Question

In a dart gun, a spring with spring constant k=412 is compressed 11.8 cm when the dart of mass 20.6g is loaded. What is the muzzle speed of the dart when the spring is released ignore friction

Answer 1

$$\dfrac{1}{2}kx^2=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{\dfrac{kx^2}{m}}=\sqrt{\dfrac{412\ \dfrac{N}{m}\cdot(0.118\ m)^2}{0.0206\ kg}}=16.7\ \dfrac{m}{s}.$$