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Math Help - Work

  1. #1
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    Red face Help!

    You lift a 10. lb physics book up in the air a distance of 1 ft. at a constant velocity of 0.5 ft/s. the work done by gravity is?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by babygirl
    You lift a 10. lb physics book up in the air a distance of 1 ft. at a constant velocity of 0.5 ft/s. the work done by gravity is?
    First note that we don't need to know that the book is moving at a constant velocity.

    The angle between the weight and displacement is 180 degrees.
    W_G = \vec w \cdot \vec s = (mg) \Delta h \, cos(180) = -mg \Delta  \, h

    Thus the work done by gravity is = -10*1 ft-lbs = -10 ft-lbs.

    -Dan

    (And what Physics book is still using English units??)
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  3. #3
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    Quote Originally Posted by topsquark
    First note that we don't need to know that the book is moving at a constant velocity.

    The angle between the weight and displacement is 180 degrees.
    W_G = \vec w \cdot \vec s = (mg) \Delta h \, cos(180) = -mg \Delta  \, h

    Thus the work done by gravity is = -10*1 ft-lbs = -10 ft-lbs.
    I think that an explanation of why g is 1 in this
    unit system, and that using g=32 ft/s^2 would give an answer
    in ft-poundals (or what ever the units are - its >30 years since
    I used them).


    -Dan

    (And what Physics book is still using English units??)
    Quite - Mars probes have been lost over this sort of thing (revenge of the
    killer-slugs (kilo-slugs) I expect).

    RonL
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  4. #4
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    Quote Originally Posted by CaptainBlack
    Quite - Mars probes have been lost over this sort of thing (revenge of the
    killer-slugs (kilo-slugs) I expect).
    Heard that story a long time ago from my father. So funny, how embarrasing is that
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack
    I think that an explanation of why g is 1 in this
    unit system, and that using g=32 ft/s^2 would give an answer
    in ft-poundals (or what ever the units are - its >30 years since
    I used them).
    Actually, g IS 32 ft/s^2. Note that the book's weight is given, not its mass. (ie. lb is a unit of weight, not mass). Thus mg = 10 lb, so the value of g is not directly used here. The 1 in my equation was the "1 ft." I suppose I should have labelled the units as I put them in the equation to make that clear.

    I've honestly forgotten how a foot-poundal is defined. I'll have to look that up sometime.

    -Dan
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    Grand Panjandrum
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    Quote Originally Posted by topsquark
    Actually, g IS 32 ft/s^2. Note that the book's weight is given, not its mass. (ie. lb is a unit of weight, not mass). Thus mg = 10 lb, so the value of g is not directly used here. The 1 in my equation was the "1 ft." I suppose I should have labelled the units as I put them in the equation to make that clear.

    I've honestly forgotten how a foot-poundal is defined. I'll have to look that up sometime.

    -Dan
    Its a dreadful feature of the Customary/Imperial Unit system that the pound is
    commonly used for weight, it is in that system's the unit of Mass. The unit of
    force is the poundal - the force that would accelerate a MASS of 1 pound
    at 1 ft/s^2.

    RonL
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker
    Heard that story a long time ago from my father. So funny, how embarrasing is that
    Good grief - now I feel old

    RonL
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack
    Its a dreadful feature of the Customary/Imperial Unit system that the pound is
    commonly used for weight, it is in that system's the unit of Mass. The unit of
    force is the poundal - the force that would accelerate a MASS of 1 pound
    at 1 ft/s^2.

    RonL
    Oh dear, I didn't know that. Okay, so we're both right!

    -Dan

    (I knew there was a reason we were switching over to metric!)
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  9. #9
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    Quote Originally Posted by topsquark
    (I knew there was a reason we were switching over to metric!)
    You know, even though the customary system is HORRIBLE for math, it is quite usefull in approximating distance in everyday life without using a ruler...

    1 inch=the length of 1 digit in your finger (I think your thumb)
    1 foot=the length of your foot
    1 yard=the length of a long stride
    1 mile=I have no idea (probably the distance from two ancient cities)
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