Results 1 to 8 of 8

Math Help - Work done by force (vector problem)

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    7

    Work done by force (vector problem)

    Find the work done by a force of magnitude of 3 pounds applied in the direction of
    v =2i + 2j to move an object 5 feet from to (0, 0) (3, 4)?

    We just started learning vectors and nothing seems familiar to me in this problem. Please guide me through step by step how to approach, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jul 2011
    Posts
    5

    Re: Work done by force (vector problem)

    Okay, I got rid of my post because I'm obviously retarded and not as cool as the dude below me. Listen to that dude.
    Last edited by icedtrees; July 30th 2011 at 01:24 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123

    Re: Work done by force (vector problem)

    Quote Originally Posted by icedtrees View Post
    ...
    It seems to me as if there is excessive information given in the question. <-- no

    Work done = Force * Distance <-- This equation is only correct if the direction of the force and the direction of the movement are equal
    Distance = 5 feet
    Force = 3 pound-force

    ...
    Quote Originally Posted by metelskiy View Post
    Find the work done by a force of magnitude of 3 pounds applied in the direction of
    v =2i + 2j to move an object 5 feet from to (0, 0) (3, 4)?

    We just started learning vectors and nothing seems familiar to me in this problem. Please guide me through step by step how to approach, thanks.
    1. Since the direction of the force and the direction of the movement differ by 8.13° the work, which must be done, has to be larger than 15ft-lb.

    2. Google for dot-product of vectors: How it is calculated and how the result can be interpreted.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2011
    Posts
    7

    Re: Work done by force (vector problem)

    We learned how dot product of vectors is calculated: v(dot product)w=||v||*||w||*cos(theta)
    How did you find out that direction of force and the direction of the movement differ by 8.13 degrees? I'm still lost about this problem.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123

    Re: Work done by force (vector problem)

    Quote Originally Posted by metelskiy View Post
    We learned how dot product of vectors is calculated: v(dot product)w=||v||*||w||*cos(theta)
    How did you find out that direction of force and the direction of the movement differ by 8.13 degrees? I'm still lost about this problem.
    1. You have made a sketch I presume (see attachment)

    2. Split the force vector into one vector acting in the dirction of (3, 4) and one which acts perpendicular to this direction (a solid would be lifted off).

    3. Use the slopes of the 2 given vectors to determine the included angle.
    Attached Thumbnails Attached Thumbnails Work done by force (vector problem)-wirksamekraft.png  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jul 2011
    Posts
    7

    Re: Work done by force (vector problem)

    Quote Originally Posted by earboth View Post
    1. You have made a sketch I presume (see attachment)

    2. Split the force vector into one vector acting in the dirction of (3, 4) and one which acts perpendicular to this direction (a solid would be lifted off).

    3. Use the slopes of the 2 given vectors to determine the included angle.
    I'm still not seeing how to achieve the final answer. I know I need length of Force vector and length of direction vector and angle between them. SO is 8.13degrees is the angle between f and d?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2011
    Posts
    2

    Re: Work done by force (vector problem)

    Quote Originally Posted by metelskiy
    I'm still not seeing how to achieve the final answer.
    The work done by a (constant) force F along a vector d is given by (dot product):
    W = F d = Fx * dx + Fy * dy (in two dimensions).
    Fx, Fy, dx, dy - are components of F and d.
    In your problem:
    F = 3 pounds (the magnitude)
    d = 5 feet (the magnitude)
     F_x = F_y (since the direction of F is: 2i + 2j)
     d_x / d_y = (3 - 0) / (4 - 0) = 3/4    -->  d_x = (3/4) d_y.

    On the other hand we know that:
    d_x^2 + d_y^2 = d^2
    F_x^2 + F_y^2 = F^2

    From the first equation (substitute dx = (3/4) dy) you get: dy = 4 feet.
    Hence: dx = 3 feet. From the second equation you get: Fx = Fy = 2.12.
    You can now use these results in the equation for W and you get:
    W = 14.8 (pound * feet).
    (I am not familiar with these units, we use SI units).
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: Work done by force (vector problem)

    Quote Originally Posted by metelskiy View Post
    Find the work done by a force of magnitude of 3 pounds applied in the direction of
    v =2i + 2j to move an object 5 feet from to (0, 0) (3, 4)?

    We just started learning vectors and nothing seems familiar to me in this problem. Please guide me through step by step how to approach, thanks.
    for two vectors expressed as components ...

    \vec{u} = a\vec{i} + b\vec{j}

    and

    \vec{v} = c\vec{i} + d\vec{j}

    the dot product is simply ...

    \vec{u} \cdot \vec{v} = ac + bd



    change the force vector to component notation ...

    \vec{F} = \frac{3}{\sqrt{2}} \vec{i} + \frac{3}{\sqrt{2}} \vec{j}

    the displacement vector was given ...

    \vec{r} = 3\vec{i} + 4\vec{j}

    finally ...

    \vec{F} \cdot \vec{r} = \frac{3}{\sqrt{2}} \cdot 3 + \frac{3}{\sqrt{2}} \cdot 4 = \frac{21}{\sqrt{2}} \, \, ft-lbs
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simple force vector problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 12th 2012, 01:11 AM
  2. 3d force vector problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: August 30th 2010, 07:31 AM
  3. Another work and force problem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: March 5th 2009, 01:06 PM
  4. Replies: 2
    Last Post: February 7th 2009, 06:14 AM
  5. Work done by a force field (Vector Fields)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 22nd 2007, 04:47 PM

Search Tags


/mathhelpforum @mathhelpforum