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Motion in the Presence of Velocity-Dependent Resistive Forces

  1. Oct 5, 2007 #1
    1. The problem statement, all variables and given/known data

    A small piece of Styrofoam packing material is dropped from a height of 2.10 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g - bv. After falling 0.400 m, the styrofoam effectively reaches terminal speed, and then takes 4.90 s more to reach the ground.

    (a) What is the value of the constant b?
    (b) What is the acceleration at t = 0?
    (c) What is the acceleration when the speed is 0.150 m/s?

    2. Relevant equations

    a = g - bv
    R = -bv
    Terminal speed = g/b

    3. The attempt at a solution
    I'm, ah.. very stuck on this.
    I know for sure (b) is 9.8 m/s (down) because when t = 0 v = 0, and thus the acceleration is just the gravity constant
    I thought I could using vf^2 = vi^2 + 2a(yf-yi) or y_f = y_o + at to find the acceleration... but those equations don't seem to fit that well.
    If have a feeling if I knew (a) I could find (c) but I'm just lost.. especially without a mass or terminal velocity.

    I appreciate any help~
     
  2. jcsd
  3. Oct 6, 2007 #2

    hotvette

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    Homework Helper

    Since you know the terminal speed, the following will allow you to calculate b:

    After falling 0.400 m, the styrofoam effectively reaches terminal speed, and then takes 4.90 s more to reach the ground.

    By the way, how did you determine the terminal speed in relevant equations?
     
    Last edited: Oct 6, 2007
  4. Oct 6, 2007 #3
    Ah.. um, thanks for your help~ but I found the answer a while ago and forgot I posted this
    ^_^
    I appreciate your help though~
     
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