Results 1 to 2 of 2

Thread: Work done moving against a force

  1. #1
    Mar 2007

    Work done moving against a force

    Currently stuck on the following question:

    A cyclist traveling on a straight road at 20km/h is subject to wind resistance proportional to the square of the wind speed. When a wind of 40km/h develops blowing in the direction perpendicular to the road, the cyclist must increase power output to maintain constant speed. By what factor must the cyclist increase power to maintain constant speed in the cross wind?

    The answer is root 5, but I don't know how to attempt the question. I did manage to work out that the resultant velocity of the cyclist is 44.7km/h at an angle of 63 degrees to the direction of travel, but I don't know what to do after that.

    Help would be hugely appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Oct 2008
    First, lets find power output of the cyclist when there is no wind:
    With the wind blowing we find that the speed of wind which the cyclist feels has value V equal to
    and makes an angle a with the vector of cyclist'sdisplacement:$\displaystyle cos(a)=Vc/V $
    Power output with the wind present is thus
    Let me explain a little: the force of the wind is proportional to V^2 but work done is $\displaystyle W=\vec F.\vec r =F.r.cos(a)$. where $\displaystyle \vec r $ is the vector of displacement. Power is therefore: $\displaystyle P_w=dW/dt=F.(dr/dt).cos(a) = F.Vc.cos(a)$
    You are sked to compute $\displaystyle P_w/P_0$. If You do the calculations you'll get required answer Sqrt[5].
    Good luck
    Attached Thumbnails Attached Thumbnails Work done moving against a force-cyclist.bmp  
    Last edited by katastrofa_nadfioletu; Oct 27th 2008 at 12:50 AM. Reason: latex error :(
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Nov 16th 2010, 11:24 PM
  2. Work Done By A Force
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Aug 23rd 2009, 09:43 PM
  3. About Work: Moving Particle
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 31st 2009, 03:13 PM
  4. Another work and force problem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: Mar 5th 2009, 01:06 PM
  5. c curve,work done by force........
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Jan 17th 2007, 11:33 AM

Search Tags

/mathhelpforum @mathhelpforum