Answer to Question #284611 in Physics for f0rGoTTen

Question

A block-spring system has a kinetic energy of 6 J and the spring has an elastic potential energy of 10 J when the block is at +4 cm. The amplitude of oscillation is 6 cm and the mass of the block is 450 gm.

(a) Find the elastic potential energy of the block and kinetic energy of the system when the block is at the equilibrium position, x = 0.

(b) Determine the velocity when the block is at x = 0.

Answer 1

(a) When the block is at the equilibrium position, x = 0, the elastic potential energy of the block is zero, and the kinetic energy of the system is

$$KE_{eq}=KE_4+EPE_4=6+10=16\text{ J}.$$

b) The velocity when the block is at x = 0:

$$v=\sqrt{2KE_{eq}/m}=8.4\text{ m/s}.$$