Results 1 to 2 of 2

Math Help - vector question in multivariable calculus

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    123

    Question vector question in multivariable calculus

    Question
    If two forces Fsub1 and Fsub2 each of magnitude 10N act on an object from perpendicular directions, then the effect is the same as that of a single force of 10N acting in a direction 45 degrees to each of the forces Fsub1 and Fsub2.

    The answer is false.

    Could you explain to me why the answer is false? If possible , could you please show me the working step? Thank you very much.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Jenny20 View Post
    Question
    If two forces Fsub1 and Fsub2 each of magnitude 10N act on an object from perpendicular directions, then the effect is the same as that of a single force of 10N acting in a direction 45 degrees to each of the forces Fsub1 and Fsub2.

    The answer is false.

    Could you explain to me why the answer is false? If possible , could you please show me the working step? Thank you very much.
    Add the two forces vectorally.

    Let \vec{F}_1 = 10 \hat{i} N and \vec{F}_2 = 10 \hat{j} N. Then
    \vec{F}_{tot} = \vec{F}_1 + \vec{F}_2

    \vec{F}_{tot} = 10\hat{i} + 10\hat{j} N

    which has a magnitude of \left | \vec{F}_{tot} \right | = \sqrt{10^2 + 10^2} = 10\sqrt{2} N, not 10 N.

    Note: The angle mentioned in the problem is correct. I leave that to you to show.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 1st 2009, 04:51 PM
  2. Replies: 1
    Last Post: June 23rd 2008, 10:17 AM
  3. basic multivariable calculus question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 16th 2008, 04:54 PM
  4. A question in Multivariable Calculus
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2006, 07:43 PM
  5. Multivariable Calculus - Vector Integration
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 12th 2006, 10:18 AM

Search Tags


/mathhelpforum @mathhelpforum