solvent interaction also break. as a result solute and solvent attraction took place.
Pathani
what is magnetism
Eze Reply
physical phenomena arising from force caused by magnets
Mohammad
is the phenomenon of attracting magnetic substance like iron, cobalt etc.
Faith
what is heat
John Reply
Heat is a form of energy where molecules move
saran
Can you please help me with some questions
Janet Reply
topic-- question
Salman
I know this is unrelated to physics, but how do I get the MCQs and essay to work. they arent clickable.
Jake Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian Reply
why is a body moving at a constant speed able to accelerate
Lilian Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian
because it changes only direction and the speed is kept constant
Justice
Why is the sky blue...?
Star Reply
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
Mike
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
fasawe Reply
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Azummiri Reply
Be raised until its distance from d lens is 27cm find d radius of curvature
Azummiri
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
FlAsH Reply
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
Fatinizzah Reply
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
Ramonyai
why is the north side is always referring to n side of magnetic
sam Reply
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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