Drag (Apparent weight, friction, drag)

Drag D

• the air exerts this force on objects moving through it

• this force can be modeled by

  • D ≈ ¼ pAv²

• this force points in the opposite direction as motion

drag force points in the opposite direction as motion

remember: drag force points in the opposite direction as motion

p 

• 1.3 kg / m³

• the density of air 

p = 1.3 kg / m³ and is the density of air 

what is p in the drag force formula? 

A

• the objects cross sectional area 

the objects cross sectional area 

what is A in the drag force formula?

V

• the objects speed

the objects speed

what is V in the drag force formula?

D ≈ ¼ pAv²

what is the drag force formula to find the magnitude of the drag?

the faster you go and the wider you are, the more drag you feel

remember: the faster you go and the wider you are, the more drag you feel 

at low speeds, the drag force is small

Remember: at low speeds, the drag force is small

• Fnet ≈ mg [downwards] (Fnet is approx. = the weight)

• a ≈ g [downwards]

• object will start falling faster and faster but as speed increases, so does the drag force  

as speed increases, drag increases

remember: as speed increases, drag increases

terminal speed

• when the object reaches a speed such that:

  • D = W (drag = weight — equal and opp so cancel each other out)

  • no longer a Fnet on the object (Fnet = 0)

  • object stops accelerating

  • object continues to fall at a constant speed

how to solve for terminal speed

• set D = w and solve for v

• ¼ pAv² = w & w = mg

• ¼ pAv² = mg —> v = √4mg/pA

v = √4mg/pA 

equation for terminal speed

the heavier you are, and the smaller your cross-sectional area, the faster you will fall

remember: the heavier you are, and the smaller your cross-sectional area, the faster you will fall (bc mass is in numerator so large mass = large speed and area is in denom. so small area = large speed)