] You use a spring to impart initial speed to a small ball that you will launch upward. The spring does not obey Hooke's Law perfectly, it follows:

_ '_ .-- _ __ Huvclwbnil@N6\\|Gl..'gl|@2.5|u001|ach'(10' u1ebc5bwckkh6a9 [511% {10) [19 points] You use a spring to impart initial speed to a small ball that you will launch upward. The spring does not obey Hooke's Law perfectly, it follows; F(x) : kx+bx2 Recall that Hooke's Law provides the force ofthe spring reacting to being compressed (x) or stretched (+x) with the final sign indicating a force in the same or opposite direction. Take k = 200 Mm and b = 360 N/mz. (a) To compress the Spring 5.0 cm, how much total externolforce is required? And to stretch it by 5.0 cm, how much external force? Which direction requires larger magnitude of force? (b) Find a symbolic expression for the potential energy function. Take U0 = U at the relaxed length of x = 0. (c) The spring is compressed 5 cm and is used to launch a 0.02 kg ball, find the energy stored in the spring and the launch speed. (d) In flight, the ball loses -0.04 joules of energy to drag (air resistance}. How high does the ball go? Use 9 = 9.81 m/sz