If it requires 7.0 J of work to stretch a particular spring by 1.8 cm from its equilibrium length, how much more work will be required to stretch it an additional 3.6 cm?

56 J

Explanation:

The following data were obtained from the question:

Energy 1 (E₁) = 7 J

Extention 1 (e₁) = 1.8 cm

Extention 2 (e₂) = 1.8 + 3.6 = 5.4 cm

Energy 2 (E₂) =?

Energy stored in a spring is given by the following equation:

E = ke²

Where E is the energy.

K is the spring constant.

e is the extension.

E = ke²

Divide both side by e²

K = E/e²

Thus,

E₁/e₁² = E₂/e₂²

7/ 1.8² = E₂/ 5.4²

7 / 3.24 = E₂/ 29.16

Cross multiply

3.24 × E₂ = 7 × 29.16

3.24 × E₂ = 204.12

Divide both side by 3.24

E₂ = 204.12 / 3.24

E₂ = 63 J

Thus, the additional energy required can be obtained as follow:

Energy 1 (E₁) = 7 J

Energy 2 (E₂) = 63 J

Additional energy = 63 – 7

Additional energy = 56 J