Now consider the same block of mass m = 2.0kg on a slope at a 30 angle above the horizontal. The block is again pressed against a spring that has been compressed by 2.5m and has a spring constant k = 80N/m. The spring is positioned so that it will slide the block up along the incline when released. We will define our origin to be the position of the block, so that U grav = 0 initially.

(a) Sketch the situation

(b) In what form(s) is the initial energy of the system? Consider gravitational potential energy, spring potential energy, and kinetic energy. What is the total initial energy of the system?

(c) When the spring is released, the block is launched up the incline. If the surface has no friction, in what form(s) will the total energy of the block be when it reaches the highest point in its path up the incline? What is the total energy of the system at this point in time?

(d) Use your answer above to determine the distance the box will travel up along the incline from its initial position.

(e) Now consider a point in time between the two above, when the block is at the equilibrium point of the spring and has just left contact with the spring. In what form(s) is the energy at this point in time? (it is partially, but not entirely, kinetic energy)