A force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 14 in. beyond its natural length?

Respuesta :

Answer:

work done=-8.166lb-ft

Explanation:

force = 8 lb       spring stretched (x)= 8 in

according to hooks law

F=-kx

k=-[tex]\frac{f}{x}[/tex]

k=-[tex]\frac{8}{8}[/tex]

k=-1 lb/in

work done=[tex]\int_{0}^{14}kx\ dx[/tex]

work done=[tex](-1)\left [\frac{x^2}{2}  \right ]^{14} _{0}[/tex]

work done=-98lb-in

1 ft =12 in

work done=[tex]\frac{-98}{12}[/tex]

                 =-8.166lb-ft