Please show work for part B, C, and D. Spring Gun Speed and Height A spring-load

Question

Please show work for part B, C, and D.

Spring Gun Speed and Height A spring-loaded toy gun is used to shoot a ball of mass m straight up in the air. (Figure 1) The spring has spring constant k. If the spring is compressed a distance x0 from its equilibrium position (y = 0) and then released, the ball reaches a maximum height h max (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume A useful statement of mechanical energy conservation is K1 + U1 = E1 = Ef = Kf + Uf. Initially, the spring was compressed a distance x0; its total initial energy was (neglecting the potential energy from the small change in height, x0). Find the total mechanical energy of the ball when it is a height h above the equilibrium position of the spring. Assume that h

Explanation / Answer

b) At top ball will only have potential energy = mgh
c) u^2 = 0 +2as = 0 +2*[(k*(xo+mg/k))/m]*(xo)
d) balancing energies of the ball
0.5k*((xo+mg/k)^2) = 0.5mv^2
v^2 = [k*((xo+mg/k)^2)]/m

v^2 = u^2 -2gh
h =( v^2 -u^2)/2g = [ {k*((xo+mg/k)^2)}/m -2*[(k*(xo+mg/k))/m]*(xo)]/2g

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