A ball with a mass of #256 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #36 (kg)/s^2# and was compressed by #12/4 m# when the ball was released. How high will the ball go?
The maximum altitude of the ball is
This can be solved using energy conservation,
Spring potential energy is given by
Gravitational potential energy is given by
Initially, the ball is not moving, so it has
When the spring is released, that potential energy is transferred to the ball. As the ball is launched, it possesses kinetic energy, and the higher it travels, the slower it moves, and the kinetic energy is transformed into gravitational potential energy with increasing height,
When the ball reaches its maximum altitude, all of the kinetic energy has been transformed into gravitational potential energy as the ball momentarily comes to a stop before falling back toward the earth. In other words, all of the spring potential energy stored in the spring initially is converted into gravitational potential energy stored in the ball at its maximum altitude. This gives us:
Note that I have converted the mass to
Hope that helps!