Force vector on falling object to determine terminal velocity and to graph it

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SUMMARY

The discussion focuses on calculating terminal velocity for a falling object using the equation Vt = √(2mg/CρA) and the force equation F = ma. However, it is clarified that the relevant equation for part (b) is FR = -kv, which is crucial for determining the correct approach. Participants emphasize the importance of understanding the relationship between force and velocity in this context, particularly for graphing the results in part (c).

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the concepts of terminal velocity and drag force
  • Knowledge of the variables involved: mass (m), gravity (g), and drag coefficient (C)
  • Ability to graph mathematical functions and interpret their behavior
NEXT STEPS
  • Study the derivation of the terminal velocity equation Vt = √(2mg/CρA)
  • Learn about the drag force and its impact on falling objects, specifically the equation FR = -kv
  • Explore graphing techniques for visualizing motion under the influence of drag
  • Investigate numerical methods for solving differential equations related to motion
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of falling objects and the effects of drag on motion.

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Homework Statement



ScreenShot2011-12-03at11613PM.png

k: constant
v: velocity
m: mass
g: gravity
View attachment qw.pdf

Homework Equations



Vt= √(2mg/CρA)
F=ma

The Attempt at a Solution


part a.
ScreenShot2011-12-03at11640PM.png

View attachment w.pdf
part b.
ScreenShot2011-12-03at11518PM.png

View attachment b.pdf
I do not know if i am doing this right and i do not understand how to do part c. If you know how to do this please explain
 
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Welcome to the forum! You've got part (a) correct.

But for part (b), I don't think the equation Vt= √(2mg/CρA) is relevant. You were explicitly given that FR=-kv, so this is the equation you should be using. In fact, I think you got the answer for (b), before you started using that other equation for the terminal velocity.

Part (c) is a bit trickier. You could either roughly draw what happens, or explicitly calculate the form of the graphs, then draw them.
 

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