Resistive Forces, Drag, Terminal Velocity, Example - Physics (Mechanics)

Drag force and terminal velocity are linked because an object reaches its terminal velocity when the upward drag force becomes equal to the downward force of gravity, resulting in zero net force and constant speed. The drag force is a resistance force that increases with velocity, while gravity is a constant downward force. The equation for terminal velocity (\(v_{t}\)) is derived by setting these two forces equal to each other and solving for velocity, yielding the formula \(v_{t}=\sqrt{\frac{2mg}{\rho AC_{d}}}\).

💡Drag force
• Drag force (\(F_{d}\)) is the force that opposes an object's motion through a fluid, like air.
• It depends on the fluid's density (\(\rho \)), the object's cross-sectional area (\(A\)), and the object's velocity (\(v\)), as well as a drag coefficient (\(C_{d}\)).
• The formula for drag force is \(F_{d}=\frac{1}{2}\rho Av^{2}C_{d}\).

💡Terminal velocity
• Terminal velocity is the maximum speed an object can attain when falling.
• This occurs when the net force on the object is zero, meaning the upward drag force exactly balances the downward force of gravity (weight).
• At this point, the object stops accelerating and falls at a constant speed.
• The equation for terminal velocity (\(v_{t}\)) is derived by setting the drag force equal to the weight (\(mg\)) and solving for \(v\):
⚬\(mg=\frac{1}{2}\rho Av_{t}^{2}C_{d}\)
⚬\(v_{t}=\sqrt{\frac{2mg}{\rho AC_{d}}}\)

💡Worksheets are provided in PDF format to further improve your understanding:
• Questions Worksheet: https://drive.google.com/file/d/1pD8nvbATuuSwvLF_nueB2KSc685rnQKr/view?usp=drive_link
• Answers: https://drive.google.com/file/d/1SYKZihxmNSOL5K4ZQI663PIthUBqC9hs/view?usp=drive_link

💡Chapters:
00:00 Drag force
01:49 Worked example

🔔Don’t forget to Like, Share & Subscribe for more easy-to-follow Calculus tutorials.

🔔Subscribe: https://rumble.com/user/drofeng
_______________________
⏩Playlist Link: https://rumble.com/playlists/d3cTgspk0Ro
_______________________
💥 Follow us on Social Media 💥
🎵TikTok: https://www.tiktok.com/@drofeng?lang=en
𝕏: https://x.com/DrOfEng
🥊: https://youtube.com/@drofeng