The work done in stretching a linear spring by 4 cm from its natural length is 10 J . The additional work required to stretch it further by another 8 cm will be:

Step-by-step solution

The work done in stretching a spring by a distance x from its natural length is given by W = 1 2 kx^2 . Given W₁ = 10 J for x₁ = 4 cm . W₁ = 1 2 k(4)^2 = 10 The final extension of the spring is x₂ = 4 cm + 8 cm = 12 cm . The total work done to stretch the spring by 12 cm is W₂ = 1 2 k(12)^2 . Taking the ratio of W₂ to W₁ : W₂ W₁ = ( 12 4 )^2 = 3^2 = 9 W₂ = 9 10 = 90 J The additional work required is W = W₂ - W₁ = 90 J - 10 J = 80 J . Answer: 80 J