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!

Terminal Velocity of a Ball Given Velocity and Acceleration

  1. Dec 17, 2012 #1
    1. The problem statement, all variables and given/known data
    A steel ball is dropped from a great height. When its velocity is 20m/s its acceleration is 7.35 m/s^2. What is it's terminal velocity?


    2. Relevant equations
    V - V_o = at
    F = ma
    (Air resistance isn't given, so I don't think drag force can be used.)


    3. The attempt at a solution
    1. I know the final net force must equal 0.
    2. The answer is 40 m/s, but I am unsure of how to get this answer.
    3. I tried calculating drag force and taking the limit as time approaches infinity, but I must be making an error.
     
  2. jcsd
  3. Dec 17, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    How about an assumption such as air resistance is proportional to velocity or perhaps it's proportional to v2 .
     
  4. Dec 17, 2012 #3
    Well I know air resistance is proportional to velocity, but I don't see how I can find air resistance without knowing surface area, mass, density, temperature, etc.
     
  5. Dec 17, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    bv = mg - ma .

    You can find b/m for the given conditions. Then, what does v have to be if a = 0 ?


    BTW: Are you sure about the answer of 40 m/s ?
    If so, then I conclude that the air resistance follows a different law .​
     
  6. Dec 17, 2012 #5
    v = mg/b

    1. What does b stand for?
    2. I'm sure it is 40 m/s. I came up with multiple answers, but they were all smaller than 40 m/s.
    3. They don't give a value for mass. (If I understand what b stands for, I may be able to figure it out.)
     
  7. Dec 17, 2012 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The forces acting on the falling ball are gravity and air resistance, which is proportional to velocity and opposite to it.
    Writing up Newton's second law, F=ma=mg-kv. The acceleration is
    a=g-(k/m) v.
    You know that a=7.35 m/s2 when v=20 m/s. Plug in: you will find k/m.

    The ball will reach the terminal velocity when the two forces - gravity and air resistance - cancel, that is, the acceleration is zero: g-(k/m) v=0. You know k/m, how big is v?
    If the given result is 40 m/s then the air resistance is taken proportional to v2.
    Do the same procedure, replacing v by v2.
     
    Last edited: Dec 17, 2012
  8. Dec 17, 2012 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    b is simply a constant of proportionality.

    If you assume that the drag force (air resistance) is proportional to v2, you will get 40 m/s for your answer.

    This whole thing is essentially just working with proportiona.
     
  9. Dec 17, 2012 #8
    Thank you so much! I forgot that air resistance can be proportional to v and v^2.
     
  10. Dec 17, 2012 #9
    a=g-kv, a is a function of veolcity(assumption) k is a constant and then we can find k, by using given data.

    then find a=0, which kv=g, you can find out v which is terminal veolcity.
     
  11. Dec 17, 2012 #10

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That works too.

    In the given problem it appears that acceleration, as well as force, is proportional to v2 .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Terminal Velocity of a Ball Given Velocity and Acceleration
Loading...