If a spring stretches 3 cm with a 4 kg mass, how much would it stretch with a 12 kg mass?

To determine how much a spring stretches when a different mass is applied, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the amount it is stretched. Mathematically, this is often expressed as ( F = kx ), where ( F ) is the force applied to the spring, ( k ) is the spring constant, and ( x ) is the extension (stretch) of the spring.

When you initially apply a 4 kg mass, the force exerted by this mass due to gravity is calculated using ( F = mg ), where ( m ) is the mass and ( g ) is the acceleration due to gravity (approximately 9.8 m/s²). Therefore, for the 4 kg mass:

• ( F = 4 , \text{kg} \times 9.8 , \text{m/s}^2 = 39.2 , \text{N} ).

This causes the spring to stretch by 3 cm (or 0.03 m):

• We can find the spring constant ( k ) using Hooke's Law rearranged to ( k = \frac{F}{x