# A spring with a constant of 6 (kg)/(s^2) is lying on the ground with one end attached to a wall. An object with a mass of 7 kg  and speed of  5 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

what is the energy of a object in movement? it is given by its kinetic energy : ${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \times 7 k g \times {\left(5 \frac{m}{s}\right)}^{2} = 87 , 5 J$ When the object is stopped its kinetic energy is Zero. Where is now the energy that without friction and anelastic strikes preserve itself? In the energy elastic of the spring: ${E}_{s} = \frac{1}{2} K \times {X}^{2}$ where X is the compress of the spring. $X = \sqrt{2 \frac{E}{K}} = \sqrt{\frac{175 J}{6 \frac{K g}{s} ^ 2}} = 5 , 4 m$