1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sunday night physics problems

  1. Jan 27, 2008 #1
    Sunday night physics problems :(

    Alright, so I'm supposed to find the displacement equation for a particle fired vertically under a constant gravitational field, where the resisting force is proportional to the instantaneous velocity of the particle. Here's where I'm at:

    Fup = ma; Fdown = -mg - kmv; Fnet = (ma) + (-mg - kmv) // Where k is a constant

    ma = (ma) + (-mg - kmv) // Force = Fup + Fdown
    dv/dt = -g - kv // m's cancel, differentiate wrt v
    dv * 1/(-g -kv) = -dt

    // Integrating...
    1/k ln(kv+ g) = -t + c0 // Where c0 represents initial velocity
    ln(kv + g) = -tk + kc0
    kv + g = e^(-tk + kc0)
    v = [ e^(-tk + kc0) - g ] / k

    Integrate wrt t, to obtain position ( v(t) )
    v(t) = -g/k + -------> ???? <----------

    The answer is supposed to simplify to: v(t) = [-g/k] + [ (kc0 + g) / k] * e^(-kt)
    I have no idea how. I have no idea where the g in the second term came from in the first place. Thanks ahead of time!
     
  2. jcsd
  3. Jan 28, 2008 #2
    you have Fdown = -mg - kmv; (k a constant), so I guess k will have units [1/seconds]?

    also, you wrote: dv/dt = -g - kv // m's cancel, differentiate wrt v

    I can see the m's cancel, but then you have (before differentiating)

    a = a + (-g-kv)

    but a IS dv/dt, so i don't know how you can get:
    dv/dt = -g - kv // m's cancel, differentiate wrt v

    AFTER differentiating wrt v... (also, dont u usually diff wrt to t??)
     
  4. Jan 28, 2008 #3
    Yeah, in order for the units to match up i believe k would technically need to have units of 1/t.

    And yes, a is dv/dt. So instead of writing:
    a = ..., I've substituted dv/dt = ...

    This way, we can say dv = blah (partial derivative dt)
    Integrating both sides, we then obtain the velocity equation.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Sunday night physics problems
  1. A Physics problem (Replies: 5)

  2. Physics problems (Replies: 4)

  3. Physic Problem (Replies: 3)

  4. Physic Problem. (Replies: 3)

  5. A physics problem. (Replies: 5)

Loading...