Projectile with Air resistance problem

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Homework Help Overview

The problem involves a projectile experiencing air resistance that is proportional to its speed. The context includes determining the constant of proportionality using terminal velocity and formulating the equation of motion for a projectile thrown vertically upwards.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between gravitational force and air resistance, questioning the signs and dimensions of the forces involved.
  • Some participants attempt to derive the constant k and express the equation of motion, while others express confusion about the correct setup of forces and the implications of terminal velocity.
  • Questions arise regarding the direction of forces acting on the projectile and the correct interpretation of acceleration in the context of the problem.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants have attempted to clarify their understanding of the forces and their signs, while others are still grappling with the dimensional consistency of their equations. Guidance has been offered regarding the need to reconsider the signs and units in their equations.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on understanding the physics concepts rather than simply arriving at a solution.

  • #31
Guys! I think I've got the answer, I'm just going to upload it now. PLEASE BE RIGHT! :nb)
 
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  • #32
Part a) F=mg and F=kv

Therefore mg=kv and v=19.6 (terminal velocity)
k = mg/v
k = mg/19.6

Part b)

Equation of motion -> -mg-kv = ma
(Sub in k =mg/v)
-2mg = ma
a = -2g
dv/dt = -2g
v = -2gt

Or maybe instead of subbing in k=mg/v It should have been mg/19.6?

Voila! Surely that's correct right?!
 
Last edited:
  • #33
ZenchiT said:
Part a) F=mg and F=kv

Therefore mg=kv and v=19.6 (terminal velocity)
k = mg/v
k = mg/19.6

Part b)

Equation of motion -> -mg-kv = ma
(Sub in k =mg/v)
-2mg = ma
a = -2g
dv/dt = -2g
v = -2gt

Or maybe instead of subbing in k=mg/v It should have been mg/19.6?

Voila! Surely that's correct right?!
For the value of k, as I mentioned, if you are going to put numbers representing dimensioned quantities in the answer then you also need units. You don't need units for m and g since symbolic variables encapsulate the physical quantity independently of units. So you just need the right units for the 1/19.6 factor. What would those be?
For part b), you have used the same symbol v for two different velocities, the terminal velocity and the initial velocity. So, yes, you should have substituted mg/19.6 (with units) for k.
 
  • #34
haruspex said:
For the value of k, as I mentioned, if you are going to put numbers representing dimensioned quantities in the answer then you also need units. You don't need units for m and g since symbolic variables encapsulate the physical quantity independently of units. So you just need the right units for the 1/19.6 factor. What would those be?
For part b), you have used the same symbol v for two different velocities, the terminal velocity and the initial velocity. So, yes, you should have substituted mg/19.6 (with units) for k.
Would it have N as the units because it has the same dimensions as force?
 
  • #35
ZenchiT said:
Would it have N as the units because it has the same dimensions as force?
The problem is the lack of units for the 19.6. What units should that have? So what units will the 1/19.6 have?
 
  • #36
haruspex said:
The problem is the lack of units for the 19.6. What units should that have? So what units will the 1/19.6 have?
m/s^-1 as its terminal velocity?

Thank you for the amount of help you've given me!
 
  • #37
ZenchiT said:
m/s^-1 as its terminal velocity?

Thank you for the amount of help you've given me!
m/s, or ms-1 (but not m/s-1) is right for the 19.6. So what should it be for 1/19.6?
 
  • #38
ZenchiT said:
Part a) F=mg and F=kv

Therefore mg=kv and v=19.6 (terminal velocity)
k = mg/v
k = mg/19.6

Part b)

Equation of motion -> -mg-kv = ma
(Sub in k =mg/v)
-2mg = ma
a = -2g
dv/dt = -2g
v = -2gt

Or maybe instead of subbing in k=mg/v It should have been mg/19.6?

Voila! Surely that's correct right?!
Well, surely that is incorrect! (sorry to rain on your parade). The initial velocity is given as +6 m/s and your formula says initial velocity = 0!
Your equation of motion is correct but you are not solving the ODE correctly. Hint: try separation of variables.
 

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