(Solved): 5. A box is pressed against a horizontal spring, compressing the spring from its relaxed le ...

5. A box is pressed against a horizontal spring, compressing the spring from its relaxed length. The box is then released, and the spring launches the box horizontally along a track that ends in a ramp, as shown above. The box has enough speed to leave the ramp, and the box reaches a maximum vertical height above the floor. Assume there is negligible friction between the box and the track and air resistance is negligible. $$k$$ is the spring constant of the spring. $$x$$ is the distance the spring is compressed. $$M$$ is the mass of the box. $$?$$ is the angle of the ramp from the horizontal. $$h$$ is the maximum height reached by the box. 1. Consider the system consisting of the box and the spring, but not Earth. How does the energy of the system when the spring is fully compressed compare to the energy of the system at the moment immediately before the box hits the ground? Justify your answer. g. If the friction between the track and the box were not negligible, state one way in which the setup could be changed such that the maximum height of the box was the same as in the original setup.