ࡱ> `  bjbj p$   (       GN^n$hO         R     Y   `y% f "q  0y ,- @- - L                  Calculus II - Applications to Physics and Engineering Work When a constant force F moves an object through a distance d, the product W = Fd is defined as the work done by the force on that object. For example, in lifting a 3-lb textbook 2 feet you do an amount of work equal to W = 2ft x 3lb = 6ft/lb. The work done by a variable force in moving an object along a line from location x = a to location x = b is found by integrating the force function from x = a to x = b EMBED Equation.DSMT4 \* MERGEFORMAT Example: When a particle is located at a distance of x feet from the origin, a force of  EMBED Equation.DSMT4 pounds acts on it. How much work is done in moving it from x=1 to x=3. Example: A principle from elementary physics known as Hookes Law states that the force required to stretch or compress a spring a distance of x units from its natural length is proportional to that distance; that is F(x) = kx, where k is known as the spring constant, which depends on the particular spring 1. A spring has spring constant k = 20lb/ft. The work done is stretching the spring 6 inches beyond its natural length is found by 2. The work done in stretching the spring in part a from 3 inches beyond its natural length to 6 in beyond its natural length is 3. A force of 40 N is required to hold a spring that has been stretched from its natural length of 10cm to 15 cm. How much work is doe in stretching the spring from 15cm to 18cm? 67<    9 : \ ] t u v w  췭xoii`VP hvkCJh@Nh@>*CJh@Nh]CJ htCJh]h]CJjh]h]CJEHUj D h]CJUVhjh]CJU h]6CJ h]CJh]h]>*CJ h@CJ-j@`> h@Nh@CJUVhmHnHujh@Nh@CJUh@Nh@OJQJh@Nh@CJh@Nh@5CJ67<0 1   `    hvkhvkCJ hvkCJ h@CJ h]CJh@Nh@CJh@NhtCJ htCJ   gdFq^gdtgdvk` 6 00PBP/ =!"#$% 6 00PBP/ =!"#$% Dd d?Z  6rrA? 2j'd;,s \FD `!>'d;,s \^ (+ x}nQA23(%h8&aI!LR&nx ĥqgwZL;|;  0 ~lIf3١;HpV1zp]ԟbτz1"(IeQi%xBb,b V]F*-qVvNīn!>V?PTD>%g ]ۚH۟ZrU O3rm,Xઌ 撪hՂt]~=`X|# ^6 v śaT;x0(N>EpYʦlMsj{&mcqtO9\pQButۈ61_LIic/ԏJmoEW5֎noJ^X}8yVz'p2fzpfeWzl[}yg-_Ǜ>#۪{g-_XkuƗAӀj*CJOJQJF@F Heading 2$@&5>*CJOJQJDAD Default Paragraph FontViV  Table Normal :V 44 la (k(No List <&< Footnote Reference:B@: Body Text CJOJQJ867<01     y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0     \tv::\}~33\w  \}_~CT^`o(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH._~C           &@pCsDvkFqy>-}t]1j@N@HP LaserJet 4000 Series PCLNe01:winspoolHP LaserJet 4000 Series PCLHP LaserJet 4000 Series PCL4C odXXLetter DINU"43 HP LaserJet 4000 Series PCL4C odXXLetter DINU"43  6P@UnknownG: Times New Roman5Symbol3& : ArialCFComic Sans MS" h;R;RYF  ! 22Q HX?&25Calculus II - Applications to Physics and EngineeringJennifer BreadyInformation Technology