Question

The natural length of massless spring is x(spring constant =k) it is slowly stretched by applying on external force .The work done to stretch the spring from length 3x to 4x is

Answer 1

Answer:

2.5kx^2

Explanation:

case I:

no force applied => lenght is x from o and energy U=0

case II:

let a force f1 be applied which elongates the spring from x to 3x

displacement(s)= 2x

=>f1 = k.(2x)

U1 = 1/2×k×(2x)^2=1/2k (4x^2)--(1)

case III:

let f2 be the force applied to displace from x to 4x

s = 3x

=> f2 = k(3x)

U2 = 1/2k(3x)^2 = 1/2k(9x^2)--(2)

wkt

work = change in potential energy

W =U2-U1=1/2k(9x^2)-1/2k(4x^2)

W=1/2k (5x^2)

W=2.5kx^1/2