1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Terminal Velocity and Bouyancy - F = kv

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data

    A rock of mass 0.400 kg is released from the surface and sinks in the ocean. As the rock descends it is acted upon by three forces: gravity, buoyancy, and drag. The buoyancy is an upward force equal to half its weight. Drag from the water can be modeled by F = kv, where k = 0.650 kg/s.

    (a) Determine the terminal speed of the sinking rock.

    (b) Determine its depth, speed, and acceleration 1.50 seconds after it is released.

    (c) At what depth will it be at 99.0% of its terminal speed?

    2. Relevant equations

    Net force (vertical), F = ma, F = kv

    3. The attempt at a solution

    The solution to a) was easy enough.

    Fnet = mg + FB + Fdrag

    Fnet = -3.92 N + 1.96 N + Fdrag = 0 N (at terminal speed)

    Fdrag = 1.96 N = 0.650 kg/s *vt

    vt = 3.02m/s.

    b) For calculating the depth, speed, and acceleration, I think I need to integrate the function of the net force with respect to time to get the equations for velocity and position. But I have not had much luck doing so because I am rusty on my integration.

    The equation for the acceleration is

    a(t) = -4.90 N + 1.63s-1 *v(t)

    so I'm thinking

    dv/dt = -4.90 N + 1.63s-1 *dx/dt

    but then I get something like

    dv = -4.90 N dt + 1.63s-1 *dx

    and I don't know what to do with dx?

    c) I'm thinking the answer for this part will be easy enough once I have the answer to b...
    Last edited: Sep 28, 2009
  2. jcsd
  3. Sep 28, 2009 #2
  4. Sep 29, 2009 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Instead of dx/dt, try leaving that as v in this equation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Terminal Velocity Bouyancy
Find the terminal voltage Vab
Dimensional analysis problem