To solve this problem, we need to use the principle of conservation of energy, which states that the total energy of an isolated system remains constant. In this case, the initial potential energy stored in the spring will be converted into kinetic energy of the box.
Given information:
- Mass of the box, m = 36 g = 0.036 kg
- Spring constant, k = 127 N/m
- Extension of the spring, x = 11 cm = 0.11 m
Step 1: Calculate the potential energy stored in the spring.
Potential energy = (1/2) × k × x^2
Potential energy = (1/2) × 127 N/m × (0.11 m)^2
Potential energy = 0.7685 J
Step 2: Set the potential energy equal to the kinetic energy of the box.
Potential energy = Kinetic energy
(1/2) × k × x^2 = (1/2) × m × v^2
Step 3: Solve for the velocity (v) of the box.
v^2 = (k × x^2) / m
v^2 = (127 N/m × (0.11 m)^2) / 0.036 kg
v^2 = 21.375 m^2/s^2
v = √(21.375 m^2/s^2)
v = 4.62 m/s
Therefore, the speed of the box, assuming the entire elastic potential energy is converted to the box's kinetic energy, is 4.62 m/s.
