Question

You want to determine the stiffness constant of a spring in the physics lab. You attach one end of the spring to a hook that lets it dangle downward. On the other end of the spring you attach a 250 gram weight. You keep holding the weight, but lower it down until the spring reaches a stretch of 5 cm. At this point you feel a slight resistance to stretching the spring any further. When you release the weight, it hangs stably in its position. What is the stiffness constant of the spring?

Answer 1

As given :

mass, m = 250 gram = 0.25 kg

displacement of mass, x = 5 cm = 0.05 m

Let k be the stiffness constant of the spring

as when the mass will be hanged with the spring in stable position then weight of the mass m will be balanced by the spring force

so, spring force, f = weight of the mass m

k*x = m*g (g is acceleration due to gravity)

k*0.05 = 0.250*9.81

só, stiffness constant of spring, k = 49.05 N/m