Question

While finding the spring constant, if X1 = 12 cm, X2 = 15 cm, and hanging mass = 22 grams, the value of spring constant K would be:________ (write your answer in newtons/meter)

Answer 1

If x₁=12 cm then k=1.7985 N/m

If x₂=15 cm then k=1.4388 N/m

Step-by-step explanation:

Hanging mass= 22 g=0.022 kg

Acceleration due to gravity g=9.81 m/s²

If x₁=displacement= 12 cm=0.12 m

k= spring constant

`F=ma\\\Rightarrow F=0.022* 9.81\\\Rightarrow F=0.21582\ N`

`\text {For spring}\\F=kx\\\Rightarrow 0.21582=k* 0.012\\\Rightarrow k=1.7985\ N/m\\`

∴k = 1.7985 N/m

If x₂=15 cm=0.15 m

Force of the hanging mass is same however the spring constant will change

`\text {For spring}\\F=kx\\\Rightarrow 0.21582=k* 0.015\\\Rightarrow k=1.4388\ N/m\\`

∴k = 1.4388 N/m

As the mass is not changing the spring constant has to change. That means that here there are two spring one with k=1.7985 N/m and the other with k= 1.4388 N/m