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Homework Help: Friction proportional to velovity. Help please

  1. Oct 15, 2009 #1
    1. A 1000kg boat is traveling across a lake when its engine is shut off. The magnitude of the frictional force between the water and the boat is proportional to the boat's speed (proportionality constant is 70) . Find the time it takes the boat to slow to one half its speed when the engine was shut off.

    2. We have to solve this problem using newton's second law: F=ma

    3. I thought about this problem for over a week now, and I really need all the help I can get!
  2. jcsd
  3. Oct 15, 2009 #2


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    first write the force as a constant times velocity, then equate with the acceleration equation you gave...

    then do you know how to integrate?
  4. Oct 15, 2009 #3
    yes i know how to integrate but im not quiet sure how to develop the integration. what should the variable be ?
  5. Oct 15, 2009 #4
    what did you get for the sum of your forces
  6. Oct 15, 2009 #5
    do you think there is an f app? or just friction force moving the boat. like a car on a road? i think it would be the same situation, do you?
  7. Oct 15, 2009 #6
    i think we use vfinal = v initial + at. as v/2= v + at. and a = (sum of forces divided by mass). i also think im in your class.
  8. Oct 15, 2009 #7
    yeah i think there exists only a friction force. so the sum of forces would be : -f=ma

    but the problem is the acceleration is not constant because the f is not constant
  9. Oct 15, 2009 #8
    so t = (v/2 + v)(1/a). and a = the 1st integral of v. and v= (frictional force/70) (is that right) but how do we get units in? and then frictinal force is the x component of the forces.... but is there an f app?
  10. Oct 15, 2009 #9


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    You said you know how to integrate so I assume you have taken Calculus. What would the force and acceleration not being constant bother you?

    Use ma= f. What does that look like in this case? What is f? Do you understand that a= dv/dt?
  11. Oct 15, 2009 #10
    why didnt i think of that earlier. so dv/dt= -70v

    divide both sides by v. then integrate one side in terms of dv and the other side in terms of t .
    Thanks for the guidance !!
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