Thread: please need help with Hooke's Law problem!?

Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component F_x=kx - bx^2 + cx^3 must be applied to the free end. Here k = 100 N/m, b=700 N/m^2, and c=12000 N/m^3. Note that x > 0 when the spring is stretched and x < 0 when it is compressed.

1) How much work must be done to stretch this spring by 0.050 m from its unstretched length?
2) How much work must be done to compress this spring by 0.050 m from its unstretched length?

Thanks

work done in stretching by dx distance
dW = F dx cos 180 = - F dx
-ve indicates that work is done external agency, 180 degree is due to restoring nature of force when extended in other direction
>> taking magnitude of W
for stretching from x=x1 to x =x2
W = (x1 to x2)?F dx
W = (x1 to x2)?[kx - bx^2 + cx^3] dx
W = (x1 to x2) [0.5 kx^2 - (b/3)x^3 + (c/4)x^4]
W = (0 to 0.05) [0.5 kx^2 - (b/3)x^3 + (c/4)x^4]
W = {0.5 k *0.05^2 - (b/3) 0.05^3 + (c/4)0.05^4} - {0}
W = {0.5*100 *0.05^2 - (700/3) 0.05^3 + (12000/4)0.05^4}
W = 0.115 J

rest do it yourself

why are you deviding by 2, 3, and 4?

you took the integral... didnt realize that at first.