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Calculate the angle between the displacement vector and the force vector

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data

    A force F = 8i-3i N acts on a particle that undergoes a displacement Δr = 2i + j m.
    (b) What is the angle between F and Δr? (state your answer to three significant figures)

    2. Relevant equations

    Angle = cos-1 (A.B/ AB)

    3. The attempt at a solution

    W=13.1 J
    AB= 8.5*2.23= 19
    cos-1 (13.1/19)= 46.4
     
  2. jcsd
  3. Mar 25, 2012 #2
    I will assume that the force is [itex]F=8\hat{i}-3\hat{j}[/itex]

    the dot product between F and delta-r:
    [itex](8,-3)\cdot (2,1) = 8\cdot 2 + (-3)\cdot 1 = 13[/itex]
    the norm of F:
    [itex]||F||=\sqrt{8^2 +3^2}[/itex]
    norm of delta-r :
    [itex]||\Delta r|| =\sqrt{1^2+2^2}[/itex]
    I got 47.12 degrees but it seems you have used different conditions :/
     
  4. Mar 25, 2012 #3
    I got 47.121 another time when I did not round, but even that gave me a wrong answer L: I am not sure what's wrong
     
  5. Mar 26, 2012 #4
    If you are sending it to some kind of online checking system:
    a. Check to see if they want it in radians.
    b. Check if all of the starting conditions are correct.
    c. Take into consideration that they make mistakes too.
     
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