Answer:
When a spring is stretched or compressed, it stores elastic potential energy. The amount of energy stored in the spring is equal to the work done on it. The formula for elastic potential energy is:
elastic potential energy = 0.5 × spring constant × (extension)²
where:
elastic potential energy (Ee) is measured in joules (J)
spring constant (k) is measured in newtons per meter (N/m)
extension (e), referring to the increase in length, is measured in meters (m)
The gravitational potential energy of an object is given by:
gravitational potential energy = mass × gravity × height
where:
mass is measured in kilograms (kg)
gravity is measured in meters per second squared (m/s²)
height is measured in meters (m)
To calculate the energy stored in the spring, we need to know the spring constant and the extension. The gravitational potential energy can be calculated if we know the mass of the object and its height above a reference point.
If we assume that all of the gravitational potential energy goes into stretching the spring, then we can equate the two formulas and solve for extension:
mass × gravity × height = 0.5 × spring constant × (extension)²
Solving for extension, we get:
extension = sqrt((2 * mass * gravity * height) / spring constant)
Once we know the extension, we can calculate the elastic potential energy stored in the spring using the formula above.
The rest of the energy might go into other forms such as heat, sound, or deformation of the object or its surroundings.