Final answer:
Without the force constant of the spring, it is not possible to calculate the equilibrium distance that a 10 kg mass would drop when attached to the spring.
Step-by-step explanation:
To find the distance dropped by the 10 kg mass attached to a freely hanging spring until it comes to rest in equilibrium, we need to use Hooke's law and the concept of the spring's force constant.
Hooke's Law states that F = kx, where 'F' is the force exerted by the spring, 'k' is the spring's force constant (also known as the stiffness), and 'x' represents the displacement of the spring from its equilibrium position.
In equilibrium, the force exerted by the spring equals the weight of the mass. Therefore, F = mg = kx, where 'm' is the mass and 'g' is the acceleration due to gravity (approximately 9.8 m/s²). However, to find 'k', the spring's force constant, we would need more information, which has not been provided in the question.
Due to the lack of information on the spring's force constant, it's not possible to precisely determine the distance the spring stretches into equilibrium. Generally, this would involve solving the equation mg = kx for 'x' to give the stretch distance once the value of 'k' is known.