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Found in: Page 186

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

Two expressions were used for the drag force experienced by a moving object in a liquid. One depended upon the speed, while the other was proportional to the square of the speed. In which types of motion would each of these expressions be more applicable than the other one?

When the object is moving through a liquid medium, such as water or another viscous liquid, we will apply the Stokes law, which states that the drag force is proportional to velocity.

See the step by step solution

Definition of Force

A force is a factor that can impact an object's motion. A force can cause a mass item to accelerate (e.g., from a standstill).

Determining the first drag force expression

In general, drag force is proportional to the square of velocity, but in other cases, such as when the object is small, moving slowly, or in a denser medium than air, drag force is related only to the velocity, not the square of velocity.

Animal living on land, if it is not very small, experiences drag force due to air which is proportional to square of the velocity and it is given by

${\text{F}}_{\text{s}}\text{=}\frac{\text{1}}{\text{2}}{\text{pCAv}}^{2}$ …………………………… ( 1 )

Where, ρ is density of medium i.e., air, C is drag coefficient, A is exposed area of the body and v is velocity.

If the object is moving in air and has a high cross-sectional area, we will utilise the quadratic expression, in which the drag force is exactly proportional to the square of velocity.

Determining the second drag force expression

The quadratic dependence of air intake on velocity does not hold when the element is small and traveling slowly, or when it is in a medium denser than air. Then the drag force and velocity are directly proportional to each other.

${F}_{s}=6\pi \eta r\nu ...........\left(2\right)$

where r is the radius of the body, $\eta$ is the viscosity of the fluid, and v is the velocity of the body, Stokes' law applies.

When comparing creatures that live on land with those that live in water (which is denser than air), equation (1) will only be applicable for enormous species like big fish, dolphins, and even massive whales that have streamlined shapes to lessen drag effects.