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AP physics exam question

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  1. May 4, 2014 #1
    1. The problem statement, all variables and given/known data
    I have this packet and one of the questions state:
    The constant force F with components Fx=3N and Fy=4N act on a body while that body moves from the point P (x=2 m, y=6 m) to the point Q (x=14 m, y=1 m). How much does the force do on the body during this process?

    the options are as follows:
    a. 16 J
    b. 30 J
    c. 46 J
    d. 56 J
    e. 65 J

    2. Relevant equations

    I have the equations to find energy:
    kinetic: K=(1/2)mv^2
    gravitational: mgh

    3. The attempt at a solution

    but I'm not sure if I'm missing something. So far I have figured out you need to keep the x and y components seperated and calculate each but I think I'm doing something wrong. I've gotten to Work = Force * cos(t) * change in distance but I'm just confusing myself. Help?

    Also, I am taking the Physics: C Mechanics exam, what are some topics and questions that would help me prepare for it?
     
    Last edited: May 4, 2014
  2. jcsd
  3. May 4, 2014 #2
    Do you know what a dot product is?
     
  4. May 4, 2014 #3
    I don't know what a dot product is other than its used in calculus
     
  5. May 4, 2014 #4
    It is quite a simple operation, I am sure you must have come across it in high school maths, but for a refresher...

    Dot product is defined as:
    [itex]
    a_{i} b_{j}\delta_{ij}=a_{i} b_{i}[/itex]

    Example:
    [itex]
    \vec{a} = (2\hat{e}_{1} +2\hat{e}_{2} + 2\hat{e}_{3} )
    [/itex]
    [itex]
    \vec{b} = (0\hat{e}_{1} +2\hat{e}_{2} + 4\hat{e}_{3} )
    [/itex]

    then
    [itex]
    a_{i} b_{j}\delta_{ij}= ( 2 \bullet 0) + (2 \bullet 2) + (2 \bullet 4)
    [/itex]
    [itex]
    a_{i} b_{j}\delta_{ij}= 12

    [/itex]
     
  6. May 4, 2014 #5
    You have the right formula. But it easier to use the dot product formula (which may be used by people that don't know calculus)

    W = Fxdx+Fydy+Fzdz.

    Those are the components of the forceF and the displacement d.

    EDIT: TheAustrian beat me to the punch
     
  7. May 4, 2014 #6
    Would the answer be a. 16 J?
    I used:
    F=(3i+4j) N
    s=(14-2i + 1-6j)
    m = 12i+-5j) m
    W=f•s=36-20=16J
    16 J?
     
  8. May 4, 2014 #7
    Yeah, that looks right.
     
  9. May 4, 2014 #8

    SammyS

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    Is this problem from a practice test or is it from a current AP test ?
     
  10. May 13, 2014 #9

    Redbelly98

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    It is from a set of free sample test questions posted on the College Board website.

    swarm17, hope everything went well for you yesterday!
     
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