Answer:
4E
Explanation:
From the question given above, the following data were obtained:
Initial elongation (e₁) = 4 cm = 4/100 = 0.04 m
Initial energy (E₁) = E
Final elongation (e₂) = 0.04 + 0.04 = 0.08 m
Final energy (E₂) =?
The energy stored in a s spring is given by:
E = ½Ke²
Where
E => is the energy
K => is the spring constant
e => is the elongation
From:
E = ½Ke²
Energy is directly proportional to the elongation. Thus,
E₁/e₁² = E₂/e₂²
With the above formula, we can obtain the final energy as follow:
Initial elongation (e₁) = 0.04 m
Initial energy (E₁) = E
Final elongation (e₂) = 0.08 m
Final energy (E₂) =?
E₁/e₁² = E₂/e₂²
E / 0.04² = E₂ / 0.08²
E / 0.0016 = E₂ / 0.0064
Cross multiply
0.0016 × E₂ = 0.0064E
Divide both side by 0.0016
E₂ = 0.0064E / 0.0016
E₂ = 4E
Therefore, the final energy is 4 times the initial energy i.e 4E
