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Differential Eq falling object + friction

  • Thread starter iloveannaw
  • Start date
  • #1
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Homework Statement


A point mass m falls from rest through a height h. The frictional force is given by [tex]-\gamma \dot{z}[/tex] and gravity by [tex]-mg[/tex].

Give the 'equation of motion' (differential equation) for the height z(t).


The Attempt at a Solution



[tex] \ddot{z} = -g - \frac{\gamma}{m} \dot{z}[/tex]

I thought about integrating then rearranging:

[tex]\Rightarrow \dot{z} = -gt - \frac{\gamma}{m}z +c_{1}[/tex]

[tex]\Rightarrow z(t) = - \frac{m}{\gamma} (\dot{z} + gt + c_{1})[/tex]

The question the asks what kind of differentional eq. this is and asks the student to make the following substitution:

[tex]\dot{z}(t) = v(t)[/tex]

and asks what kind of equation it is now! Well I haven't got a clue what its is on about. I assume something like [tex]s = ut +\frac{1}{2}at^{2}[/tex] should come out. Have to hand this in tomorrow so please help!
 

Answers and Replies

  • #2
tiny-tim
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hi iloveannaw! :smile:
The question the asks what kind of differentional eq. this is and asks the student to make the following substitution …
it means substitute in the original equation (the one beginning z'') :wink:
 
  • #3
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thanks, so you think I should start by working from [tex]\frac{dv}{dt} = -g -\frac{\gamma}{m}v[/tex] ?

I have already done that, but the question is quite clear it asks for the diff. eq. in terms of [tex]\dot{z}(t)[/tex] and then asks the student to make substitution. And it also asks for type of differential equation before and after.
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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that is the differential equation in terms of z' (your other one was in terms of z' and z) …

and you should be able to solve it :smile:
 

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