Answer to Question #218546 in Physics for Nath

Question

A spring has a spring constant of 150 N/m and mass of 100 g is attached to it. The spring sits on horizontal frictionless surface and other end of the spring is attached to a solid block. The mass is pulled by 10 cm to stretch the spring and then let go. What will the highest velocity of the mass?

Answer 1

When the mass is moving with the highest velocity, all of the stored elastic potential energy of the spring will have been transferred to kinetic energy:

$$PE_s=KE,$$ $$\dfrac{1}{2}kx^2=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{\dfrac{kx^2}{m}}=\sqrt{\dfrac{150\ \dfrac{N}{m}\cdot(0.1\ m)^2}{0.1\ kg}}=3.87\ \dfrac{m}{s}.$$