Final answer:
The displacement of the end of the spring when a 446-g mass is suspended from it is 58.02 cm. This is calculated using Hooke's Law and accounting for the spring constant and the weight of the mass.
Step-by-step explanation:
To determine the displacement of the spring due to the weight of the mass, we must first convert the mass from grams to kilograms by dividing 446 grams by 1000, which gives us 0.446 kilograms. Secondly, we use Hooke's Law, which states that the force exerted by a spring is equal to the spring constant (k) multiplied by the displacement (x): F = kx. The weight of the mass (mg) is the force exerted due to gravity, so we have: mg = kx. Solving for x gives us x = mg/k.
Substitute m = 0.446 kg (mass of the object), g = 9.81 m/s² (acceleration due to gravity), and k = 7.55 N/m (spring constant) into the equation.
x = (0.446 kg * 9.81 m/s²) / 7.55 N/m = 0.5802 m or 58.02 cm.
Therefore, the spring is displaced by 58.02 cm when the 446-g mass is suspended from it and it is hung vertically.